From Discrete Intuition to Computational Revolution in the Context of American Chooser Option

Research Article
Open access

From Discrete Intuition to Computational Revolution in the Context of American Chooser Option

Zhixiang Wang 1* , Liwei Su 2 , Shanggeng Zhong 3 , Shaobo Cai 4
  • 1 Cornell University    
  • 2 The University of Sheffield    
  • 3 Middleton Hall Lane    
  • 4 The Hong Kong University of Science and Technology    
  • *corresponding author zw658@cornell.edu
Published on 26 November 2025 | https://doi.org/10.54254/2754-1169/2025.GL30023
AEMPS Vol.246
ISSN (Print): 2754-1169
ISSN (Online): 2754-1177
ISBN (Print): 978-1-80590-571-4
ISBN (Online): 978-1-80590-572-1

Abstract

This paper illustrates the valuation of chooser options within the broader intellectual lineage of modern option pricing theory, providing both a theoretical and methodological framework. Our analysis is anchored in the discrete-time valuation methodology proposed by Cox, Ross, and Rubinstein, commonly known as the CRR model, which remains one of the most influential and practical approaches for demonstrating no-arbitrage pricing. While acknowledging the continuous-time paradigm of the Black–Scholes–Merton (BSM) model as a theoretical benchmark, we leverage the intuitive and adaptable nature of the binomial framework to deconstruct the chooser option’s unique structure. Furthermore, by drawing a conceptual parallel to the work on barrier options by Reiner and Rubinstein, we argue that the analytical treatment of path-dependent but contractually fixed boundaries provides a blueprint for decomposing the chooser’s distinctive payoff mechanism. The core contribution of this work lies in the systematic construction of a binomial pricing model tailored to this instrument. We conclude by outlining pathways for future research, including the extension of this framework to the more complex American-style chooser option—a challenge that requires advanced numerical methods such as the Least-Squares Monte Carlo (LSM) algorithm. Finally, this study proposes a testable hypothesis for future validation: that the structural flexibility embedded in the chooser option may justify a higher premium. Further empirical research is needed to confirm this conjecture and to highlight its potential for both practical implementation and continued academic exploration in complex financial contexts.

Keywords:

Chooser Option, Binomial Pricing Model, Monte Carlo Simulation

Wang,Z.;Su,L.;Zhong,S.;Cai,S. (2025). From Discrete Intuition to Computational Revolution in the Context of American Chooser Option. Advances in Economics, Management and Political Sciences,246,12-25.
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ICFTBA_GL_0258

References

[1]. Hull, J. (2015). Options, Futures, and Other Derivatives. Pearson Education.

[2]. Bampou, D., & Dufresne, D. (2008). Numerical pricing of chooser options. Applied Mathematical Finance, 15(5–6), 425–439.

[3]. Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.

[4]. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.

[5]. Reiner, E., & Rubinstein, M. (1991). Breaking down the barriers. Risk Magazine, 4(8), 28–35.

[6]. Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14(1), 113–147.

[7]. Martinkute-Kauliene, R. (2012). Exotic options: A chooser option and its pricing. Business, Management and Education, 10(2), 289–301.

[8]. Detemple, J., & Emmerling, T. (2009). American chooser options. Journal of Economic Dynamics and Control, 33(1), 128–153. https://doi.org/10.1016/j.jedc.2008.05.004

[9]. Qiu, S., & Mitra, S. (2018). Mathematical properties of American chooser options. International Journal of Theoretical and Applied Finance, 21(8), 1850062. https://doi.org/10.1142/S0219024918500620

[10]. Amin, K., & Khanna, A. (1994). Convergence of American option values from discrete to continuous time financial models. Mathematical Finance, 4(4), 289–304.

[11]. Hutchinson, J. M., Lo, A. W., & Poggio, T. (1994). A nonparametric approach to pricing and hedging derivative securities via learning networks. The Journal of Finance, 49(3), 851–889. https://doi.org/10.1111/j.1540-6261.1994.tb00083.x

[12]. Ruf, J., & Wang, W. (2020). Neural networks for option pricing and hedging: A literature review. arXiv preprint arXiv:1911.05620.

