Search results for: Garman–Kohlhagen Model on FX Option USD/IDR

Authors: Bangkit Adhi Nugraha, Bambang Suripto

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On September 2016 Bank Indonesia (BI) release regulation no.18/18/PBI/2016 that permit bank clients for using the FX option call spread USD/IDR. Basically, this product is a combination between clients buy FX call option (pay premium) and sell FX call option (receive premium) to protect against currency depreciation while also capping the potential upside with cheap premium cost. BI classifies this product as a structured product. The structured product is combination at least two financial instruments, either derivative or non-derivative instruments. The call spread is the first structured product against IDR permitted by BI since 2009 as response the demand increase from Indonesia firms on FX hedging through derivative for protecting market risk their foreign currency asset or liability. The composition of hedging products on Indonesian FX market increase from 35% on 2015 to 40% on 2016, the majority on swap product (FX forward, FX swap, cross currency swap). Swap is formulated by interest rate difference of the two currency pairs. The cost of swap product is 7% for USD/IDR with one year USD/IDR volatility 13%. That cost level makes swap products seem expensive for hedging buyers. Because call spread cost (around 1.5-3%) cheaper than swap, the most Indonesian firms are using NDF FX call spread USD/IDR on offshore with outstanding amount around 10 billion USD. The cheaper cost of call spread is the main advantage for hedging buyers. The problem arises because BI regulation requires the call spread buyer doing the dynamic hedging. That means, if call spread buyer choose strike price 1 and strike price 2 and volatility USD/IDR exchange rate surpass strike price 2, then the call spread buyer must buy another call spread with strike price 1’ (strike price 1’ = strike price 2) and strike price 2’ (strike price 2’ > strike price 1‘). It could make the premium cost of call spread doubled or even more and dismiss the purpose of hedging buyer to find the cheapest hedging cost. It is very crucial for the buyer to choose best optimum strike price before entering into the transaction. To help hedging buyer find the optimum strike price and avoid expensive multiple premium cost, we observe ten years 2005-2015 historical data of USD/IDR volatility to be compared with the price movement of the call spread USD/IDR using Garman–Kohlhagen Model (as a common formula on FX option pricing). We use statistical tools to analysis data correlation, understand nature of call spread price movement over ten years, and determine factors affecting price movement. We select some range of strike price and tenor and calculate the probability of dynamic hedging to occur and how much it’s cost. We found USD/IDR currency pairs is too uncertain and make dynamic hedging riskier and more expensive. We validated this result using one year data and shown small RMS. The study result could be used to understand nature of FX call spread and determine optimum strike price for hedging plan.

Keywords: FX call spread USD/IDR, USD/IDR volatility statistical analysis, Garman–Kohlhagen Model on FX Option USD/IDR, Bank Indonesia Regulation no.18/18/PBI/2016

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: equivalent martingale measure, European put option, girsanov theorem, martingales, monte carlo method, option price valuation formula

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Authors: Manas Shah

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Black Scholes option pricing model is one of the most important concepts in modern world of computational finance. However, its practical use can be challenging as one of the input parameters must be estimated; implied volatility of the underlying security. The more precisely these values are estimated, the more accurate their corresponding estimates of theoretical option prices would be. Here, we present a novel model based on Cuckoo Search Optimization (CS) which finds more precise estimates of implied volatility than Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

Keywords: black scholes model, cuckoo search optimization, particle swarm optimization, genetic algorithm

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Authors: Ali Safdari-Vaighani

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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

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Authors: Muhammad Sheraz, Vasile Preda, Silvia Dedu

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Concepts of econophysics are usually used to solve problems related to uncertainty and nonlinear dynamics. In the theory of option pricing the risk neutral probabilities play very important role. The application of entropy in finance can be regarded as the extension of both information entropy and the probability entropy. It can be an important tool in various financial methods such as measure of risk, portfolio selection, option pricing and asset pricing. Gulko applied Entropy Pricing Theory (EPT) for pricing stock options and introduced an alternative framework of Black-Scholes model for pricing European stock option. In this article, we present solutions to maximum entropy problems based on Tsallis, Weighted-Tsallis, Kaniadakis, Weighted-Kaniadakies entropies, to obtain risk-neutral densities. We have also obtained the value of European call and put in this framework.

