Reload option pricing in fuzzy framework

In this paper we consider the reload option pricing problem. We assume that the underlying stock price follows a geometric Brownian motion. By means of the relationship between 2-variate normal distribution function and 1-variate normal distribution function we derive the analytical pricing formula for reload option based on Johnson and Tian´s “closed-form solution” for the value of a reload option. Considering the uncertainty of a financial market includes risk and vagueness and some parameters such as the interest rate and volatility cannot be precisely described and therefore we apply fuzzy numbers to the pricing model. We present the fuzzy price of reload option by fuzzing the interest rate and volatility in reload option analytical pricing formula. For a given α, the interval for fuzzy price is obtained according to the fuzzy arithmetic and the definition of fuzzy-valued function. Finally, we conduct some numerical analysis to illustrate the previous theoretical results in fuzzy framework.