﻿ 随机利率模型下二叉树方法期权定价

# 随机利率模型下二叉树方法期权定价Binomial Option Pricing under Stochastic Interest Rates

Abstract: This paper discusses the standard binary tree method for European option pricing under the Vasicek stochastic interest rate model. The article makes some transfor- mations based on the Vasicek stochastic interest rate model, which is to simplify the model equation by simplifying the diffusion term coefficients in the stochastic differ- ential equations of stock price and interest rate, and transform the original model into the standard type required for this paper. Then we construct a simple joint binary tree to price European options, and get an iterative formula for the option price.

[1] Bachelier, L. (1900) Théorie de la spéculation. Gauthier-Villars, Paris.
https://doi.org/10.24033/asens.476

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

[3] Merton, R. C. Influence of Mathematical Models in Finance on Practice: Past, Present and Future[J]. Mathematical Model in Finance, 1995, 48 (22): 190-208.

[4] Cox, J.C., Ingersoll, J.E. and Ross, J. (1985) A Theory of the Term Structure of Interest Rate. Econometrica, 53, 385-407.

[5] 刘敬伟. Vasicek随机利率模型下指数O-U的型期权定价[J]. 数学的实践与认识,39(1):31-39.

[6] He, X.-J. and Zhu, S.-P. (2018) A Closed-Form Pricing Formula for European Options un- der the Heston Model with Stochastic Interest Rate. Journal of Computational and Applied Mathematics, 335, 323-333.
https://doi.org/10.1016/j.cam.2017.12.011

[7] Cox, J.C., Ross, S.A. and Rubinstein, M. (1979) Option Pricing: A Simplified Approach. Journal of Financial Economics, 7, 229-263.
https://doi.org/10.1016/0304-405X(79)90015-1

[8] Amin, K.I. (1993) Jump Diffusion Option Valuation in Discrete Time. The Journal of Finance, 48, 1833-1863.
https://doi.org/10.1111/j.1540-6261.1993.tb05130.x

[9] Hilliard, J.E. and Schwartz, A. (2005) Pricing European and American Derivatives under a Jump-Diffusion Process: A Bivariate Tree Approach. Journal of Financial and Quantitative Analysis, 40, 671-691.
https://doi.org/10.1017/S0022109000001915

[10] Derman, E. and Kani, I. (1998) Stochastic Implied Trees: Arbitrage Pricing with Stochas- tic Term and Strike Structure of Volatility. International Journal of Theoretical and Applied Finance, 1, 61-110.
https://doi.org/10.1142/S0219024998000059

[11] Costabile, M., Massabo, I. and Russo, E. (2006) An Adjusted Binomial Model for Pricing Asian Options. Review of Quantitative Finance and Accounting, 27, 285-296.
https://doi.org/10.1007/s11156-006-9432-9

[12] 任芳玲, 蒋登智. 基于交易成本和红利的欧式期权二叉树模型及算法[J]. 山东科学, 2018, 31(5): 101-108.

[13] Lo, C., Nguyen, D. and Skindilias, K. (2017) A Unified Tree Approach for Options Pricing under Stochastic Volatility Models. Finance Research Letters, 20, 260-268.
https://doi.org/10.1016/j.frl.2016.10.009

[14] Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure. Journal of Finan- cial Economics, 5, 177-188.
https://doi.org/10.1016/0304-405X(77)90016-2

Top