A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model. (March 2021)

• Record Type: Journal Article
• Authors: Lin, Sha; He, Xin-Jiang
• Is Part Of: Chaos, solitons and fractals. Volume 144(2021)
• Publication Date: 2021-03
• Subjects: Forward start options -- Regime-switching -- Stochastic volatility -- Closed-form; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110644
• Languages: English
• ISSNs: 0960-0779

Abstract

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.