Expressions of forward starting option price in Hull–White stochastic volatility model

• DOI: 10.1007/s10203-021-00343-w
• Publication Date: 2021-07-20T03:32:11Z
• Authors: Hiroaki Hata; Nien-Lin Liu; Kazuhiro Yasuda
• Keywords: 0502 economics and business; 05 social sciences

We are interested in problems related to forward starting options for Hull–White stochastic volatility model. Our objective is to obtain analytical, semi-analytical, or approximated expressions of its price for simulation. To obtain an analytical representation of the price, we use Yor’s formula. However, the analytical formula is difficult to implement. Next we consider semi-analytical expressions for the price. In order to have them, we use the tower property for conditional expectations with a certain filtration and explicitly calculate it. Then, we consider an expansion expression for the price using the semi-analytical expression to have a simple expression. The semi-analytical expressions and the expansion expression can reduce computational costs and standard errors when the Monte Carlo method is used. Finally, some numerical results are given to show their accuracy and efficiency.