《山东大学学报(理学版)》 ›› 2018, Vol. 53 ›› Issue (12): 80-89.

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### 交叉熵蝙蝠算法求解期权定价模型参数估计问题

1. 1.皖西学院金融与数学学院, 安徽 六安 237012;2.河南师范大学数学与信息科学学院, 河南 新乡 453007
• 出版日期:2018-12-20 发布日期:2018-12-18
• 作者简介:李国成(1976— ),男,博士,副教授,研究方向为金融工程与计算智能. E-mail:liguocheng@wxc.edu.cn*通信作者简介:王继霞(1978— ),女,博士,副教授,研究方向为过程统计推断与金融风险管理. E-mail:jixiawang_78@163.com
• 基金资助:
国家自然科学基金资助项目(U1504701);安徽省科技厅软科学研究项目(1607a0202027);安徽省高等学校省级人文社会科学研究重点项目(SK2016A0971)

### Calibrating option pricing models with cross entropy bat algorithm

LI Guo-cheng1, WANG Ji-xia2*

1. 1. School of Finance &
Mathematics, West Anhui University, Luan 237012, Anhui, China;
2. School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453007, Henan, China
• Online:2018-12-20 Published:2018-12-18

Abstract: Parameter estimation of option pricing model is usually a nonlinear optimization problem with no convex, which leads to the classical optimization method cannot be applied. Based on cross entropy bat algorithm, we studied how to solve parameter estimation problems of option pricing models such as Mertons jump-diffusion model, Hestons stochastic volatility model and Batess stochastic volatility with jump model. The empirical results show that the cross entropy bat algorithm is feasible and effective for solving the parameter estimation problems of option pricing model.

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 [1] BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81:637-659.[2] MERTON R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3:125-144.[3] HESTON S L. A closed-form solution for options with stochastic volatility with applications to bonds and currency options[J]. Review of Financial Studies, 1993, 6(2):327-343.[4] BATES D S. Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options[J]. Review of Financial Studies, 1996, 9(1):69-107.[5] 吴嘉伟, 孙升雪, 王力卉,等. 与期权定价模型相关的参数估计的研究综述[J]. 时代金融, 2015(11):268-269. WU Jiawei, SUN Shengxue, WANG Lihui, et al. A survey of parameter estimation related to option pricing model J]. Times Finance, 2015(11):268-269.[6] ZHYLYEVSKYY O. A fast Fourier transform technique for pricing American options under stochastic volatility[J]. Review of Derivatives Research, 2010, 13(1):1-24.[7] CONT R, TANKOV P. Non-parametric calibration of jump-diffusion option pricing models[J]. Journal of Computational Finance, 2004, 7(3):1-50.[8] AVELLANEDA M, BUFF R, FRIEDMAN C, et al. Weighted Monte Carlo: a new technique for calibrating asset-pricing models[J]. International Journal of Theoretical and Applied Finance, 2001, 4(1):91-119.[9] 李斌, 何万里. 一种寻找Heston期权定价模型参数的新方法[J]. 数量经济技术经济研究, 2015(3):129-146. LI Bin, HE Wanli. A new method of finding the parameters of Hestons option pricing model[J]. The Journal of Quantitative & Technical Economics, 2015(3):129-146.[10] GERLICH F, GIESE A M, MARUHN J H, et al. Parameter identification in financial market models with a feasible point SQP algorithm[J]. Computational Optimization & Applications, 2012, 51(3):1137-1161.[11] HE C, KENNEDY J S, COLEMAN T F, et al. Calibration and hedging under jump diffusion[J]. Review of Derivatives Research, 2006, 9(1):1-35.[12] CHAN K C, KAROLYI G A, LONGSTAFF F A, et al. An empirical comparison of alternative models of the short-term interest rate[J]. Journal of Finance, 1992, 47(3):1209-1227.[13] ESCOBAR M, GSCHNAIDTNER C. Parameters recovery via calibration in the Heston model: a comprehensive review[J]. Wilmott, 2016, 2016(86):60-81.[14] GILLI M, SCHUMANN E. Calibrating option pricing models with heuristics[M] // BRABAZON A, ONEILL M, MARINGER D. Natural computing in computational finance. Berlin: Springer-verlag, 2011: 9-37.[15 ] 王林, 张蕾, 刘连峰. 用模拟退火算法寻找Heston期权定价模型参数[J]. 数量经济技术经济研究, 2011(9):131-139. WANG Lin, ZHANG Lei, LIU Lianfeng. Calibration of Hestons option pricing model by using simulated annealing algorithm[J]. The Journal of Quantitative & Technical Economics, 2011(9):131-139.[16] 王平, 王垣苏, 黄运成. 支持向量回归方法的跳跃扩散汇率期权定价[J]. 管理工程学报, 2011, 25(1):134-139. WANG Ping, WANG Hengsu, HUANG Yuncheng. Pricing jump-diffusion currency options with support vector regression[J]. Journal of Industrial Engineering and Engineering Management, 2011, 25(1):134-139.[17] GILLI M, SCHUMANN E. Calibrating the Heston model with differential evolution[C] //International Conference on Applications of Evolutionary Computation. Berlin: Springer-verlag, 2010: 242-250.[18] ARDIA D, DAVID J, ARANGO O, et al. Jump-diffusion calibration using differential evolution[J]. Wilmott, 2011,(55):76-79.[19] 郭恒烨. 基于神经网络的优化Black-Scholes期权定价模型数值求解[J]. 哈尔滨师范大学自然科学学报, 2016, 32(4):41-44. GUO Henghua. Numerical solution of optimal Black-Scholes option pricing model based on neural network[J]. Natural Science Journal of Harbin Normal University, 2016, 32(4):41-44.[20] FAN K, BRABAZON A, OSULLIVAN C, et al. Quantum-inspired evolutionary algorithms for calibration of the VG option pricing model[M] // GIACOBINI M. Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2007: 189-198.[21] 李国成, 肖庆宪. 求解期末亏损最小对冲问题的交叉熵蝙蝠算法[J]. 系统工程, 2014,(11):11-18. LI Guocheng, XIAO Qingxian. Cross-entropy-inspired bat algorithm for hedging problems with minimum shortfall[J]. Systems Engineering, 2014,(11):11-18.
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