Pricing rainbow option for uncertain financial market

Abstract

Rainbow option refers to the option whose payoff depends on at least two underlying risky assets, which is justifiably one of the most significant tool to hedge risk brought by the uncertainty from financial market. Hence, option pricing problem is always an issue with great attention. In this paper, we assume that the multiple dynamic stock prices obey uncertain differential equations without sharing dividends in the framework of uncertainty theory. Then we discuss the rainbow option pricing problem for multiple stocks in a financial market with uncertain information, give the concepts and derive pricing formulas for five scenarios including maximum call, minimum call, maximum put, minimum put, and put on 2 and call on 1. Moreover, some corresponding examples are respectively taken to illustrate the pricing formulas in five cases.