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Turbo warrants under stochastic volatility

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  • Hoi Ying Wong
  • Chun Man Chan

Abstract

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005) has considered the pricing of turbo warrants under the Black-Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.

Suggested Citation

  • Hoi Ying Wong & Chun Man Chan, 2008. "Turbo warrants under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 739-751.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:7:p:739-751
    DOI: 10.1080/14697680701691469
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    1. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    2. Yu, Jianfeng & Xu, Weidong, 2016. "Pricing turbo warrants under mixed-exponential jump diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 490-501.
    3. Han, Heejae & Jeon, Junkee & Kang, Myungjoo, 2016. "Pricing chained dynamic fund protection," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 267-278.
    4. Li, Xindan & Subrahmanyam, Avanidhar & Yang, Xuewei, 2018. "Can financial innovation succeed by catering to behavioral preferences? Evidence from a callable options market," Journal of Financial Economics, Elsevier, vol. 128(1), pages 38-65.
    5. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    6. Zhong, Yinhui & Bao, Qunfang & Li, Shenghong, 2015. "FX options pricing in logarithmic mean-reversion jump-diffusion model with stochastic volatility," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 1-13.
    7. Yoon, Ji-Hun & Park, Chang-Rae, 2016. "Pricing turbo warrants under stochastic elasticity of variance," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 107-118.

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