Journal of Guangdong University of Technology ›› 2024, Vol. 41 ›› Issue (01): 127-134.doi: 10.12052/gdutxb.220185

• Comprehensive Studies • Previous Articles    

Behavioral Option Pricing under Prospect Theory Framework and Heston Model

Sun You-fa, Peng Wen-yan   

  1. School of Economics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2022-12-07 Online:2024-01-25 Published:2024-02-01

Abstract: Behavioral option pricing has been one of the hottest frontiers in the area of international finance. Stochastic volatility model has become the de facto standard model of international derivatives pricing, but it is not accurate enough in the pricing of short-term options, especially for OTM. One of the reasons is that the traditional option pricing methods ignore the irrational psychological and behavioral factors in the real market. To solve this problem,prospect theory is brought into the traditional option pricing framework, the different value judgments of investors facing gains and losses are described by introducing the subjective value function, the subjective decision weight function is used to modify the probability density function of the asset price path described by Heston model, and then the cash flow in the two periods of signing and executing European option contracts is regarded as two separate mental accounts. Prices of European options under Heston model are derived under the condition of market equilibrium. The empirical results of SSE 50ETF option show that the Heston stochastic volatility model considering the prospect theory can significantly improve the pricing accuracy of short maturity OTM option. The model parameter correction results show that the improvement of pricing performance is due to the behavioral parameters representing irrational psychology and emotion included in Heston model. Relatively speaking, investors' risk attitude towards ITM options is nearly neutral, so the improvement of behavior parameters on its pricing accuracy is limited.

Key words: behavioral option pricing, prospect theory, mental account, Heston model, SSE 50ETF option

CLC Number: 

