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Analytical pricing of vulnerable options under a generalized jump–diffusion model

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  • Fard, Farzad Alavi

Abstract

In this paper we propose a model to price European vulnerable options. We formulate their credit risk in a reduced form model and the dynamics of the spot price in a completely random generalized jump–diffusion model, which nests a number of important models in finance. We obtain a closed-form price for the vulnerable option by (1) determining an equivalent martingale measure, using the Esscher transform and (2) manipulating the pay-off structure of the option four further times, by using the Esscher–Girsanov transform.

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  • Fard, Farzad Alavi, 2015. "Analytical pricing of vulnerable options under a generalized jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 19-28.
    • Handle: RePEc:eee:insuma:v:60:y:2015:i:c:p:19-28
    DOI: 10.1016/j.insmatheco.2014.10.007
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    More about this item

    Keywords

    Vulnerable options; Reduced form; Esscher–Girsanov transform; Generalized jump; Credit risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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