IMPLEMENTATION OF MONTE CARLO MOMENT MATCHING METHOD FOR PRICING LOOKBACK FLOATING STRIKE OPTION
Abstract
Monte Carlo method was a numerical method that was popular in finance. This method had disadvantages at convergences, so the moment matching was used to improve the efficiency from Monte Carlo method. The research has discussed about pricing of the lookback floating strike option using the Monte Carlo moment matching method. The monthly stock price of PT TELKOM from 2004 to 2021 that used in this research. The results obtained by adding variance reduction moment matching in Monte Carlo method, which produces a relatively had smaller error when compared to the relative error of the standard Monte Carlo method. The orders of convergence from Monte Carlo method with variance reduction moment matching for call and put option are about 1.1 and 1.4. The conclusion that addition of the moment matching can increase the efficiency of the Monte Carlo method in determining the price of the lookback floating strike option.
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References
N. Li and S. Wang, “Pricing options on investment project expansions under commodity price uncertainty,” J. Ind. Manag. Optim., vol. 15, no. 5, pp. 261–273, 2019, doi: 10.3934/JIMO.2018042.
Y. Liang and X. Xu, “Variance and dimension reduction Monte Carlo method for pricing European multi-asset options with stochastic volatilities,” Sustain., vol. 11, no. 3, 2019, doi: 10.3390/su11030815.
S. R. Chakravarty and P. Sarkar, An Introduction To Algorithmic Finance, Algorithmic Trading and Blockchain. USA: Emerald Publishing Limited, 2020.
J. C. Hull, Options, Futures, and Other Derivatives: Solutions Manual, Ninth Edit., vol. 59, no. 2. New Jersey (US): Pearson Education, 2015.
R. Martinkutė-Kaulienė, “Exotic Options: a Chooser Option and Its Pricing,” Business, Manag. Educ., vol. 10, no. 2, pp. 289–301, 2012, doi: 10.3846/bme.2012.20.
J.-J. Sun, S. Zhou, Y. Zhang, M. Han, and F. Wang, “Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion,” Int. Sch. Res. Not., vol. 2014, pp. 1–7, 2014, doi: 10.1155/2014/746196.
J. Li and X. Xu, “The Valuation of Basket-lookback Option,” vol. 648, no. Icfied, pp. 2110–2115, 2022.
Z. Liu, “Lookback option pricing problems of uncertain mean-reverting stock model,” J. Adv. Comput. Intell. Intell. Informatics, vol. 25, no. 5, pp. 539–545, 2021, doi: 10.20965/jaciii.2021.p0539.
Y. Gao and L. Jia, “Pricing formulas of barrier-lookback option in uncertain financial markets,” Chaos, Solitons and Fractals, vol. 147, p. 110986, 2021, doi: 10.1016/j.chaos.2021.110986.
F. Mostafa, T. Dillon, and E. Chang, Computational Intelligence Applications to Option Pricing, Volatility Forecasting and Value at Risk, vol. 697. 2017.
S. Y. Choi, J. H. Yoon, and J. Jeon, “Pricing of Fixed-Strike Lookback Options on Assets with Default Risk,” Math. Probl. Eng., vol. 2019, 2019, doi: 10.1155/2019/8412698.
Y. Zhang, “The value of Monte Carlo model-based variance reduction technology in the pricing of financial derivatives,” PLoS One, vol. 15, no. 2, pp. 1–13, 2020, doi: 10.1371/journal.pone.0229737.
A. Horvath and P. Medvegyev, “Pricing Asian Options: A Comparison of Numerical and Simulation Approaches Twenty Years Later,” J. Math. Financ., vol. 06, no. 05, pp. 810–841, 2016, doi: 10.4236/jmf.2016.65056.
I. Syata, S. D. Anugrawati, Nurwahidah, and A. Mariani, “Estimate cash-or-nothing option by Monte Carlo - Moment matching (MC-MM) method: The case of Indonesian rice prices,” AIP Conf. Proc., vol. 2326, no. February, 2021, doi: 10.1063/5.0039278.
R. H. Chan, Y. Zy, S. T. Lee, and X. Li, Financial Mathematics , Derivatives and Structured. Singapore: Springer, 2019.
K. Nouri and B. Abbasi, “Implementation of the modified Monte Carlo simulation for evaluate the barrier option prices,” J. Taibah Univ. Sci., vol. 11, no. 2, pp. 233–240, 2017, doi: 10.1016/j.jtusci.2015.02.010.
R. U. Seydel, Tools for computational finance, Sixth., vol. 40, no. 07. United Kingdom: Springer, 2017. doi: 10.5860/choice.40-4121.
M. Alfeus and S. Kannan, “Pricing Exotic Derivatives for Cryptocurrency Assets—A Monte Carlo Perspective,” J. Math. Financ., vol. 11, no. 04, pp. 597–619, 2021, doi: 10.4236/jmf.2021.114033.
P. Glasserman, Monte Carlo Methods in Financial Engineering. New York: Springer, 2003.
P. Boyle, M. Broadie, and P. Glasserman, “Monte Carlo methods for security pricing,” J. Econ. Dyn. Control, vol. 21, no. 8–9, pp. 1267–1321, 1997, doi: 10.1016/s0165-1889(97)00028-6.
Y.-K. Kwok, Mathematical Models of Financial Derivatives, Second Edi. Singapore: Springer, 2008. doi: 10.1007/978-3-540-31299-4.
D. C. Lesmana and S. Wang, “An upwind finite difference method for a nonlinear Black-Scholes equation governing European option valuation under transaction costs,” Appl. Math. Comput., vol. 219, no. 16, pp. 8811–8828, 2013, doi: 10.1016/j.amc.2012.12.077.
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