Search results for: Exchange rate volatility

Authors: Wong Hock Tsen

Abstract:

This study aims to investigate the impact of exchange rate volatility on real export in Malaysia. The moving standard deviation with order three (MSD(3)) is used for the measurement of exchange rate volatility. The conventional and partially asymmetric autoregressive distributed lag (ARDL) models are used in the estimations. This study finds exchange rate volatility to have significant impact on real total export and some sub-categories of real total export. Moreover, this study finds that the positive or negative exchange rate volatility tends to have positive or negative impact on real export. Exchange rate volatility can be harmful to export of Malaysia.

Keywords: Exchange rate volatility, autoregressive distributed lag, export, Malaysia.

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Authors: Chimaobi V. Okolo, Onyinye S. Ugwuanyi, Kenneth A. Okpala

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This study evaluated the effect of exchange rate volatility on the manufacturing sector of Nigeria. The flow and stock market theories of exchange rate determination was adopted considering macroeconomic determinants such as balance of trade, trade openness, and net international investment. Furthermore, the influence of changes in parallel exchange rate, official exchange rate and real effective exchange rate was modeled on the manufacturing sector output. Vector autoregression techniques and vector error correction mechanism were adopted to explore the macroeconomic determinants of exchange rate fluctuation in Nigeria and to examine the influence of exchange rate volatility on the manufacturing sector output in Nigeria. The exchange rate showed an unstable and volatile movement in Nigeria. Official exchange rate significantly impacted on the manufacturing sector of Nigeria and shock to previous manufacturing sector output caused 60.76% of the fluctuation in the manufacturing sector output in Nigeria. Trade balance, trade openness and net international investments did not significantly determine exchange rate in Nigeria. However, own shock accounted for about 95% of the variation of exchange rate fluctuation in the short-run and long-run. Among other macroeconomic variables, net international investment accounted for about 2.85% variation of the real effective exchange rate fluctuation in the short-run and in the long-run. Monetary authorities should maintain stability of the exchange rates through proper management so as to encourage local production and government should formulate and implement policies that will develop other sectors of the economy as this will widen the country’s revenue base, reduce our over reliance on oil sector for our foreign exchange earnings and in turn reduce the shocks on our domestic economy.

Keywords: Exchange rate volatility, exchange rate determinants, manufacturing sector, official exchange rate, parallel exchange rate, real effective exchange rate.

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Authors: Pavla Ruzickova, Petr Teply

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There are many debates now regarding undervalued and overvalued currencies currently traded on the world financial market. This paper contributes to these debates from a theoretical point of view. We present the three most commonly used methods of estimating the equilibrium real effective exchange rate (REER): macroeconomic balance approach, external sustainability approach and equilibrium real effective exchange rate approach in the reduced form. Moreover, we discuss key concepts of the calculation of the real exchange rate (RER) based on applied explanatory variables: nominal exchange rates, terms of trade and tradable and non-tradable goods. Last but not least, we discuss the three main driving forces behind real exchange rates movements which include terms of trade, relative productivity growth and the interest rate differential.

Keywords: real exchange rate, real effective exchange rate, foreign exchange, terms of trade

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Authors: Nikolaos Sariannidis, Grigoris Giannarakis, Nikolaos Litinas, Nikos Kartalis

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This study investigates the relationship between 10 year bond value, Yen/U.S dollar exchange rate, non-farm payrolls (all employs) and crude oil to U.S. Dow Jones Sustainability Index. A GARCH model is used to test these relationships for the period January 1st 1999 to January 31st 2008 using monthly data. Results show that an increase of the 10 year bond and non farm payrolls (all employs) lead to an increase of the D.J.S.I returns. On the contrary the volatility of the Yen/U.S dollar exchange rates as well as the increase of crude oil returns has negative effects on the U.S D.J.S.I returns. This study aims at assisting investors to understand the influences certain macroeconomic indicators have on the companies- stock returns as reported by the D.J.S.I.

Keywords: Bond value, Corporate Social Responsibility, Crudeoil, D.J.S.I United States, Exchange rate, GARCH, Non-farmpayrolls.

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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.

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Authors: Aleksandre Ergeshidze

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The exchange rate is a pivotal pricing instrument that simultaneously impacts various components of the economy. Depreciation of nominal exchange rate is export promoting, which might be a desired export-led growth policy, and particularly critical to closing-down the widening current account imbalance. However, negative effects resulting from high dollarization and high share of imported intermediate inputs can outweigh positive effect. The aim of this research is to quantify impact of change in nominal exchange rate and test contractionary depreciation hypothesis on Georgian economy using structural and Bayesian vector autoregression. According to the acquired results, appreciation of nominal exchange rate is expected to decrease inflation, monetary policy rate, interest rate on domestic currency loans and economic growth in the medium run; however, impact on economic growth in the short run is statistically not significant.

