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Seminar
FIELD Computational Sciences
DATE January 31 (Fri), 2020
TIME 16:00-17:00
PLACE 7323
SPEAKER Ji-Hun Yoon
HOST Huh, Jeonggyu
INSTITUTE 부산대학교 수학과
TITLE A closed-form formula for vulnerable option price under stochastic elasticity of variance
ABSTRACT The stochastic elasticity of variance model introduced by Kim, Lee, Zhu & Yu (2014) is a useful model for forecasting extraordinary volatility behavior which would take place in a financial crisis. High volatility of market could be linked to default risk of option contracts. So, the model is a desirable choice for the pricing of vulnerable option. This paper is an extended study of a previous work by Lee, Yang & Kim (2017) but obtains an explicit closed-form analytic expression of the price of vulnerable option under a framework with two separate scales that could minimize the number of necessary parameters for calibration but reflect the essential character of the underlying risky asset of the option and the firm value of the option writer. Using singular perturbation and double Mellin transform techniques, we obtain the formula which is given by the Black-Scholes formula for the vulnerable option plus correction terms that consist of simple derivatives of the Black-Scholes solution. This formula provides us to compute the vulnerableoption price easily and to perform the sensitivity analysis for the price with respect to default risk eectively.
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