Search results for: comonotonicity

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

Abstract:

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: Raj Kumari Bahl, Sotirios Sabanis

Abstract:

In this paper, we are concerned with the valuation of the first Catastrophic Mortality Bond that was launched in the market namely the Swiss Re Mortality Bond 2003. This bond encapsulates the behavior of a well-defined mortality index to generate payoffs for the bondholders. Pricing this bond is a challenging task. We adapt the payoff of the terminal principal of the bond in terms of the payoff of an Asian put option and present an approach to derive model-independent bounds exploiting comonotonic theory. We invoke Jensen’s inequality for the computation of lower bounds and employ Lagrange optimization technique to achieve the upper bound. The success of these bounds is based on the availability of compatible European mortality options in the market. We carry out Monte Carlo simulations to estimate the bond price and illustrate the strength of these bounds across a variety of models. The fact that our bounds are model-independent is a crucial breakthrough in the pricing of catastrophic mortality bonds.

Keywords: mortality bond, Swiss Re Bond, mortality index, comonotonicity

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