The Quanto Option Pricing With Transaction Costs

Option is a kind of important financial derivatives, when it appeared in the financial markets, option pricing theory and method have became hot issues. With the global economic integration and the deepening of financial integration, investors can invest in domestic stock market and also invest in overseas stock. In order to meet the different needs of investors, all kinds of options emerged. Quanto option is a kind of exotic options and its income depends on not only the change of price in foreign assets, but also the fluctuations of exchange rate. Therefore, the study about the quanto option pricing is of great significance under the assumption in a more realistic.This paper investigates the pricing of the quanto option with transaction costs by using option replicating principle, no-arbitrage hedge theory,change of numeraire, stochastic differential equations and other tools. In order to reflect the fact that different risk assets have different volatility through the design of the new friction coefficient.In the paper, it draws the pricing methods of Leland-Lott's deal with the transaction costs. We considerd discrete trading that we still assume the risk of assets subject to random Brownian motion, made full use of the hedging principles and formulas to establish the corresponding mathematical model, and got the formula with the methods about partial differential equations, then I have concluded the partial differential equation and the pricing formula of the quanto option with transaction costs. As the pricing formula is the analytic form, it can be calculated to compare the corresponding derivative of the static analysis to obtain the corresponding parameters of the various hedgeing. So this kind of display expressions compared with numerical solutions to demonstrate the superiority of some.Through these studies, we can be found that the formula of quanto option with transaction costs is similar with the formula of quanto option with no transaction costs in form, but volatility will be adjusted. And the text has been obtained adjusted volatility. As long as the position adjustment control in a given time interval, the pricing of quanto option with transaction costs equal to the pricing of quanto option with greater volatility in a market with no transaction costs on option pricing.