The Pricing Of Exchange Options With Transaction Costs Under The CEV Process

Option is a kind of important financial derivatives, when it appeared, option pric-ing theory and method have became hot issues. With the global economic integration,produce some exotic options. The exchange option is one kind. it has wide applicationin the international financial trade and investment, so that the study about exchangeoption pricing has great significance. The Black-Scholes formula assumes that stockprice volatility is constant and the investor does not pay any transaction costs. Obvi-ously, it reverses the basic laws of the real financial market.This paper investigates the pricing of the European call option and exchange op-tion with transaction costs by using option replicating principle, no-arbitrage hedgetheory, stochastic diferential equations and other principle of finance and mathe-matical tools. In the paper, it draws the pricing methods of Leland’s deal with thetransaction costs. Our works can be listed as followes:1Basing on the CEV model, we obtain the European call option pricing equationin continuous dividend payment with the transaction costs.2Basing on the research of European option pricing with time delays of Arriojasetal, in the paper, it draws the pricing methods of leland’s deal with transaction costs.By using option replicating, no-arbitrage hedge theory tools we study the Europeancall option pricing whether to pay dividends and transaction costs in a specific timeinterval, and the corresponding closed solution.3In order to be closer to the reality of the financial market, really reflect the stockprice movement law, this article will take into account both the current stock price’sinfluence, and the history of stock price’s influence.we assumes that the stock pricemeet the CEV model with time delayed. in the paper, it draws the pricing methodsof leland’s deal with transaction costs. By using option replicating, no-arbitrage hedgetheory tools we study the European call option pricing whether to pay dividends andtransaction costs in a specific time interval, and the corresponding closed solution.Through these studies, we can be found that: first, the formula of exchangeoption with transaction costs is similar with the formula of exchange option with notransaction costs in form, but volatility will be adjusted. And the text has beenobtained adjusted volatility. Second, the pricing of option with delayed response notonly on the present price but also on the past price. Specially, the formula of the abovecan be reduced as the Black-Scholes formula in a specific time interval.