The Pricing Of Quanto Option With Delayed Response

With the development of economic globalization,more and more domestic investors pay attention to the international market.And Quanto option is just the kind of option that is designed for investors to purchase foreign securities in the country or region.How to price Quanto option reasonably is not only a theoretical demand but also a practical need.In the paper,we first find that exchange rate is influenced by the past,behaviour,which can be understood as delay factors.Secondly,based on the model in the work of Arriojas,Mohammed and Hu et al,we assume that exchange rate and stock price have time-delay in the drift term and diffusion term,then under the risk neutral probability measure,we obtain the stochastic delay differential equations concerning exchange rate and stock price.Finally,we study the price of Quanto options with delay response by using Girsanov theorem,martingale representation theorem,no-arbitrage property and risk neutral valuation principle.In the paper,our works can be listed as follows:1.Based on the results of European option pricing with time delay in the paper by Arriojas,Mohammed and Hu et al,we assume that exchange rate and stock price havetime-delay,then use the changes of numeraire and the theory of Ito lemma,to derive the stochastic delay differential equations that exchange rate and stock price satisfy by finding some appropriate traded securities in the domestic currency word.2.Followed by obtaining the risk neutral probability measure,we establish the completeness of the market with the help of martingale representation theorem,self-financial trading strategy and no-arbitrage property.Furthermore,since every contingent is attainable,we derive a closed form representation of the Quanto call option in the sub-interval of the option duration,and obtain the price of put option by using put-call parity relation.In the end of this paper,we derive the B-S partial differential equation for a Quanto option with delay response.