Approximate Solution Of Pricing Of Passport Options And Statistic Analysis

With the development of the diversification, the liberalization and the globalization of the international financial market, the financial derivatives has become important. The option is one of derivatives which have the largest trading volume, and pricing and hedging new types of options appears par-ticularly important.This article introduces a new kind of option-the passport option, which was introduced into market by Banker Trust in 1990s. It gives the holder such a power:the holder could keep a trading amount of the underlying and trade on it till maturity. The payoff of the option is determined by the balance of the trading amount at maturity, and the losses would be borne by the option seller. The passport option is a call option with the maturity T and with the strike 0. As this option is related to the holder's strategies, the pricing prob-lem is actually an optimal control problem. Andersen et al.[1] has shown the optimal strategy under Black-Scholes condition, and Henderson[8] has shown the strategy is optimal for more general models with stochastic volatility.The main arrangements for this article are:·Introduce the background and describe pricing and heaging nrnhlems of simple passport option with Black-Scholes model.·Introduce passport option with stochastic volatility, derive approximate formula solutions of specific models such as the Hull-White model, etc, by Taylor expansion method in[10].·Compare numerical results calculated by Monte Carlo method with the formula solutions to check whether it is correct to use Taylor expansion method, compare and analyze approximate solution with the corresponding simple passport options.