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A Numerical Approach to Pricing Exchange Options under Stochastic Volatility and Jump-Diffusion Dynamics

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  • Len Patrick Dominic M. Garces
  • Gerald H. L. Cheang

Abstract

We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other numerical scheme for PDEs, becomes increasingly complex when higher dimensions are involved, we first simplify the problem by transforming the exchange option into a call option written on the ratio of the yield processes of the two assets. This is achieved by taking the second asset yield process as the numeraire. We also characterize the near-maturity behavior of the early exercise boundary of the American exchange option and analyze how model parameters affect this behavior. Using the MOL scheme, we conduct a numerical comparative static analysis of exchange option prices with respect to the model parameters and investigate the impact of stochastic volatility and jumps to option prices. We also consider the effect of boundary conditions at far-but-finite limits of the computational domain on the overall efficiency of the MOL scheme. Toward these objectives, a brief exposition of the MOL and how it can be implemented on computing software are provided.

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  • Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2021. "A Numerical Approach to Pricing Exchange Options under Stochastic Volatility and Jump-Diffusion Dynamics," Papers 2106.07362, arXiv.org.
    • Handle: RePEc:arx:papers:2106.07362
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    References listed on IDEAS

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    1. Carl Chiarella & Boda Kang & Gunter H. Meyer & Andrew Ziogas, 2009. "The Evaluation Of American Option Prices Under Stochastic Volatility And Jump-Diffusion Dynamics Using The Method Of Lines," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 393-425.
    2. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
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    13. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2020. "A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics," Papers 2002.10194, arXiv.org.
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    Cited by:

    1. Enrique Villamor & Pablo Olivares, 2023. "Valuing Exchange Options under an Ornstein-Uhlenbeck Covariance Model," IJFS, MDPI, vol. 11(2), pages 1-24, March.
    2. Alessandro Ramponi, 2022. "Spread Option Pricing in Regime-Switching Jump Diffusion Models," Mathematics, MDPI, vol. 10(9), pages 1-15, May.

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