  • F830.9
[1] BLACK F, SCHOLES M. The pricing of options and corporate liabilities [J]. Journal of Political Economy, 1973, 81(3): 637-654.
[2] MERTON R C. Option pricing when underlying stock returns are discontinuous [J]. Journal of Financial Economics, 1976, 3(1-2): 125-144.
[3] BATES D S. Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options [J]. The Review of Financial Studies, 1996, 9(1): 69-107.
[4] HULL J. An analysis of the bias in option pricing caused by a stochastic volatility [J]. Advances in Futures and Options Research, 1988, 3: 29-61.
[5] HESTON S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options [J]. The Review of Financial Studies, 1993, 6(2): 327-343.
[6] GARLEANU N, PEDERSEN L H, POTESHMAN A M. Demand-based option pricing [J]. The Review of Financial Studies, 2008, 22(10): 4259-4299.
[7] JONES C S, SHEMESH J. Option mispricing around nontrading periods [J]. The Journal of Finance, 2018, 73(2): 861-900.
[8] HAN B. Investor sentiment and option prices [J]. The Review of Financial Studies, 2008, 21(1): 387-414.
[9] SIDDIQI H. Anchoring-adjusted option pricing models [J]. Journal of Behavioral Finance, 2019, 20(2): 139-153.
[10] 孙有发, 姚宇航, 邱梓杰, 等. 基于特征函数局部结构微扰法的行为期权定价研究[J]. 系统工程理论与实践, 2022, 42(12): 3247-3264.
SUN Y F, YAO Y H, QIU Z J, et al. Behavioral option pricing method based on perturbation in the local structure of characteristic function [J]. Systems Engineering-Theory & Practice, 2022, 42(12): 3247-3264.
[11] JANG B G, KIM C, KIM K T, et al. Psychological barriers and option pricing [J]. Journal of Futures Markets, 2015, 35(1): 52-74.
[12] SONG S, WANG Y. Pricing double barrier options under a volatility regime-switching model with psychological barriers [J]. Review of Derivatives Research, 2017, 20: 255-280.
[13] SONG S, WANG G, WANG Y. Pricing European options under a diffusion model with psychological barriers and leverage effect [J]. The European Journal of Finance, 2020, 26(12): 1184-1206.
[14] 孙有发, 邱梓杰, 姚宇航, 等. 基于深度学习算法的行为期权定价[J]. 系统管理学报, 2021, 30(4): 697-708.
SUN Y F, QIU Z J, YAO Y H, et al. Behavioral option pricing based on deep-learning algorithm [J]. Journal of Systems & Management, 2021, 30(4): 697-708.
[15] RACHEV S, STOYANOV S, FABOZZI F J. Behavioral finance option pricing formulas consistent with rational dynamic asset pricing[EB/OL]. arXiv:1710. 03205(2017-10-09) [2022-11-30]. https: //doi. org/10.48550/arXiv. 1710. 03205.
[16] RACHEV S, FABOZZI F J, RACHEV B, et al. Option pricing with greed and fear factor: The rational finance approach[EB/OL]. arXiv: 1709.08134(2017-09-24) [2022-11-30]. https: //doi. org /10. 48550/arXiv. 1709.08134.
[17] DAI J, SHIRVANI A, FABOZZI F J. Rational finance approach to behavioral option pricing[EB/OL]. arXiv: 2005.05310(2020-05-10) [2022-11-30]. https: //doi. org/10.48550/arXiv. 2005. 05310.
[18] BAELE L, DRIESSEN J, EBERT S, et al. Cumulative prospect theory, option returns, and the variance premium [J]. The Review of Financial Studies, 2019, 32(9): 3667-3723.
[19] 姜继娇, 杨乃定. 基于两心理账户BPT的复合实物期权定价模型[J]. 管理科学学报, 2008, 11(1): 89-94.
JIANG J J, YANG N D. Compound real option pricing model based on BPT with two mental accounts [J]. Journal of Management Sciences in China, 2008, 11(1): 89-94.
[20] SHEFRIN H, STATMAN M. Behavioral aspects of the design and marketing of financial products [J]. Financial Management, 1993, 22(2): 123-134.
[21] SHILLER R J. Human behavior and the efficiency of the financial system [J]. Handbook of Macroeconomics, 1999, 1: 1305-1340.
[22] BREUER W, PERST A. Retail banking and behavioral financial engineering: the case of structured products [J]. Journal of Banking & Finance, 2007, 31(3): 827-844.
[23] SUZUKI K, SHIMOKAWA T, MISAWA T. Agent-based approach to option pricing anomalies [J]. IEEE Transactions on Evolutionary Computation, 2009, 13(5): 959-972.
[24] BAR-GILL O. Pricing legal options: a behavioral perspective [J]. Review of Law & Economics, 2005, 1(2): 204-240.
[25] BENARTZI S, THALER R H. Myopic loss aversion and the equity premium puzzle [J]. The Quarterly Journal of Economics, 1995, 110(1): 73-92.
[26] VERSLUIS C, LEHNERT T, WOLFF C C P. A cumulative prospect theory approach to option pricing[EB/OL]. (2010-11-30) [2022-11-30]. https: //ssrn. com/ abstract=1717015.
[27] KAHNEMAN D, TVERSKY A. Prospect theory: an analysis of decision under risk [J]. Econometrica, 1979, 47(2): 363-391.
[28] TVERSKY A, KAHNEMAN D. Advances in prospect theory: cumulative representation of uncertainty [J]. Journal of Risk and Uncertainty, 1992, 5: 297-323.
[29] THALER R H. Mental accounting and consumer choice [J]. Marketing Science, 1985, 4(3): 199-214.
[30] THALER R H. Mental accounting matters [J]. Journal of Behavioral Decision Making, 1999, 12(3): 183-206.
[31] PENA A, ALEMANNI B, ZANOTTI G. On the role of behavioral finance in the pricing of financial derivatives: the case of the S&P 500[EB/OL]. (2010-08-26) [2022-11-30]. https://ssrn.com/abstract=1798607.
[32] NARDON M, PIANCA P. A behavioral approach to the pricing of European options[M] //Mathematical and Statistical Methods for Actuarial Sciences and Finance. Switzerland: Springer International Publishing, 2014: 219-230.
[33] NARDON M, PIANCA P. European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions [J]. Computational Management Science, 2019, 16: 249-274.
[34] 吴鑫育, 李心丹, 马超群. 基于随机波动率模型的上证50ETF期权定价研究[J]. 数理统计与管理, 2019, 38(1): 115-131.
WU X Y, LI X D, MA C Q. The pricing of SSE 50 ETF options based on stochastic volatility model [J]. Journal of Applied Statistics and Management, 2019, 38(1): 115-131.
[35] 孙有发, 吴碧云, 郭婷, 等. 非仿射随机波动率模型下的50ETF期权定价: 基于Fourier-Cosine方法[J]. 系统工程理论与实践, 2020, 40(4): 888-904.
SUN Y F, WU B Y, GUO T, et al. Fourier-cosine based option pricing for SSE 50ETF under non-affine stochastic volatility model [J]. Systems Engineering-Theory & Practice, 2020, 40(4): 888-904.
[36] SUN Y F. Efficient pricing and hedging under the double Heston stochastic volatility jump-diffusion model [J]. International Journal of Computer Mathematics, 2015, 92(12): 2551-2574.
[37] DAVIES G B, SATCHELL S E. The behavioural components of risk aversion [J]. Journal of Mathematical Psychology, 2007, 51(1): 1-13.
[38] PRELEC D. The probability weighting function [J]. Econometrica, 1998, 66(3): 497-527.
[39] GIL-PELAEZ J. Note on the inversion theorem [J]. Biometrika, 1951, 38(3-4): 481-482.
[40] WITKOVSKY V. Numerical inversion of a characteristic function: an alternative tool to form the probability distribution of output quantity in linear measurement models[J]. Acta IMEKO, 2016, 5(3): 32-44.
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