Option Pricing with Heavy Tailed Distribution : Application to Barrier Options

Although the market prefers the Black-Scholes model, there are problems that the BS model doesn¡¯t reflect the skewness or kurtosis of the return distribution. Under the GEV model, Markose(2001) derives the closed-form solutions for vanilla options, and also removes the distortion of the market only with an additional parameter. In this paper, we use the technique in Rubinstein(1991) to get the closed-form solutions for GEV-based vanilla options, and to compare those solutions with the BS model applying to the Global credit crisis. As the BS model underestimate the probability of barrier hit while the credit crisis, we can confirm that the model undervalue in-type barrier options and overvalue out-type barrier options.