Keywords: option pricing, Black-Scholes model, Tsallis entropy, Kaniadakis entropy, weighted entropy, risk-neutral density

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Authors: Changhong Guo, Shaomei Fang, Yong He

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In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional g-Brownian motion, Taylor's series of fractional order, uncertain volatility

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Authors: S. Dhib, S. A. Addouche, T. Loukil, A. Elmhamedi

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In this paper, a reverse supply chain network is investigated for a decision making. This decision is surrounded by complex flows of returned products, due to the increasing quantity, the type of returned products and the variety of recovery option products (reuse, recycling, and refurbishment). The most important problem in the reverse logistic network (RLN) is to orient returned products to the suitable type of recovery option. However, returned products orientations from collect sources to the recovery disposition have not well considered in performance model. In this study, we propose a performance model for designing a network configuration on reverse logistics. Conceptual and analytical models are developed with taking into account operational, economic and environmental factors on designing network.

Keywords: reverse logistics, network design, performance model, open loop configuration

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Authors: T. J. B. van Niekerk, J. Viviers, E. J. Cilliers

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Substantial efforts were made in South Africa, stemming from a historic political change in 1994, to remedy the inequality and injustice, resulting from a dispensation where spatial patterns were largely based on racial segregation. Spatially distorted patterns predominantly originated from colonialism in the beginning of the twentieth century, ensuing a physical imprint on South African cities relating to architecture, urban layout and planning, frequently reflecting European norms and standards. As a consequence of physical and land use barriers, and well-established dual cities, attempts to address spatial injustices, apart from limited occurrences in metropolitan areas, gravely failed. Interception of incessant segregated growth, combined with urban sprawl is becoming increasingly evident. Intervention is a prerequisite to duly address the impact of colonial planning and its legacy still prevalent in most urban areas. During 1998, the National Department of Transport prepared the “Moving South Africa” strategy; presenting the Corridor Densification Option Model for the first time, as it was deemed more fitting to the existing South African urban tenure patterns than more familiar planning approaches. Urban planners are progressively contemplating the Corridor Densification Option Model and its attributes, besides its transportation emphasis, as an alternative approach to address spatial imbalances and to attain the physical integration of contemporary urban forms. In attaining a clearer understanding of the Corridor Densification Option Model, its rationale was analysed in greater detail. This research further investigated the provisional applications of the model in spatially segregated cities and illustrated that viable options are present to effectively employ it. Research revealed that the application of the model will, however, be dependent on the occurrence of specific characteristics in spatially segregated cities to warrant augmentation thereof.

Keywords: corridor densification option model, spatially segregated settlements, integration, urban restructuring

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Authors: Abootaleb Shirvani, Svetlozar Rachev

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ESG stands for Environmental, Social, and Governance and is a non-financial factor that investors use to specify material risks and growth opportunities in their analysis process. ESG ratings provide a quantitative measure of socially responsible investment, and it is essential to incorporate ESG ratings when modeling the dynamics of asset returns. In this article, we propose a triple subordinated Lévy process for incorporating numeric ESG ratings into dynamic asset pricing theory to model the time series properties of the stock returns. The motivation for introducing three layers of subordinator is twofold. The first two layers of subordinator capture the skew and fat-tailed properties of the stock return distribution that cannot be explained well by the existing Lévy subordinated model. The third layer of the subordinator introduces ESG valuation and incorporates numeric ESG ratings into dynamic asset pricing theory and option pricing. We employ the triple subordinator Lévy model for developing the ESG-valued stock return model, derive the implied ESG score surfaces for Microsoft, Apple, and Amazon stock returns, and compare the shape of the ESG implied surface scores for these stocks.

