Recovery of time-dependent volatility in option pricing model ☆The work described in this paper was partially supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. CityU 101112) and grants from the NNSF of China (Nos. 11261029, 11461039), and NSF grants DMS 10-08902 and 15-14886 and by Emylou Keith and Betty Dutcher Distinguished Professorship at the Wichita State University (USA). (29th September 2016) - Deng, Zui-Cha
Abstract: In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective.