Weighted average price in the Heston stochastic volatility model

被引：2
作者：
Papi M. [1 ]
Pontecorvi L. [1 ]
Donatucci C. [2 ]
机构：
[1] Facoltà Dipartimentale di Ingegneria, Università Campus Biomedico, Rome
[2] Department of Mathematics, Università Rome TRE, Rome
来源：
Decisions in Economics and Finance | 2017年 / 40卷 / 1-2期
关键词：
Calibration; Heston model; Option price; Stochastic volatility;
D O I：
10.1007/s10203-017-0197-5
中图分类号：
学科分类号：
摘要：
We propose a weighted average formulation for the Heston stochastic volatility option price to avoid the estimation of the initial volatility. This approach has been developed in the literature for the estimation of the distribution of stock price changes (returns), showing an excellent agreement with real market data. We extend this method to the calibration of option prices considering a large class of probability distributions assumed for the initial volatility parameter. The estimation error is shown to be less than the case of the simple pricing formula. Our results are also validated with a numerical comparison on observed call prices, between the proposed calibration method and the classical approach. © 2017, Springer-Verlag Italia S.r.l.
引用
收藏
页码：351 / 373
页数：22
相关论文
共 33 条
  • [1] Bakshi G., Cao C., Chen Z., Empirical performance of alternative option pricing models, J. Financ., 52, pp. 2003-2049, (1997)
  • [2] Broadie M., Kaya O., Exact simulation of stochastic volatility and other affine jump diffusion processes, Oper. Res., 54, 2, pp. 217-231, (2006)
  • [3] Carr P., Madan D.B., Option valuation using the fast Fourier transform, J. Comput. Financ., 2, 4, (1999)
  • [4] The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology. Research Paper Series 39, Quantitative Finance Research Centre, University of Technology, Sydney
  • [5] Cont R., Recovering volatility from option prices by evolutionary optimization, J. Comput. Financ., 8, 4, pp. 43-76, (2005)
  • [6] Costantini C., Papi M., D'Ippoliti F., Singular risk-neutral valuation equations, Financ. Stoch., 16, 2, pp. 249-274, (2012)
  • [7] Crandall M.G., Ishii H., Lions P.L., User’s guide to viscosity solutions of second order partial differential equations, Am. Math. Soc. Bull. New Ser., 27, 1, (1992)
  • [8] Dragulescu A.A., Yakovenko V.M., Probability distribution of returns in the Heston model with stochastic volatility, Quant. Financ., 2, pp. 443-453, (2002)
  • [9] Duffie D., Pan J., Singleton K., Transform analysis and asset pricing for affine jump-diffusions, Econometrica, 68, pp. 1343-1376, (2000)
  • [10] Ekstrom E., Tysk J., The Black–Scholes equation in stochastic volatility models, J. Math. Anal. Appl., 368, pp. 498-507, (2010)
1234