Keywords: Bayesian vector autoregression, contractionary depreciation, dollarization, nominal exchange rate, structural vector autoregression.

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Authors: Thomas I. Kounitis

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The purpose of this paper is to investigate the influence of a number of variables on the conditional mean and conditional variance of credit spread changes. The empirical analysis in this paper is conducted within the context of bivariate GARCH-in- Mean models, using the so-called BEKK parameterization. We show that credit spread changes are determined by interest-rate and equityreturn variables, which is in line with theory as provided by the structural models of default. We also identify the credit spread change volatility as an important determinant of credit spread changes, and provide evidence on the transmission of volatility between the variables under study.

Keywords: Credit spread changes, GARCH-in-Mean models, structural framework, volatility transmission.

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Authors: Ivan Lovrinović, Gordana Kordić, Martina Nakić

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There are little subjects in macroeconomics that are so widely discussed, but at the same time controversial and without a clear solution such as the choice of exchange rate regime. National authorities need to take into consideration numerous fundamentals, trying to fulfil goals of economic growth, low and stable inflation and international stability. This paper focuses on the countries of ex- Yugoslavia and their exchange rate history as independent states. We follow the development of the regimes in 6 countries during the transition through the financial crisis of the second part of the 2000s to the prospects of their final goal: full membership in the European Union. Main question is to what extent has the exchange regime contributed to their economic success, considering other objective factors.

Keywords: European Union, exchange rate regime, ex- Yugoslavia countries

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Authors: L. Basha, E. Gjika

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The exchange rate is one of the most important economic variables, especially for a small, open economy such as Albania. Its effect is noticeable on one country's competitiveness, trade and current account, inflation, wages, domestic economic activity and bank stability. This study investigates the fluctuation of Albania’s exchange rates using monthly average foreign currency, Euro (Eur) to Albanian Lek (ALL) exchange rate with a time span from January 2008 to June 2021 and the macroeconomic factors that have a significant effect on the exchange rate. Initially, the Random Forest Regression algorithm is constructed to understand the impact of economic variables in the behavior of monthly average foreign currencies exchange rates. Then the forecast of macro-economic indicators for 12 months was performed using time series models. The predicted values received are placed in the random forest model in order to obtain the average monthly forecast of Euro to Albanian Lek (ALL) exchange rate for the period July 2021 to June 2022.

Keywords: Exchange rate, Random Forest, time series, Machine Learning, forecasting.

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Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

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This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model.

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Authors: Sang Hoon Kang, Seong-Min Yoon

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Little attention has been paid to information transmission between the portfolios of large stocks and small stocks in the Korean stock market. This study investigates the return and volatility transmission mechanisms between large and small stocks in the Korea Exchange (KRX). This study also explores whether bad news in the large stock market leads to a volatility of the small stock market that is larger than the good news volatility of the large stock market. By employing the Granger causality test, we found unidirectional return transmissions from the large stocks to medium and small stocks. This evidence indicates that pat information about the large stocks has a better ability to predict the returns of the medium and small stocks in the Korean stock market. Moreover, by using the asymmetric GARCH-BEKK model, we observed the unidirectional relationship of asymmetric volatility transmission from large stocks to the medium and small stocks. This finding suggests that volatility in the medium and small stocks following a negative shock in the large stocks is larger than that following a positive shock in the large stocks.

Keywords: Asymmetric GARCH-BEKK model, Asymmetric volatility transmission, Causality, Korean stock market, Spillover effect

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Authors: R. Mechgoug, A. Titaouine

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Fuzzy systems have been successfully used for exchange rate forecasting. However, fuzzy system is very confusing and complex to be designed by an expert, as there is a large set of parameters (fuzzy knowledge base) that must be selected, it is not a simple task to select the appropriate fuzzy knowledge base for an exchange rate forecasting. The researchers often look the effect of fuzzy knowledge base on the performances of fuzzy system forecasting. This paper proposes a genetic fuzzy predictor to forecast the future value of daily US Dollar/Euro exchange rate time’s series. A range of methodologies based on a set of fuzzy predictor’s which allow the forecasting of the same time series, but with a different fuzzy partition. Each fuzzy predictor is built from two stages, where each stage is performed by a real genetic algorithm.

Keywords: Foreign exchange rate, time series forecasting, Fuzzy System, and Genetic Algorithm.

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Authors: N. Sopipan, A. Intarasit, K. Chuarkham

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 In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: Volatility, Markov Regime Switching, Forecasting.

