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Pricing discrete path-dependent options under a double exponential jump–diffusion model

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  • Fuh, Cheng-Der
  • Luo, Sheng-Feng
  • Yen, Ju-Fang

Abstract

We provide methodologies to price discretely monitored exotic options when the underlying evolves according to a double exponential jump diffusion process. We show that discrete barrier or lookback options can be approximately priced by their continuous counterparts’ pricing formulae with a simple continuity correction. The correction is justified theoretically via extending the corrected diffusion method of Siegmund (1985). We also discuss the jump effects on the performance of this continuity correction method. Numerical results show that this continuity correction performs very well especially when the proportion of jump volatility to total volatility is small. Therefore, our method is sufficiently of use for most of time.

Suggested Citation

  • Fuh, Cheng-Der & Luo, Sheng-Feng & Yen, Ju-Fang, 2013. "Pricing discrete path-dependent options under a double exponential jump–diffusion model," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2702-2713.
    • Handle: RePEc:eee:jbfina:v:37:y:2013:i:8:p:2702-2713
    DOI: 10.1016/j.jbankfin.2013.03.023
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    References listed on IDEAS

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    Cited by:

    1. Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    2. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    3. Chen, Rongda & Zhou, Hanxian & Yu, Lean & Jin, Chenglu & Zhang, Shuonan, 2021. "An efficient method for pricing foreign currency options," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    4. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
    5. Lee, Hangsuck & Lee, Gaeun & Song, Seongjoo, 2023. "Min–max multi-step barrier options and their variants," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    6. Lee, Hangsuck & Choi, Yang Ho & Lee, Gaeun, 2022. "Multi-step barrier products and static hedging," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).
    7. Carlos Esparcia & Elena Ibañez & Francisco Jareño, 2020. "Volatility Timing: Pricing Barrier Options on DAX XETRA Index," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    8. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    9. Xie, Fei & He, Zhijian & Wang, Xiaoqun, 2019. "An importance sampling-based smoothing approach for quasi-Monte Carlo simulation of discrete barrier options," European Journal of Operational Research, Elsevier, vol. 274(2), pages 759-772.
    10. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun & Zhang, Yue, 2019. "Pricing discrete barrier options under jump-diffusion model with liquidity risk," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 347-368.
    11. Carole Bernard & Junsen Tang, 2016. "Simplified Hedge For Path-Dependent Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-32, November.
    12. Sheng-Feng Luo & Hsin-Chieh Wong, 2023. "Continuity correction: on the pricing of discrete double barrier options," Review of Derivatives Research, Springer, vol. 26(1), pages 51-90, April.
    13. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    14. Jinzhi Li, 2021. "Bayesian estimation of the stochastic volatility model with double exponential jumps," Review of Derivatives Research, Springer, vol. 24(2), pages 157-172, July.

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    More about this item

    Keywords

    Barrier options; Lookback options; Jump diffusion models; Continuity correction; Laplace transform;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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