Barrier options pricing under stochastic volatility using Monte Carlo simulation

Authors

  • Yacin Jerbi
  • Rania Bouzid Bouzid

DOI:

https://doi.org/10.20525/ijfbs.v12i3.2851

Keywords:

barrier options, Option pricing, stochastic volatility, Heston model

Abstract

The aim of this paper is to evaluate barrier options by considering volatility as stochastic following the CIR process used in Heston (1993). To solve this problem, we used Monte Carlo simulation. We studied the effects of stochastic volatility on the value of the barrier option by considering different values of the determinants of the option. We illustrated these effects in twelve graphs. We found that in general, regardless of the parameter under study, the stochastic volatility model significantly overvalues the in-the-money (ITM) barrier options, and slightly the deep-in-the money (DIP) options, while slightly undervaluing the near-out-the money (NTM) options.

Downloads

Download data is not yet available.

References

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The journal of political economy, 637-654. https://www.jstor.org/stable/1831029

Chiarella, C., & al. (2012). The valuation of barrier option prices under stochastic volatility. Computers and mathematics with applications, 2034-2048. https://doi.org/10.1016/j.camwa.2012.03.103

Cox, J., Ingersoll, J., & SA Ross. (1985). A theory of the term structure of interest rates. Econometrica, 385–408. https://www.jstor.org/stable/1911242

Hi, X.-J., & Lin, S. (2021). An Analytical Approximation Formula for Barrier Option Prices under the Heston Model. Computational economics, 1413-1425. https://doi.org/10.1007/s10614-021-10186-7

JP Kahane. (1998). Le mouvement brownien : un essai sur les origines de la théorie mathématique . Mathematics subject classification, 124-154.

K Cheng. (2003). An over view of barrier options. Global derivatives working paper, 1-18.

KS Moon. (2008). Efficient Monte Carlo algorithm for pricing barrier options. communications of Korean mathematical society, 285-294. https://DOI:10.4134/CKMS.2008.23.2.285

M Rubinstein. (2000). On the relation of binomial and trinomial option pricing models. Journal of derivatives, 1-6. DOI 10.3905/jod.2000.319149

Merton, R. (1973). Theory of rational option pricing. The bell journal of economics and management science, 141-183. https://doi.org/10.2307/3003143

P Boyle. (1986). Option valuation using a three-jump process. International options journal, 7-12 .

P Ritchken. (1995). On pricing barrier options. Journal of derivatives, 19-28. http://dx.doi.org/10.3905/jod.1995.407939

Rubinstein, M., & Reiner, E. (1991). Breaking down the barrier. Risk magazine, 28-35.

S Heston. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 327-343. https://www.jstor.org/stable/2962057

Tian, M., Yang, X. F., & Zhang, Y. (2019). Barrier option pricing of mean-reverting stock model in uncertain environment. Mathematics and Computers in Simulation, 126-143. DOI: 10.1016/j.matcom.2019.04.009

W Feller. (1951). Diffusion processes in genetics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, (pp. 227–246). California.

Yao, K., & Zhongfeng Qin. (2020). Barrier option pricing formulas of an uncertain stock model. Fuzzy Optimization and Decision Making, 81-100. DOI: 10.1007/s10700-020-09333-w.

Downloads

Published

2023-10-06

How to Cite

Jerbi, Y., & Bouzid, R. (2023). Barrier options pricing under stochastic volatility using Monte Carlo simulation. International Journal of Finance & Banking Studies (2147-4486), 12(3), 32–39. https://doi.org/10.20525/ijfbs.v12i3.2851

Issue

Section

Articles