Application of Malliavin Calculus in Mean-Variance Hedging Strategy. (5th December 2022)

• Record Type: Journal Article
• Authors: Liu, Kefan; Chen, Jingyao; Zhang, Jichao; Tan, Xili
• Other Names: Cacace Filippo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2022(2022)
• Publication Date: 2022-12-05
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2022/3096866
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper considers an approach of Malliavin calculus to obtain the hedging ratio for mean-variance hedging (MVH) strategy under the stochastic volatility model with pure jump Lévy process (SVJ). Specifically speaking, there exists a correspondence between the martingale representation theorem and the Clark-Ocone formula for a square integrable contingent claim. Therefore, we can replace the diffusion term coefficients with the functions containing Malliavin derivatives to get a closed-form representation for the MVH strategy. By fast Fourier transform (FFT) algorithm, some numerical examples are performed to analyze the sensitivity of MVH strategy concerning strike price and current time.