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

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...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2015-01, Vol.60, p.19-28
Main Author: Fard, Farzad Alavi
Format: Article
Language:English
Subjects:
Credit
Credit risk
Economic dynamics
Equivalence
Esscher–Girsanov transform
Europe
Generalization
Generalized jump
Mathematical models
Pay-off
Pricing
Reduced form
Securities prices
Studies
Vulnerable options
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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2014.10.007