Keywords: ESG scores, dynamic asset pricing theory, multiple subordinated modeling, Lévy processes, option pricing

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Authors: Mohammad Saber Rohi, Saghar Heidari

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In this paper, we studied the pricing problem of American options under a regime-switching model with the possibility of a non-optimal exercise policy (early or late exercise time) which is called an irrational strategy. For this, we consider a Markovmodulated model for the dynamic of the underlying asset as an alternative model to the classical Balck-Scholes-Merton model (BSM) and an intensity-based model for the irrational strategy, to provide more realistic results for American option prices under the irrational behavior in real financial markets. Applying a partial differential equation (PDE) approach, the pricing problem of American options under regime-switching models can be formulated as coupled PDEs. To solve the resulting systems of PDEs in this model, we apply a finite element method as the numerical solving procedure to the resulting variational inequality. Under some appropriate assumptions, we establish the stability of the method and compare its accuracy to some recent works to illustrate the suitability of the proposed model and the accuracy of the applied numerical method for the pricing problem of American options under the regime-switching model with irrational behaviors.

Keywords: irrational exercise strategy, rationality parameter, regime-switching model, American option, finite element method, variational inequality

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Authors: W. T. A. Mohammed, M. Eltaeb, R. Kashani

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The first bending modes of tall asymmetric structures in the two lateral X and Y-directions have two different natural frequencies. To add tuned damping to these bending modes, one needs to either a) use two pendulum-tuned mass dampers (PTMDs) with one tuning frequency, each PTMD targeting one of the bending modes, or b) use one PTMD with two tuning frequencies (one in each lateral directions). Option (a), being more massive, requiring more space, and being more expensive, is less attractive than option (b). Considering that the tuning frequency of a pendulum depends mainly on the pendulum length, one way of realizing option (b) is by constraining the swinging length of the pendulum in one direction but not in the other; such PTMD is dubbed passive Bi-PTMD. Alternatively, option (b) can be realized by actively setting the tuning frequencies of the PTMD in the two directions. In this work, accurate physical models of passive Bi-PTMD and active PTMD are developed and incorporated into the numerical model of a tall asymmetric structure. The model of PTMDs plus structure is used for a)synthesizing such PTMDs for particular applications and b)evaluating their damping effectiveness in mitigating the dynamic lateral responses of their target asymmetric structures, perturbed by wind load in X and Y-directions. Depending on how elaborate the control scheme is, the active PTMD can either be made to yield the same damping effectiveness as the passive Bi-PTMD of the same size or the passive Bi-TMD twice as massive as the active PTMD.

Keywords: active tuned mass damper, high-rise building, multi-frequency tuning, vibration control

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Authors: Mimi Hafizah Abdullah, Hanani Farhah Harun, Nik Ruzni Nik Idris

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With the implied volatility as an important factor in financial decision-making, in particular in option pricing valuation, and also the given fact that the pricing biases of Leland option pricing models and the implied volatility structure for the options are related, this study considers examining the implied adjusted volatility smile patterns and term structures in the S&P/ASX 200 index options using the different Leland option pricing models. The examination of the implied adjusted volatility smiles and term structures in the Australian index options market covers the global financial crisis in the mid-2007. The implied adjusted volatility was found to escalate approximately triple the rate prior the crisis.

Keywords: implied adjusted volatility, financial crisis, Leland option pricing models, Australian index options

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Authors: Young Yoon, Jinsoo Kim

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The adoption of information and communication technologies (ICT) in all industry is growing under industry 4.0. Many oil companies also are increasingly adopting ICT to improve the efficiency of existing operations, take more accurate and quicker decision making and reduce entire cost by optimization. It is true that ICT is playing an important role in the process of unconventional oil and gas development and companies must take advantage of ICT to gain competitive advantage. In this study, real option approach has been applied to Unconventional gas R&D project to evaluate ICT of them. Many unconventional gas reserves such as shale gas and coal-bed methane(CBM) has developed due to technological improvement and high energy price. There are many uncertainties in unconventional development on the three stage(Exploration, Development, Production). The traditional quantitative benefits-cost method, such as net present value(NPV) is not sufficient for capturing ICT value. We attempted to evaluate the ICT valuation by applying the compound option model; the model is applied to real CBM project case, showing how it consider uncertainties. Variables are treated as uncertain and a Monte Carlo simulation is performed to consider variables effect. Acknowledgement—This work was supported by the Energy Efficiency & Resources Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20152510101880) and by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-205S1A3A2046684).

