Binomial Method in Bermudan Option
Keywords:option, bermudan option, binomial method
AbstractThe Bermudan option allows the contract holders to make and buy a hybrid contract between American and European options. Bermudan option contract can be executed at certain times until the due of the contract. The purpose of this research is to determine the price of the Bermudan option using the binomial method, and then to compare the binomial method result of n steps with the market option price. In determining stock prices at each point, there will be two branches of the binomial method: up and down branches. These branches represent the movement of stock prices in the market. The result shows the price of Bermudan option is convergent at a certain value when the binomial procedure is enlarged. The comparison of the Bermudan option price using a binomial method to the market price shows that the price of Bermudan option is an approach to the market price in certain conditions. Empirically, the price of Bermudan call option is in approach to the market option price or has a minimum error when the exercise price is below the current stock price. The price of Bermudan put option empirically is in approach to the market option price or having a minimum error when the exercise price is above the current stock price.
 D. Sornette and R. Woodard. (2010). In: " M. Takayasu, T. Watanabe, and H. Takayasu (Eds) Econophysics Approaches to Large-Scale Business Data and Financial Crisis". Springer, Tokyo. 10.1007/978-4-431-53853-0_6.
 J. Li, Q. Li, and X. Wei. (2020). "Financial literacy, household portfolio choice and investment return". Pacific-Basin Finance Journal. 62 10.1016/j.pacfin.2020.101370.
 K.-Y. Woo, C. Mai, M. McAleer, and W.-K. Wong. (2020). "Review on Efficiency and Anomalies in Stock Markets". Economies. 8 (1). 10.3390/economies8010020.
 R. T. Vulandari. (2020). "Black-Scholes Model of European Call Option Pricing in Constant Market Condition". International Journal of Computing Science and Applied Mathematics. 6 (2): 46–49.
 J. C. Hull.(2021)." Options, Futures, and other Derivatives, Global Edition". Prentice-Hall, Upper Saddle River.
 M. Alghalith. (2021). "The price of the Bermudan option: A simple, explicit formula". Communications in Statistics - Theory and Methods. 52 (9): 3174-3177. 10.1080/03610926.2021.1969407.
 Z. Pan, Y. Gao, and L. Yuan. (2021). "Bermudan options pricing formulas in uncertain financial markets". Chaos, Solitons & Fractals. 152 111327. 10.1016/j.chaos.2021.111327.
 J. C. Cox, S. A. Ross, and M. Rubinstein. (1979). "Option pricing: A simplified approach". Journal of Financial Economics. 7 (3): 229-263. 10.1016/0304-405x(79)90015-1.
 J. M. Fayolle, V. Lemaire, T. Montes, and G. Pagès. (2022). "Quantization-Based Bermudan Option Pricing in the Foreign Exchange World". Journal of Computational Finance. 25 (2).
 M. Odin, J. A. Aduda, and C. O. Omari. (2022). "Pricing Bermudan Option with Variable Transaction Costs under the Information-Based Model". Open Journal of Statistics. 12 (05): 549-562. 10.4236/ojs.2022.125033.
 A. Ibáñez and C. Velasco. (2017). "The optimal method for pricing Bermudan options by simulation". Mathematical Finance. 1–38.
 S. Jain and C. W. Oosterlee. (2012). "Pricing high-dimensional Bermudan options using the stochastic grid method". International Journal of Computer Mathematics. 89 (9): 1186-1211. 10.1080/00207160.2012.690035.
 P. P. Boyle, A. W. Kolkiewicz, and K. S. Tan. (2013). "Pricing Bermudan options using low-discrepancy mesh methods". Quantitative Finance. 13 (6): 841-860. 10.1080/14697688.2013.776699.
 L. Feng and X. Lin. (2013). "Pricing Bermudan Options in Lévy Process Models". SIAM Journal on Financial Mathematics. 4 (1): 474-493. 10.1137/120881063.
 H. Lim, S. Lee, and G. Kim. (2014). "Efficient pricing of Bermudan options using recombining quadratures". Journal of Computational and Applied Mathematics. 271 : 195-205. 10.1016/j.cam.2014.04.007.
 H. Zhu, F. Ye, and E. Zhou. (2014). "Fast estimation of true bounds on Bermudan option prices under jump-diffusion processes". Quantitative Finance. 15 (11): 1885-1900. 10.1080/14697688.2014.971520.
 F. Cong and C. W. Oosterlee. (2015). "Pricing Bermudan options under Merton jump-diffusion asset dynamics". International Journal of Computer Mathematics. 92 (12): 2406-2432. 10.1080/00207160.2015.1070838.
