A Probabilistic Approach for Valuing Exchange Option with Default Risk
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We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for mod- eling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumu- lative function via a change of measure technique and a multidimensional Girsanov’s theorem.
Abstract
We study a probabilistic approach for valuing an exchange option with default risk. The structural model of Klein [6] is used for mod- eling default risk. Under the structural model, we derive the closed-form pricing formula of the exchange option with default risk. Specifically, we provide the pricing formula of the option with the bivariate normal cumu- lative function via a change of measure technique and a multidimensional Girsanov’s theorem.
참고문헌 (7)
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- J. -H. Kim, "A multiscale extension of the Margrabe formula under stochastic volatility", Chaos Soliton Fract, 97, pp.59~65 (2017)
- P. Klein, "Pricing Black-Scholes options with correlated credit risk", J. Bank. Financ, 50, pp.1211~1229 (1996)
- W. Margrabe, "The value of an option to exchange one asset for another", J. Financ, 33(1), pp.177~186 (1978)