Keywords: information and communication technologies, R&D, real option, unconventional gas

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Authors: Miroslav Čulík, Petr Gurný

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This paper is aimed at the financial assessment of the hard coal mining in a given region by real option methodology application. Hard coal mining in this mine makes net loss for the owner during the last years due to the long-term unfavourable mining conditions and significant drop in the coal prices during the last years. Management is going to shut down the operation and abandon the project to reduce the loss of the company. The goal is to assess whether the shutting down the operation is the only and correct solution of the problem. Due to the uncertainty in the future hard coal price evolution, the production might be again restarted if the price raises enough to cover the cost of the production. For the assessment, real option methodology is applied, which captures two important aspect of the financial decision-making: risk and flexibility. The paper is structured as follows: first, current state is described and problem is analysed. Next, methodology of real options is described. At last, project is evaluated by applying real option methodology. The results are commented and recommendations are provided.

Keywords: real option, investment, option to abandon, option to shut down and restart, risk, flexibility

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Authors: Krishang Surapaneni

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The goal of this project is to determine how to predict important aspects of options, including the ask price. We want to compare different machine learning models to learn the best model and the best hyperparameters for that model for this purpose and data set. Option pricing is a relatively new field, and it can be very complicated and intimidating, especially to inexperienced people, so we want to create a machine learning model that can predict important aspects of an option stock, which can aid in future research. We tested multiple different models and experimented with hyperparameter tuning, trying to find some of the best parameters for a machine-learning model. We tested three different models: a Random Forest Regressor, a linear regressor, and an MLP (multi-layer perceptron) regressor. The most important feature in this experiment is the ask price; this is what we were trying to predict. In the field of stock pricing prediction, there is a large potential for error, so we are unable to determine the accuracy of the models based on if they predict the pricing perfectly. Due to this factor, we determined the accuracy of the model by finding the average percentage difference between the predicted and actual values. We tested the accuracy of the machine learning models by comparing the actual results in the testing data and the predictions made by the models. The linear regression model performed worst, with an average percentage error of 17.46%. The MLP regressor had an average percentage error of 11.45%, and the random forest regressor had an average percentage error of 7.42%

Keywords: finance, linear regression model, machine learning model, neural network, stock price

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Authors: Arnab Adhikari, Arnab Bisi

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Since the inception, the fashion apparel supply chain is facing the problem of high demand uncertainty. Often the demand volatility compels the corresponding supply chain member to incur substantial holding cost and opportunity cost in case of the overproduction and the underproduction scenario, respectively. It leads to an uncoordinated fashion apparel supply chain. There exist several scholarly works to achieve coordination in the fashion apparel supply chain by employing the different contracts such as the buyback contract, the revenue sharing contract, the option contract, and so on. Specially, the application of option contract in the apparel industry becomes prevalent with the changing global scenario. Exploration of existing literature related to the option contract reveals that most of the research works concentrate on the one direction demand adjustment i.e. either to match the demand upwards or downwards. Here, we present a holistic approach to coordinate a dyadic fashion apparel supply chain comprising one manufacturer and one retailer with the help of bidirectional option contract. We show a combination of wholesale price contract and bidirectional option contract can coordinate the under expanded supply chain. We also propose a framework that captures the variation of the apparel retailer’s order quantity and the apparel manufacturer’s production quantity with the changing exercise price for the different ranges of the option price. We analytically explore that corresponding cost parameters of the supply chain members along with the nature of demand distribution play an instrumental role in the coordination as well as the retailer’s ordering decision.

Keywords: fashion apparel supply chain, supply chain coordination, wholesale price contract, bidirectional option contract

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Authors: Majid Galoie, Khodadad Safavi, Abdolreza Karami Nejad, Reza Roshan

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Scour downstream of a flip bucket in a plunge pool is caused by impingement of water jet force. In order to reduce this force and consequently reduce scour hole depth, flip buckets may equip by dents. The minimum scour hole depth might be occurred by optimization of dents (number, shape, placement) on flip buckets. In this study, a comprehensive physical model has been developed and various options for dents have been investigated. The experimental data for each dent option such as scour hole depth, angle of impingement jet, piezometric pressure in tail-water and jet trajectory have been measured for various discharges. Finally, the best option can be found by analysis of the experimental results which has been expressed in this paper.