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Authors: L. Bartoňová, Z. Klika

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Modes of occurrence of Pb, As, Cr, Co, Cu, and Ni in bituminous coal and lignite were determined by means of sequential extraction using NH4OAc, HCl, HF and HNO3 extraction solutions. Elemental affinities obtained were then evaluated in relation to volatility of these elements during the combustion of these coals in two circulating fluidised-bed power stations. It was found out that higher percentage of the elements bound in silicates brought about lower volatility, while higher elemental proportion with monosulphides association (or bound as exchangeable ion) resulted in higher volatility. The only exception was the behavior of arsenic, whose volatility depended on amount of limestone added during the combustion process (as desulphurisation additive) rather than to its association in coal.

Keywords: Coal combustion, sequential extraction, trace elements, volatility.

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Authors: Pinho C., Madaleno M.

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German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after calibrating for the Merton jump diffusion (MJD), variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman, Madan and Yor (CGMY) and the Black and Scholes (B&S) model. Implied volatility is examined for the entire sample period, revealing some curious features about market evolution, where data fitting performances of the five models are compared. It is shown that variance gamma processes provide relatively better results and that implied volatility shows significant differences through time, having increasingly evolved. Volatility changes for changed uncertainty, or else, increasing futures prices and there is evidence for the need to account for seasonality when modelling both electricity spot/futures prices and volatility.

Keywords: Calibration, Electricity Markets, Implied Volatility, Lévy Models, Options on Futures, Pricing

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Authors: S. Al Wadi, Mohd Tahir Ismail, Samsul Ariffin Abdul Karim

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It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.

Keywords: Fast Fourier transforms, Haar wavelet transform, Matlab (Wavelet tools), stocks market, Volatility.

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Authors: Katleho D. Makatjane, Kalebe M. Kalebe

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The present paper used time-varying parameters which are based on the score function of a probability density at time t to model volatility of saving rate. We used a scaled likelihood function to update the parameters of the model overtime. Our results revealed high diligence of time-varying since the location parameter is greater than zero. Furthermore, we discovered a leptokurtic condition on saving rate’s distribution. Kapetanios, Shin-Shell Nonlinear Augmented Dickey-Fuller (KSS-NADF) test showed that the saving rate has a nonlinear unit root; therefore, it can be modeled by a generalised autoregressive score (GAS) model. Additionally, value at risk (VaR) and conditional tail expectation (CTE) indicate that 99% of the time people in Lesotho are saving more than spending. This puts the economy in high risk of not expanding. Therefore, the monetary policy committee (MPC) of Lesotho should revise their monetary policies towards this high saving rates risk.

Keywords: Generalized autoregressive score, time-varying, saving rate, Lesotho.

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Authors: Chatchai Pesee

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This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

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Authors: G. L. C. Yap

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Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.

Keywords: Long-memory, Gaussian process, Whittle estimator, normalization, volatility, value-at-risk.

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Authors: Tea Poklepović, Zdravka Aljinović, Mario Matković

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Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and compares three efficient frontiers on the Croatian Stock Market. The results show that range-based volatility estimator outperforms both mean-variance and lower semi-variance model.

Keywords: Variance, lower semi-variance, range-based volatility.

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Authors: Nadira Kaimova

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In this paper it was examined the influence of margin regulation on stock market volatility in EU 1993 – 2014. Regulating margin requirements or haircuts for securities financing transactions has for a long time been considered as a potential tool to limit the build-up of leverage and dampen volatility in financial markets. The margin requirement dictates how much investors can borrow against these securities. Margin can be an important part of investment. Using daily and monthly stock returns and there is no convincing evidence that EU Regulation margin requirements have served to dampen stock market volatility. In this paper was detected the expected negative relation between margin requirements and the amount of margin credit outstanding. Also, it confirmed that changes in margin requirements by the EU regulation have tended to follow than lead changes in market volatility. For the analysis have been used the modified Levene statistics to test whether the standard deviation of stock returns in the 25, 50 and 100 days preceding margin changes is the same as that in the succeeding 25, 50 and 100 days. The analysis started in May 1993 when it was first empowered to set the initial margin requirement and the last sample was in May 2014. To test whether margin requirements influence stock market volatility over the long term, the sample of stock returns was divided into 14 periods, according to the 14 changes in margin requirements.

Keywords: Levene statistic, Margin Regulation, Stock Market, Volatility.

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Authors: Shamsuddin Ahmed, M. G. M. Khan, Biman Prasad, Avlin Prasad

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The focus of this paper is to construct daily time series exchange rate forecast models of Samoan Tala/USD and Tala/AUD during the year 2008 to 2012 with neural network The performance of the models was measured by using varies error functions such as Root Square mean error (RSME), Mean absolute error (MAE), and Mean absolute percentage error (MAPE). Our empirical findings suggest that AR (1) model is an effective tool to forecast the Tala/USD and Tala/AUD.

