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Pricing vulnerable options under cross-asset markov-modulated jump-diffusion dynamics

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  • Lian, Yu-Min
  • Chen, Jun-Home

Abstract

In this study, the dynamics of the underlying asset price and the counterparty's asset price are governed by a cross-asset Markov-modulated jump-diffusion model that captures the time-inhomogeneity and systematic cojumps. Additionally, the forward interest rate processes are driven by a Markov-modulated Heath–Jarrow–Morton model to depict stochastic volatilities. Under an incomplete-market setting, we apply the Markov-modulated Esscher transform technique to determine a risk-neutral martingale measure. After determining the Markov-modulated Esscher parameters, we obtain an integral expression on the prices of vulnerable European-style Black–Scholes options. The numerical illustrations indicate that the findings are consistent with Klein (1996) and contribute to the extant literature on cojumping impacts on vulnerable option prices.

Suggested Citation

  • Lian, Yu-Min & Chen, Jun-Home, 2024. "Pricing vulnerable options under cross-asset markov-modulated jump-diffusion dynamics," International Review of Economics & Finance, Elsevier, vol. 94(C).
    • Handle: RePEc:eee:reveco:v:94:y:2024:i:c:s1059056024003848
    DOI: 10.1016/j.iref.2024.103392
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    More about this item

    Keywords

    Cross-asset markov-modulated jump-diffusion model; Markov-modulated; Heath–jarrow–morton model; Time-inhomogeneity; Systematic cojump; Markov-modulated esscher transform;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G01 - Financial Economics - - General - - - Financial Crises
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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