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Application of Malliavin Calculus in Mean-Variance Hedging Strategy

Author

Listed:
  • Kefan Liu
  • Jingyao Chen
  • Jichao Zhang
  • Xili Tan
  • Filippo Cacace

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.

Suggested Citation

  • Kefan Liu & Jingyao Chen & Jichao Zhang & Xili Tan & Filippo Cacace, 2022. "Application of Malliavin Calculus in Mean-Variance Hedging Strategy," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-17, December.
    • Handle: RePEc:hin:jnlmpe:3096866
    DOI: 10.1155/2022/3096866
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