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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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    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
    3. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    4. David Archer, 2005. "Foreign exchange market intervention: methods and tactics," BIS Papers chapters, in: Bank for International Settlements (ed.), Foreign exchange market intervention in emerging markets: motives, techniques and implications, volume 24, pages 40-55, Bank for International Settlements.
    5. George F. Tannous & Clifton Lee‐Sing, 2008. "Expected Time Value Decay of Options: Implications for Put‐Rolling Strategies," The Financial Review, Eastern Finance Association, vol. 43(2), pages 191-218, May.
    6. repec:bla:scandj:v:78:y:1976:i:2:p:229-48 is not listed on IDEAS
    7. Christopher J. Neely, 2005. "An analysis of recent studies of the effect of foreign exchange intervention," Review, Federal Reserve Bank of St. Louis, vol. 87(Nov), pages 685-718.
    8. Baillie, Richard T. & Osterberg, William P., 1997. "Why do central banks intervene?," Journal of International Money and Finance, Elsevier, vol. 16(6), pages 909-919, December.
    9. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    10. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(1), pages 87-100, March.
    11. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    12. Mauricio Villamizar-Villegas & David Perez-Reyna, 2017. "A Theoretical Approach To Sterilized Foreign Exchange Intervention," Journal of Economic Surveys, Wiley Blackwell, vol. 31(1), pages 343-365, February.
    13. Arango-Lozano, Lucía & Menkhoff, Lukas & Rodríguez-Novoa, Daniela & Villamizar-Villegas, Mauricio, 2024. "The effectiveness of FX interventions: A meta-analysis," Journal of Financial Stability, Elsevier, vol. 74(C).
    14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    15. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    16. Kuersteiner, Guido M. & Phillips, David C. & Villamizar-Villegas, Mauricio, 2018. "Effective sterilized foreign exchange intervention? Evidence from a rule-based policy," Journal of International Economics, Elsevier, vol. 113(C), pages 118-138.
    17. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 06-83, Wharton School Rodney L. White Center for Financial Research.
    18. Lukas Menkhoff, 2013. "Foreign Exchange Intervention in Emerging Markets: A Survey of Empirical Studies," The World Economy, Wiley Blackwell, vol. 36(9), pages 1187-1208, September.
    19. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    20. Mr. Jorge I Canales Kriljenko & Mr. Cem Karacadag & Roberto Guimarães-Filho & Mr. Shogo Ishii, 2006. "Official Foreign Exchange Intervention," IMF Occasional Papers 2006/001, International Monetary Fund.
    21. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    22. Douglas Emery & Weiyu Guo & Tie Su, 2008. "A closer look at Black–Scholes option thetas," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 32(1), pages 59-74, January.
    23. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    24. Scott B. Laprise & Michael C. Fu & Steven I. Marcus & Andrew E. B. Lim & Huiju Zhang, 2006. "Pricing American-Style Derivatives with European Call Options," Management Science, INFORMS, vol. 52(1), pages 95-110, January.
    25. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
    26. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    27. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    28. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    29. Mr. Ousmene J Mandeng, 2003. "Central Bank Foreign Exchange Market Intervention and Option Contract Specification: The Case of Colombia," IMF Working Papers 2003/135, International Monetary Fund.
    30. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 6-83, Wharton School Rodney L. White Center for Financial Research.
    31. Ryan McKeon, 2017. "Empirical patterns of time value decay in options," China Finance Review International, Emerald Group Publishing Limited, vol. 7(4), pages 429-449, September.
    32. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    33. Szu‐Lang Liao & Chou‐Wen Wang, 2003. "The valuation of reset options with multiple strike resets and reset dates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(1), pages 87-107, January.
    34. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
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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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