 B. Lapeyre and J. Lelong. (2021). "Neural network regression for Bermudan option pricing". Monte Carlo Methods and Applications. 27 (3): 227-247. 10.1515/mcma-2021-2091.
 Z. E. F. Ech-Chafiq, P. Henry-Labordere, and J. Lelong. (2021). "Pricing Bermudan options using regression trees/random forests". Arxiv. 10.48550/arXiv.2201.02587.
 G. Yuan, D. Ding, J. Duan, W. Lu, and F. Wu. (2022). "Total value adjustment of Bermudan option valuation under pure jump Levy fluctuations". Chaos. 32 (2): 023127. 10.1063/5.0072500.
 I. Fahria. (2018). "Pricing Bermudan-Type Call Option Through Binomial Tree Method". AFEBI Accounting Review. 3 (1): 16–24.
 J. Lin and J. Liang. (2007). "Pricing of perpetual American and Bermudan options by binomial tree method". Frontiers of Mathematics in China. 2 (2): 243-256. 10.1007/s11464-007-0017-2.
 A. Prékopa and T. Szántai. (2012). "On the binomial tree method and other issues in connection with pricing Bermudan and American options". Quantitative Finance. 12 (1): 21-26. 10.1080/14697688.2011.649605.
 D. Xie, D. A. Edwards, and X. Wu. (2022). "Optimal exercise frontier of Bermudan options by simulation methods". International Journal of Financial Engineering. 09 (03). 10.1142/s242478632250013x.
 N. Halidias. (2021). "On the Option Pricing by the Binomial Model". Preprints. 1–6. 10.20944/preprints202107.0407.v1.
 D. Obradovic and L. N. Mishra. (2020). "Properties of binomial coefficients". Journal of Mathematical Problems, Equations and Statistics. 1 (1): 1–3.
 C. Annamalai, H. M. Srivastava, and V. N. Mishra. (2020). "Recursive Computations and Differential and Integral Equations for Summability of Binomial Coefficients with Combinatorial Expressions". International Journal of Scientific Research in Mechanical and Materials Engineering. 4 (1): 27–31.
 C. Annamalai, J. Watada, and V. N. Mishra. (2022). "Series and Summations on Binomial Coefficients of Optimized Combination". The Journal of Engineering and Exact Sciences. 8 (3): 14123-01e. 10.18540/jcecvl8iss3pp14123-01e.
 K. Bayram and N. Ganikhodjaev. (2013). "On pricing futures options on random binomial tree". Journal of Physics: Conference Series. 435. 10.1088/1742-6596/435/1/012043.
 S. Nadia, E. Sulistianingsih, and N. Imro'ah. (2018). "Penentuan Harga Opsi Tipe Eropa dengan Metode Binomial". Bimaster: Buletin Ilmiah Matematika, Statistika dan Terapannya. 7 (2): 127–134.
 M. Syazali, Y. Novia, and S. Wahyuningsih. (2015). "Penentuan Harga Opsi Saham Tipe Amerika dengan Model Binomial". Jurnal Eksponensial. 6 (2): 121–126.
 Y. Hu, A. Shirvani, S. Stoyanov, Y. S. Kim, F. J. Fabozzi, and S. T. Rachev. (2020). "Option Pricing in Markets with Informed Traders". International Journal of Theoretical and Applied Finance. 23 (6).
 J. H. van Binsbergen, W. F. Diamond, and M. Grotteria. (2022). "Risk-free interest rates". Journal of Financial Economics. 143 (1): 1-29. 10.1016/j.jfineco.2021.06.012.
 Y. Yashkir.(2007). "Option Price Calculator: European, American, Bermudan". Binomial Tree.
 D. Josheski and M. Apostolov. (2020). "A review of the binomial and trinomial models for option pricing and their convergence to the Black-Scholes model determined option prices". Econometrics. 24 (2): 53–85.
 Y. Ratibenyakool and K. Neammanee. (2019). "Rate of convergence of binomial formula for option pricing". Communications in Statistics - Theory and Methods. 49 (14): 3537-3556. 10.1080/03610926.2019.1590600.
 Riaman, K. Parmikanti, I. Irianingsih, K. Joebaedi, and S. Supian. (2019). "Convergence of binomial tree methods to Black Scholes model on determining stock option prices". IOP Conference Series: Materials Science and Engineering. 567 (1): 10.1088/1757-899x/567/1/012013.
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