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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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    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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