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Fourier-cosine method for pricing forward starting options with stochastic volatility and jumps

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  • Sumei Zhang
  • Junhao Geng

Abstract

This article provides an efficient method for pricing forward starting options under stochastic volatility model with double exponential jumps. The forward characteristic function of the log asset price is derived and thereby forward starting options are well evaluated by Fourier-cosine technique. Based on adaptive simulated annealing algorithm, the model is calibrated to obtain the estimated parameters. Numerical results show that the pricing method is accurate and fast. Double exponential jumps have pronounced impacts on long-term forward starting options prices. Stochastic volatility model with double exponential jumps fits forward implied volatility smile pretty well in contrast to stochastic volatility model.

Suggested Citation

  • Sumei Zhang & Junhao Geng, 2017. "Fourier-cosine method for pricing forward starting options with stochastic volatility and jumps," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 9995-10004, October.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:20:p:9995-10004
    DOI: 10.1080/03610926.2016.1228960
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    Cited by:

    1. Lazar, Emese & Qi, Shuyuan, 2022. "Model risk in the over-the-counter market," European Journal of Operational Research, Elsevier, vol. 298(2), pages 769-784.
    2. Huang, Shoude & Guo, Xunxiang, 2022. "Valuation of European-style vulnerable options under the non-affine stochastic volatility and double exponential jump," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Allan Jonathan da Silva & Jack Baczynski & José Valentim Machado Vicente, 2020. "Efficient Solutions for Pricing and Hedging Interest Rate Asian Options," Working Papers Series 513, Central Bank of Brazil, Research Department.
    4. Huang, Chun-Sung & O'Hara, John G. & Mataramvura, Sure, 2022. "Highly efficient Shannon wavelet-based pricing of power options under the double exponential jump framework with stochastic jump intensity and volatility," Applied Mathematics and Computation, Elsevier, vol. 414(C).

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