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Pricing the exotic: Path-dependent American options with stochastic barriers

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  • Rojas-Bernal, Alejandro
  • Villamizar-Villegas, Mauricio

Abstract

We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate ratchet, Asian, and barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, compared to the traditional Monte Carlo simulations method, we highlight that our estimation’s prediction is more accurate and requires less than 1% of the computational time.

Suggested Citation

  • Rojas-Bernal, Alejandro & Villamizar-Villegas, Mauricio, 2021. "Pricing the exotic: Path-dependent American options with stochastic barriers," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 2(1).
    • Handle: RePEc:eee:lajcba:v:2:y:2021:i:1:s2666143821000053
    DOI: 10.1016/j.latcb.2021.100025
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    Cited by:

    1. Freddy A. Pinzón-Puerto & Mauricio Villamizar-Villegas, 2023. "Do Actions Speak Louder than Words? A Foreign Exchange Intervention Analysis," Borradores de Economia 1223, Banco de la Republica de Colombia.

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    More about this item

    Keywords

    Option pricing; Exotic currency options; Ratchet options; Asian options; American options; Barrier options; Weighted time value methodology; Least squares Monte Carlo;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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