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Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate

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  • Ji-Hun Yoon

Abstract

Even though interest rates fluctuate randomly in the marketplace, many option-pricing models do not fully consider their stochastic nature owing to their generally limited impact on option prices. However, stochastic dynamics in stochastic interest rates may have a significant impact on option prices as we take account of issues of maturity, hedging, or stochastic volatility. In this paper, we derive a closed form solution for European options in Black-Scholes model with stochastic interest rate using Mellin transform techniques.

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  • Ji-Hun Yoon, 2014. "Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, October.
    • Handle: RePEc:hin:jnljam:759562
    DOI: 10.1155/2014/759562
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    Cited by:

    1. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing of vulnerable options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 645-656.
    2. Panumart Sawangtong & Kamonchat Trachoo & Wannika Sawangtong & Benchawan Wiwattanapataphee, 2018. "The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense," Mathematics, MDPI, vol. 6(8), pages 1-14, July.
    3. Kim, Donghyun & Kim, Geonwoo & Yoon, Ji-Hun, 2022. "Pricing of vulnerable exchange options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    4. Sun-Yong Choi & Ji-Hun Yoon & Junkee Jeon, 2019. "Pricing of Fixed-Strike Lookback Options on Assets with Default Risk," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    5. Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
    6. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    7. Jiling Cao & Jeong-Hoon Kim & Xi Li & Wenjun Zhang, 2022. "Pricing Path-dependent Options under Stochastic Volatility via Mellin Transform," Papers 2205.00573, arXiv.org.
    8. Kim, Geonwoo & Koo, Eunho, 2016. "Closed-form pricing formula for exchange option with credit risk," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 221-227.

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