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A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model

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  • Lin, Sha
  • He, Xin-Jiang

Abstract

In this paper, we consider the pricing problem of forward start options in the presence of stochastic volatility and regime-switching. By making use of the measure transform technique, with the underlying price as a new numeraire, a closed-form pricing formula is derived in which the only unknown term is the so-called forward characteristic function of the underlying price. The analytical expression of the forward characteristic function under the new measure is subsequently obtained in two steps; the first step treats the regime-switching Heston model as a time-dependent Heston model with the information of the Markov chain beingassumed to be given in advance, while the second step takes the expectation with respect to the Markov chain. Finally, the influence of introducing regime-switching into the Heston model is investigated to show the difference in terms of forward start option pricing between the two models.

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  • Lin, Sha & He, Xin-Jiang, 2021. "A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077920310353
    DOI: 10.1016/j.chaos.2020.110644
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    3. Kim, Sangkwon & Kim, Junseok, 2021. "Robust and accurate construction of the local volatility surface using the Black–Scholes equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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