Exotic options pricing in continuous time with Monte Carlo simulations

Yunsheng Lu; Haoyu Zhang

doi:10.54254/2753-8818/34/20240765

Research Article

Open access

Published on 11 July 2024

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Lu,Y.;Zhang,H. (2024). Exotic options pricing in continuous time with Monte Carlo simulations. Theoretical and Natural Science,34,315-329.

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Exotic options pricing in continuous time with Monte Carlo simulations

Yunsheng Lu *^,1, Haoyu Zhang ²

¹ University of Virginia
² Imperial College London

* Author to whom correspondence should be addressed.

https://doi.org/10.54254/2753-8818/34/20240765

Abstract

Exotic options are options with special properties. The holder of an exotic option may have some unusual rights, for example decide the time to start the contract or the decision to become a call or a put. The payoff of an exotic option may have unique characteristic, for example it may depend on the max or min of the underlying price in the history. Based on Black-Schole’s Model, these options can be viewed from two different perspectives. One is to specify the distribution and compute the expectation. The other is using replicating portfolio. The former is related to martingale theory, while the latter involves solving a PDE. In this essay, we’ll look at how to value various kinds of options and contrast analytical and Monte Carlo simulation pricing approaches. Chooser, Barrier, Look-back, and Asian choices are the exotic alternatives discussed in our article.

Keywords

Black-Scholes model, Exotic option, Martingale method, Monte-Carlo simulation

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References

[1]. Akyıldırım, E., Soner, H. (2014). A brief history of mathematics in finance. Borsa Istanbul Review, 14(1): 57-63.

[2]. Yan, J., (2022) Martingale Approach to Option Pricing. [online] Ims.cuhk.edu.hk. http://www.ims.cuhk.edu.hk/conference/june99/yanabs.html

[3]. Evans, L. (2014). An Introduction to Stochastic Differential Equations American Mathematical Society: Washington D.C.

[4]. Black, F., Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3): 637-654.

[5]. Musiela, M., Rutkowski, M. (2010). Martingale methods in financial modelling. Springer, Berlin.

[6]. Saari, D. (2019). Mathematics of finance. Springer, Cham.

[7]. Hull, J. (2014) Options, futures, and other derivatives. Prentice Hall, Upper Saddle River.

[8]. Bendob, A., Bentouir, N., (2019). Options Pricing by Monte Carlo Simulation, Binomial Tree and BMS Model: a comparative study of Nifty50 options index. Journal of Banking and Financial Economics, 1/2019(11): 79-95.

[9]. Wilmott, P., Dewynne, J., Howison, Sam., (1994). Oxford Financial Press, New York.

[10]. Bingham, N., Kiesel, R. (2004) Risk-Neutral Valuation. Springer London, London.

[11]. Rogers, L., Shi, Z. (1995). The value of an Asian option. Journal of Applied Probability, 32(04): 1077-1088.

Cite this article

Lu,Y.;Zhang,H. (2024). Exotic options pricing in continuous time with Monte Carlo simulations. Theoretical and Natural Science,34,315-329.

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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 the 3rd International Conference on Computing Innovation and Applied Physics

Conference website: https://www.confciap.org/

ISBN：978-1-83558-369-2(Print) / 978-1-83558-370-8(Online)

Conference date: 27 January 2024

Editor：Yazeed Ghadi

Series: Theoretical and Natural Science

Volume number: Vol.34

ISSN：2753-8818(Print) / 2753-8826(Online)

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