[13]. Cox, J. C., & Ross, S. A. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics, 3(1–2), 145–166. https://doi.org/10.1016/0304-405X(76)90023-4

[14]. Sharma, B., Thulasiram, R. K., & Thulasiraman, P. (2013). Normalized particle swarm optimization for complex chooser option pricing on graphics processing unit. The Journal of Super-computing, 66(1), 170–192. https://doi.org/10.1007/s11227-013-0935-7

[15]. Barria, J., & Hall, S. (2002). A non-parametric approach to pricing and hedging derivative securities: With an application to LIFFE data. Computational Economics, 19(3), 303–322. https://doi.org/10.1023/A:1015291711614

[16]. Rubinstein, M. (1991). Comments on the Black–Scholes option-pricing model.Financial Analysts Journal, 47(1), 79–88.

[17]. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1–2), 125–144.

Cite this article

Wang,Z.;Su,L.;Zhong,S.;Cai,S. (2025). From Discrete Intuition to Computational Revolution in the Context of American Chooser Option. Advances in Economics, Management and Political Sciences,246,12-25.

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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of ICFTBA 2025 Symposium: Financial Framework's Role in Economics and Management of Human-Centered Development

ISBN：978-1-80590-571-4(Print) / 978-1-80590-572-1(Online)
Editor：Lukášak Varti, Florian Marcel Nuţă Nuţă
Conference website: https://2025.icftba.org/Galati.html
Conference date: 17 October 2025
Series: Advances in Economics, Management and Political Sciences
Volume number: Vol.246
ISSN：2754-1169(Print) / 2754-1177(Online)

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References

[1]. Hull, J. (2015). Options, Futures, and Other Derivatives. Pearson Education.

[2]. Bampou, D., & Dufresne, D. (2008). Numerical pricing of chooser options. Applied Mathematical Finance, 15(5–6), 425–439.

[3]. Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229–263.

[4]. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.

[5]. Reiner, E., & Rubinstein, M. (1991). Breaking down the barriers. Risk Magazine, 4(8), 28–35.

[6]. Longstaff, F. A., & Schwartz, E. S. (2001). Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 14(1), 113–147.

[7]. Martinkute-Kauliene, R. (2012). Exotic options: A chooser option and its pricing. Business, Management and Education, 10(2), 289–301.

[8]. Detemple, J., & Emmerling, T. (2009). American chooser options. Journal of Economic Dynamics and Control, 33(1), 128–153. https://doi.org/10.1016/j.jedc.2008.05.004

[9]. Qiu, S., & Mitra, S. (2018). Mathematical properties of American chooser options. International Journal of Theoretical and Applied Finance, 21(8), 1850062. https://doi.org/10.1142/S0219024918500620

[10]. Amin, K., & Khanna, A. (1994). Convergence of American option values from discrete to continuous time financial models. Mathematical Finance, 4(4), 289–304.

[11]. Hutchinson, J. M., Lo, A. W., & Poggio, T. (1994). A nonparametric approach to pricing and hedging derivative securities via learning networks. The Journal of Finance, 49(3), 851–889. https://doi.org/10.1111/j.1540-6261.1994.tb00083.x

[12]. Ruf, J., & Wang, W. (2020). Neural networks for option pricing and hedging: A literature review. arXiv preprint arXiv:1911.05620.

[13]. Cox, J. C., & Ross, S. A. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics, 3(1–2), 145–166. https://doi.org/10.1016/0304-405X(76)90023-4

[14]. Sharma, B., Thulasiram, R. K., & Thulasiraman, P. (2013). Normalized particle swarm optimization for complex chooser option pricing on graphics processing unit. The Journal of Super-computing, 66(1), 170–192. https://doi.org/10.1007/s11227-013-0935-7

[15]. Barria, J., & Hall, S. (2002). A non-parametric approach to pricing and hedging derivative securities: With an application to LIFFE data. Computational Economics, 19(3), 303–322. https://doi.org/10.1023/A:1015291711614

[16]. Rubinstein, M. (1991). Comments on the Black–Scholes option-pricing model.Financial Analysts Journal, 47(1), 79–88.

[17]. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1–2), 125–144.

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