Keywords: scouring process, plunge pool, scour hole depth, physical model, flip bucket

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Authors: Amol Parikh

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The goal of this study is to understand the most preferred ways to spend time at an airport while waiting for a flight to board. Survey was done on 1639 people of the United States of America. In the overall data, it was found that majority people always preferred spending time doing something in their mobile phone. Second most preferred option was reading something, followed by wanting a companion to talk to or to eat/drink. Least preferred option was to eat/drink alone. Overall data was then filtered based on age, gender, income and urban density groups. Percentage of people wanting to use a mobile phone was highest in the age group of 18-24. People aged 45 and above chose reading as the most preferred option. In any of the ranges of income, gender or urban density using mobile phone was the most preferred option. Conclusion of this study is that introducing a mobile app to search for a companion at an airport to do like minded activity would get noticed by majority travelers and would be a business idea worth trying as wanting a companion to talk or eat/drink with is not the least preferred option.

Keywords: waiting for a flight, airport, mobile phone, companion

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Authors: Saghar Heidari

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In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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Authors: Manoel Pereira, Alvaro Veiga, Camila Epprecht, Renato Costa

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This paper introduces an empirical version of the Esscher transform for risk-neutral option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability distributions for the returns of the underlying. In our proposal, we make only mild assumptions on the pricing kernel and there is no need for the formulation of the risk-neutral model for the returns. First, we simulate sample paths for the returns under the physical distribution. Then, based on the empirical Esscher transform, the sample is reweighted, giving rise to a risk-neutralized sample from which derivative prices can be obtained by a weighted sum of the options pay-offs in each path. We compare our proposal with some traditional parametric pricing methods in four experiments with artificial and real data.

Keywords: esscher transform, generalized autoregressive Conditional Heteroscedastic (GARCH), nonparametric option pricing

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Authors: Jingwen Shi, Qi Wu

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We study the role played interest rate risk in carry trade return in order to understand the forward premium puzzle. In this study, our goal is to investigate to what extent carry trade return is indeed due to compensation for risk taking and, more important, to reveal the nature of these risks. Using option data not only on exchange rates but also on interest rate swaps (swaptions), our first finding is that, besides the consensus currency risks, interest rate risks also contribute a non-negligible portion to the carry trade return. What strikes us is our second finding. We find that large downside risks of future exchange rate movements are, in fact, priced significantly in option market on interest rates. The role played by interest rate risk differs structurally from the currency risk. There is a unique premium associated with interest rate risk, though seemingly small in size, which compensates the tail risks, the left tail to be precise. On the technical front, our study relies on accurately retrieving implied distributions from currency options and interest rate swaptions simultaneously, especially the tail components of the two. For this purpose, our major modeling work is to build a new international asset pricing model where we use an orthogonal setup for pricing kernels and specify non-Gaussian dynamics in order to capture three sets of option skew accurately and consistently across currency options and interest rate swaptions, domestic and foreign, within one model. Our results open a door for studying forward premium anomaly through implied information from interest rate derivative market.

Keywords: carry trade, forward premium anomaly, FX option, interest rate swaption, implied volatility skew, uncovered interest rate parity

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Authors: Wajih Abbassi, Zouhaier Ben Khelifa

