Asymptotic Properties And Global Approximation Of The Early Exercise Boundaries For American Strangle Options

Strangle option is a combination of a call option and a put option,which can greatly help us decrease risk in the financial markets.However,since American strangle option can be executed before the expiry date,we can not calculate its value by directly adding the values of the relative American call option and put option together.The analytic solutions of most American options' pricing problems are difficult to get.For American strangles,such analytic solutions are more difficult,because they have two linked free boundaries.Therefore,in all relative available literature,they have to use numerical methods more or less.We want to find approximate explicit formulas of the early exercise boundaries of American strangle options in this paper,which can help us price options more efficiently.Chiarella and Ziogas get a system of integral equations of early exercise boundaries of American strangle options.In this paper,through rearranging the integral equations and omitting some higher-order infinitesimals,we can get the asymptotic expansions of the early exercise boundaries when the duration tends to 0 and positive infinite,respectively.Then we combine them to get explicit formulas for approximating the early exercise boundaries.We also use Newton's method to get the numerical solution of the integral equations in Chiarella and Ziogas and then use it to test the accuracy of our explicit formulas.Numerical examples show that our global approximation is accurate and efficient.