Keywords: Neural Network Forecasting Model, Autoregressive time series, Exchange rate, Tala/AUD, winters model.

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Authors: Josip Visković, Josip Arnerić, Ante Rozga

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Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models. When financial returns exhibit sudden jumps that are due to structural breaks, standard GARCH models show high volatility persistence, i.e. integrated behavior of the conditional variance. In such situations models in which the parameters are allowed to change over time are more appropriate. This paper compares different GARCH models in terms of their ability to describe structural changes in returns caused by financial crisis at stock markets of six selected central and east European countries. The empirical analysis demonstrates that Markov regime switching GARCH model resolves the problem of excessive persistence and outperforms uni-regime GARCH models in forecasting volatility when sudden switching occurs in response to financial crisis.

Keywords: Central and east European countries, financial crisis, Markov switching GARCH model, transition probabilities.

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Authors: Ivo Jánský, Milan Rippel

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The paper evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the ARMA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting accuracy is evaluated on the out-of-sample data, which are more volatile. The main aim of the paper is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index separately. The primary result of the paper is that the volatility is best modelled using a GARCH process and that an ARMA process pattern cannot be found in analyzed time series.

Keywords: VaR, risk analysis, conditional volatility, garch, egarch, tarch, moving average process, autoregressive process

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Authors: Petr Seďa

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This paper deals with heterogeneous autoregressive models of realized volatility (HAR-RV models) on high-frequency data of stock indices in the USA. Its aim is to capture the behavior of three groups of market participants trading on a daily, weekly and monthly basis and assess their role in predicting the daily realized volatility. The benefits of this work lies mainly in the application of heterogeneous autoregressive models of realized volatility on stock indices in the USA with a special aim to analyze an impact of the global financial crisis on applied models forecasting performance. We use three data sets, the first one from the period before the global financial crisis occurred in the years 2006-2007, the second one from the period when the global financial crisis fully hit the U.S. financial market in 2008-2009 years, and the last period was defined over 2010-2011 years. The model output indicates that estimated realized volatility in the market is very much determined by daily traders and in some cases excludes the impact of those market participants who trade on monthly basis.

Keywords: Global financial crisis, heterogeneous autoregressive model, in-sample forecast, realized volatility, U.S. stock market.

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Authors: Yuzhi Cai

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In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: Exchange rate, quantile regression, combining forecasts.

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Authors: Kunya Bowornchockchai

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The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins Method, Holt’s Method, Mean Absolute Percentage Error (MAPE).

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Authors: Gordana Kordić, Petra Palić

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The European countries that during the past two decades based their exchange rate regimes on currency board arrangement (CBA) are usually analysed from the perspective of corner solution choice’s stabilisation effects. There is an open discussion on the positive and negative background of a strict exchange rate regime choice, although it should be seen as part of the transition process towards the monetary union membership. The focus of the paper is on the Baltic countries that after two decades of a rigid exchange rate arrangement and strongly influenced by global crisis are finishing their path towards the euro zone. Besides the stabilising capacity, the CBA is highly vulnerable regime, with limited developing potential. The rigidity of the exchange rate (and monetary) system, despite the ensured credibility, do not leave enough (or any) space for the adjustment and/or active crisis management. Still, the Baltics are in a process of recovery, with fiscal consolidation measures combined with (painful and politically unpopular) measures of internal devaluation. Today, two of them (Estonia and Latvia) are members of euro zone, fulfilling their ultimate transition targets, but de facto exchanging one fixed regime with another. The paper analyses the challenges for the CBA in unstable environment since the fixed regimes rely on imported stability and are sensitive to external shocks. With limited monetary instruments, these countries were oriented to the fiscal policies and used a combination of internal devaluation and tax policy measures. Despite their rather quick recovery, our second goal is to analyse the long term influence that the measures had on the national economy.

Keywords: Currency Board Arrangement, internal devaluation, exchange rate regime, Great recession.

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Authors: K. Bokreta, D. Benanaya

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The objective of this study is to examine the relative effectiveness of monetary and fiscal policy in Algeria using the econometric modelling techniques of cointegration and vector error correction modelling to analyse and draw policy inferences. The chosen variables of fiscal policy are government expenditure and net taxes on products, while the effect of monetary policy is presented by the inflation rate and the official exchange rate. From the results, we find that in the long-run, the impact of government expenditures is positive, while the effect of taxes is negative on growth. Additionally, we find that the inflation rate is found to have little effect on GDP per capita but the impact of the exchange rate is insignificant. We conclude that fiscal policy is more powerful then monetary policy in promoting economic growth in Algeria.

Keywords: Economic growth, fiscal policy, monetary policy, VECM.

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic.

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