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Pricing discounted American capped options

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  • Zaevski, Tsvetelin S.

Abstract

The purpose of this paper is to present an efficient method for pricing discounted American capped options. They differ from the corresponding uncapped ones by the existing trigger level for the underlying asset. In such a way the option’s seller is preserved from the possible large movements of the underlying asset. We first obtain the optimal exercise region and by the use of some hitting properties we derive the fair option price. We use the Crank-Nicolson finite difference approach together with a Monte Carlo method to implement the obtained formulas. This method applied for the pricing problem of the ordinary American options has its own significance. Finally, we present some numerical results.

Suggested Citation

  • Zaevski, Tsvetelin S., 2022. "Pricing discounted American capped options," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000443
    DOI: 10.1016/j.chaos.2022.111833
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. Michael, Fredrick, 2020. "Black–Scholes like closed form formulas and numerical solutions for American style options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    3. Zhang, Xiang & Li, Lingfei & Zhang, Gongqiu, 2021. "Pricing American drawdown options under Markov models," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1188-1205.
    4. Zaevski, Tsvetelin S. & Kim, Young Shin & Fabozzi, Frank J., 2014. "Option pricing under stochastic volatility and tempered stable Lévy jumps," International Review of Financial Analysis, Elsevier, vol. 31(C), pages 101-108.
    5. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2020. "Early exercise boundaries for American-style knock-out options," European Journal of Operational Research, Elsevier, vol. 285(2), pages 753-766.
    6. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    7. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    8. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    9. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    10. Junkee Jeon & Jeonggyu Huh & Kyunghyun Park, 2020. "An Analytic Approximation for Valuation of the American Option Under the Heston Model in Two Regimes," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 499-528, August.
    11. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, vol. 48(7), pages 917-937, July.
    12. Dongya Deng & Cuiye Peng, 2014. "New Methods with Capped Options for Pricing American Options," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, April.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Woo, Min Hyeok & Choe, Geon Ho, 2020. "Pricing of American lookback spread options," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6300-6318.
    15. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-191.
    16. Min-Ku Lee & Jeong-Hoon Kim & Kyu-Hwan Jang, 2014. "Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, January.
    17. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    18. Tat Lung (Ron) Chan, 2020. "An SFP–FCC method for pricing and hedging early-exercise options under Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 20(8), pages 1325-1343, August.
    19. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    20. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Junkee Jeon & Geonwoo Kim, 2022. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment," Mathematics, MDPI, vol. 10(15), pages 1-19, July.

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    More about this item

    Keywords

    American capped options; Optimal boundary; Optimal stopping time; Crank-Nicolson finite difference approach;
    All these keywords.

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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