The Pricing Of Better-of Option With Delayed Response

The stock price volatility was assumed to be a constant in the Black-Scholes model of option pricing. However, a large number of empirical tests found that stock return volatility was not constant and influenced by the past stock price, which could be understood as delay factors. In the paper, basing on the studies for the single asset options pricing with time delay in the papers by Arriojas and Li Yaqiong et al., we further expand to study the pricing of European Better-of Option with delay response. In the dissertation, our working can be listed as follow:(1) Basing on the results of European option pricing with time delay in the paper by Li Yaqiong and Huang Lihong, we discussed the impact of delay on the European option prices with the payment of continuous dividends, and obtained some results.(2) For two cases of risk assets paying no dividends and continuous dividends, we chose the research framework in the paper by Arriojas et al., and used the changes of numeraire, the theory of equivalent martingale measure and no-arbitrage property to study the pricing of European Better-of option with delay response, we derived a closed-form representation of the option price in the subinterval of the option duration, and further verified the formula by using the method of partial differential equations.(3) Followed by getting the closed-solution, we made the comparative static analy-sis to examine the rate of change of option price with respect to the central parameters and got some results, and made a comparison with results of the non-delay case.Through these studies, we can obtain the following conclusions:(1) The impact of delay on the European option price relates to the past stock price at present and maturity.(2) The price of Better-of option with delayed response depends not only on the current stock price, but also on the past segment of stock price.(3) No matter whether assets paying no dividends or continue dividends, the price of Better-of option will increase with the increasing of stock prices, and is a convex function of stock prices. However, the impact of the duration on the price of Better-of option connect with the dividends; In addition, we show that the delay can only to change the size of the interval that the relations of the Better-of option price and asset prices can be got, but didn’t change the nature of relations between the option price and asset prices.