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The present research points towards the empirical validation of three options valuation models, the ad-hoc Black-Scholes model as proposed by Berkowitz (2001), the constant elasticity of variance model of Cox and Ross (1976) and the Kou jump-diffusion model (2002). Our empirical analysis has been conducted on a sample of 26,974 options written on three indexes, the S&P 500, Nasdaq 100 and the Russell 2000 that were negotiated during the year 2007 just before the sub-prime crisis. We start by presenting the theoretical foundations of the models of interest. Then we use the technique of trust-region-reflective algorithm to estimate the structural parameters of these models from cross-section of option prices. The empirical analysis shows the superiority of the Kou jump-diffusion model. This superiority arises from the ability of this model to portray the behavior of market participants and to be closest to the true distribution that characterizes the evolution of these indices. Indeed the double-exponential distribution covers three interesting properties that are: the leptokurtic feature, the memory less property and the psychological aspect of market participants. Numerous empirical studies have shown that markets tend to have both overreaction and under reaction over good and bad news respectively. Despite of these advantages there are not many empirical studies based on this model partly because probability distribution and option valuation formula are rather complicated. This paper is the first to have used the technique of nonlinear curve-fitting through the trust-region-reflective algorithm and cross-section options to estimate the structural parameters of the Kou jump-diffusion model.

Keywords: jump-diffusion process, Kou model, Leptokurtic feature, trust-region-reflective algorithm, US index options

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Authors: Mohamed Muse Hassan

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Selling through the Internet is changing the norms of doing business globally. Today, selling and buying from the Internet is not only an option but the dominant form of shopping. But, this phenomenon is not thriving in the developing countries, mainly in Africa. Therefore, although previous studies focused on the e-retailers’ side, this study investigates the effect of consumer trust and online payment options on the awareness and perception of e-commerce in Africa. We developed a five-construct model and empirically tested the model by targeting professionals and college students who reside in Somalia. We employed structural equation modeling (SEM) technique for path analysis to probe answers for the variables under study. The main findings of the study show that there is significant evidence that online payment option impacts both the awareness level and perception of e-commerce in Somalia. Consumer trust was also found to determine both the awareness and perception of online shopping in the country. Moreover, the current global payment options available ignore local technologies popular in Africa. For example, the inclusion of a mobile payment option alone would make a big difference in Africa. The paper also determined that consumer trust toward online retailers is very low and this can be solved if consumers are given assurances for their financial transactions. The paper concludes that increased online payment options are needed in Somalia and, in Africa, in general. Limitations and further research suggestions are also included at the end of this paper.

Keywords: Africa, consumer trust, e-commerce, online payment

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Authors: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. However, most of the option pricing models have no analytical solution. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, we solve the American option under jump diffusion models by using efficient time-dependent numerical methods. several techniques are integrated to reduced the overcome the computational complexity. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). Partial fraction decomposition technique is applied to rational approximation schemes to overcome the complexity of inverting polynomial of matrices. The proposed method is easy to implement on serial or parallel versions. Numerical results are presented to prove the accuracy and efficiency of the proposed method.

Keywords: integral differential equations, jump–diffusion model, American options, rational approximation

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Authors: Md. Mizanur Rahman, Chu Chi Ming, Mohd Suffian Bin Misaran

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Chimney is an important part of the industries to remove waste heat from the processes side to the atmosphere. The increased demand of energy helps to restart to think about the efficiency of chimney as well as to find out a valid option to replace forced draft chimney system from industries. In this study natural draft chimney model is air flow rate; exit air temperature and pressure losses are studied through modification with wire mesh screen and compare the results with without wire mesh screen chimney model. The heat load is varies from 0.1 kW to 1kW and three different wire mesh screens that have pore size 0.15 mm2, 0.40 mm2 and 4.0 mm2 respectively are used. The experimental results show that natural draft chimney model with wire mesh screens significantly restored the flow losses compared to the system without wire mesh screen. The natural draft chimney model with 0.40 mm2 pore size wire mesh screen can minimize the draft losses better than others and able to enhance velocity about 54 % exit air temperature about 41% and pressure loss decreased by about 20%. Therefore, it can be decided that the wire mesh screens significantly minimize the draft losses in the natural draft chimney and 0.40 mm2 pore size screen will be a suitable option.

