An Inverse Volatility Problem of Financial Products Linked with Gold Price

This paper investigates an inverse problem of identifying the implied volatility in the financial products linked with gold price, which has important application infinancial derivatives pricing. Based on the optimal control framework, the existence and necessary condition of the minimizer for the control function are obtained. Since the optimal control problem is non-convex, one may not expect a unique solution in general. However, the local uniqueness of the solution is proved in this paper. In the end of the paper, an algorithm is proposed and some numerical experiments are given. Numerical results show that our algorithm is stable and effective. The results obtained in the paper are interesting and useful and can be extended to other inverse problems arising in financial market.