Closed-form American Options Pricing Models on Foreign Assets
Yongxin Yan *
Tianjin Normal University, Tianjin, China.
*Author to whom correspondence should be addressed.
Abstract
The closed-form solution for European options on foreign assets did not consider the impact of strike price volatility. Therefore, these models overestimate the value of European options [1,2]. Using the pricing relationships among European, American and Bermudan option proposed by Yan [3-5], the article establishes four kinds closed-form solution for American and Bermudan option pricing models on foreign assets. The article contribution has three aspects. First, the volatility of underlying assets and strike price together determine the value of American options struck in foreign assets or exchange rate. The greater the strike price volatility, the smaller the American options value. Second, if underlying assets volatility is less than the volatility of strike price, the value of these two kinds of American options equals zero. Third, the bigger the correlation coefficient between exchange rate and foreign assets logarithm yields, the greater the value of these two kinds of American options. We can obtain European and Bermudan options pricing models on foreign assets from American options pricing models.
Keywords: American options on foreign assets, European options on foreign assets, Bermudan options on foreign assets, continuous martingale, measure transformation, domestic and foreign currency measure transformation