Keywords: natural draft dhimney, wire mesh screen, natural draft flow, mechanical engineering

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Authors: Ishay Wolf

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In this study, the financial position of pension actors in the market during the pension system transition toward a more funded capitalized scheme is explored, mainly via an option benefit model. This is enabled by not considering the economy as a single earning cohort. We analytically demonstrate a socio-economic anomaly in the funded pension system, which is in favor of high earning cohorts on at the expense of low earning cohorts. This anomaly is realized by a lack of insurance and exposure to financial and systemic risks. Furthermore, the anomaly might lead to pension re-reform back to unfunded scheme, mostly due to political pressure. We find that a minimum pension guarantee is a rebalance mechanism to this anomaly, which increases the probability to of the sustainable pension scheme. Specifically, we argue that implementing the guarantee with an intra-generational, risk-sharing mechanism is the most efficient way to reduce the effect of this abnormality. Moreover, we exhibit the convergence process toward implementing minimum pension guarantee in many countries which have capitalized their pension systems during the last three decades, particularly among Latin America and CEE countries.

Keywords: benefits, pension scheme, put option, social security

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Authors: A. Chateauneuf, M. Mostoufi, D. Vyncke

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Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model.

Keywords: control variate Monte Carlo, comonotonicity, option pricing, scientific computing

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Authors: Ons Triki, Fathi Abid

Abstract:

The basic objective of this paper is twofold. It resides in designing a model for a contingent convertible lease contract that can ensure the financial stability of a company and recover the losses of the parties to the lease in the event of default. It also aims to compare the convertible lease contract on inefficiencies resulting from the debt-overhang problem and asset substitution with other financing policies. From this perspective, this paper highlights the interaction between investments and financing policies in a dynamic model with existing assets and a growth option where the investment cost is financed by a contingent convertible lease and equity. We explore the impact of the contingent convertible lease on the capital structure. We also check the reliability and effectiveness of the use of the convertible lease contract as a means of financing. Findings show that the rental convertible contract with a sufficiently high conversion ratio has less severe inefficiencies arising from risk-shifting and debt overhang than those entailed by risky debt and pure-equity financing. The problem of underinvestment pointed out by Mauer and Ott (2000) and the problem of overinvestment mentioned by Hackbarth and Mauer (2012) may be reduced under contingent convertible lease financing. Our findings predict that the firm value under contingent convertible lease financing increases globally with asset volatility instead of decreasing with business risk. The study reveals that convertible leasing contracts can stand for a reliable solution to ensure the lessee and quickly recover the counterparties of the lease upon default.

Keywords: contingent convertible lease, growth option, debt overhang, risk-shifting, capital structure

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Authors: Rachid Belhachemi, Pierre Rostan, Alexandra Rostan

Abstract:

This paper develops a discrete-time option pricing model for index options. The model consists of two key ingredients. First, daily stock return innovations are driven by a continuous hidden threshold mixed skew-normal (HTSN) distribution which generates conditional non-normality that is needed to fit daily index return. The most important feature of the HTSN is the inclusion of a latent state variable with a continuum of states, unlike the traditional mixture distributions where the state variable is discrete with little number of states. The HTSN distribution belongs to the class of univariate probability distributions where parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. It has been shown empirically that this distribution outperforms its main competitor, the mixed normal (MN) distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence. Second, heteroscedasticity in the model is captured by a threeexogenous-factor GARCH model (GARCHX), where the factors are taken from the principal components analysis of various world indices and presents an application to option pricing. The factors of the GARCHX model are extracted from a matrix of world indices applying principal component analysis (PCA). The empirically determined factors are uncorrelated and represent truly different common components driving the returns. Both factors and the eight parameters inherent to the HTSN distribution aim at capturing the impact of the state of the economy on price levels since distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. The PCA identifies statistically independent factors affecting the random evolution of a given pool of assets -in our paper a pool of international stock indices- and sorting them by order of relative importance. The PCA computes a historical cross asset covariance matrix and identifies principal components representing independent factors. In our paper, factors are used to calibrate the HTSN-GARCHX model and are ultimately responsible for the nature of the distribution of random variables being generated. We benchmark our model to the MN-GARCHX model following the same PCA methodology and the standard Black-Scholes model. We show that our model outperforms the benchmark in terms of RMSE in dollar losses for put and call options, which in turn outperforms the analytical Black-Scholes by capturing the stylized facts known for index returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.

Keywords: continuous hidden threshold, factor models, GARCHX models, option pricing, risk-premium

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