Barrier options pricing under stochastic volatility using Monte Carlo simulation


  • Yacin Jerbi
  • Rania Bouzid Bouzid



barrier options, Option pricing, stochastic volatility, Heston model


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.


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Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The journal of political economy, 637-654.

Chiarella, C., & al. (2012). The valuation of barrier option prices under stochastic volatility. Computers and mathematics with applications, 2034-2048.

Cox, J., Ingersoll, J., & SA Ross. (1985). A theory of the term structure of interest rates. Econometrica, 385–408.

Hi, X.-J., & Lin, S. (2021). An Analytical Approximation Formula for Barrier Option Prices under the Heston Model. Computational economics, 1413-1425.

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.

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.

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.

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.




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.