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Rare Shock, Two-Factor Stochastic Volatility and Currency Option Pricing

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  • Guanying Wang
  • Xingchun Wang
  • Yongjin Wang

Abstract

In this paper, we develop an option valuation model where the dynamics of the spot foreign exchange rate is governed by a two-factor Markov-modulated jump-diffusion process. The short-term fluctuation of stochastic volatility is driven by a Cox--Ingersoll--Ross (CIR) process and the long-term variation of stochastic volatility is driven by a continuous-time Markov chain which can be interpreted as economy states. Rare events are governed by a compound Poisson process with log-normal jump amplitude and stochastic jump intensity is modulated by a common continuous-time Markov chain. Since the market is incomplete under regime-switching assumptions, we determine a risk-neutral martingale measure via the Esscher transform and then give a pricing formula of currency options. Numerical results are presented for investigating the impact of the long-term volatility and the annual jump intensity on option prices.

Suggested Citation

  • Guanying Wang & Xingchun Wang & Yongjin Wang, 2014. "Rare Shock, Two-Factor Stochastic Volatility and Currency Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(1), pages 32-50, March.
  • Handle: RePEc:taf:apmtfi:v:21:y:2014:i:1:p:32-50
    DOI: 10.1080/1350486X.2013.798452
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    Cited by:

    1. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    2. Jeon, Junkee & Kim, Geonwoo, 2022. "Pricing European continuous-installment currency options with mean-reversion," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    3. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.

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