不完全市场中的期权定价:一种基于动态经验投影定价核的期权定价方法

周海林, 吴鑫育, 丁忠明

系统工程理论与实践 ›› 2014, Vol. 34 ›› Issue (s1) : 120-130.

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系统工程理论与实践 ›› 2014, Vol. 34 ›› Issue (s1) : 120-130. DOI: 10.12011/1000-6788(2014)s1-120
论文

不完全市场中的期权定价:一种基于动态经验投影定价核的期权定价方法

    周海林, 吴鑫育, 丁忠明
作者信息 +

Option pricing based on dynamic empirical projected pricing kernels in incomplete asset markets

    ZHOU Hai-lin, WU Xin-yu, DING Zhong-ming
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文章历史 +

摘要

经典的资产定价理论认为,不完全市场中存在多个 定价核,导致期权存在多个可能的理论价格,与现实中期权只有一个价格不符. 考虑到期权定价时投影定价核具有与原始定价核 完全相同的意义,并且投影定价核的信息隐含于相关历史信息中,动态的经验定价核隐含了投资者风险偏好的时变性,本文建立了一种基于动态经验投影定价核的期权定价方法. 通过对Rosenberg-Engle的经验定价核的动态性和标的资产未来收益率估计方法进行扩展,本文还给出了动态投影经验定价核的估计方法. 这种方法能适用于单只期权单只标的资产、多只期权单只标的资产和若干只期权单只标的资产等情形. 本文基于此方法为沪深交易所的部分具有欧式性质的权证进行了实证研究,结果表明:考虑了投资者时变偏好的动态经验投影定价核期权定价方法的定价效果远好于 Black-Scholes-Merton 和常弹性方差(CEV)期权定价模型.

Abstract

Classic asset pricing theory tells us that there are more than one theoretic price since there exit more than one equivalent martingale measure, which conflicts the phenomenon that there is only one price in real financial market. Since the projected pricing kernels are the same to original pricing kernels in options pricing, the real projected pricing kernels are indicated in history data, and the dynamics of pricing kernels imply the time-varying risk preference of investors, an option pricing method based on dynamic empirical projected pricing kernels is suggested in this paper. With the modification of dynamics estimation and the future return of underlying asset in Rosenberg and Engle, the estimation of dynamic empirical projected pricing kernels is presented, which is appropriate in the circumstance of one, few or many options listed on the same underlying asset. The empirical studies show that the dynamic empirical pricing kernels option pricing model which can catch the time-varying risk preference of investors performs quite better than Black-Scholes-Merton and constant elasticity of variance option pricing model.

关键词

期权定价 / 不完全市场 / 动态经验投影定价核估计方法 / 时变风险偏好

Key words

option pricing / incomplete market / dynamic empirical projected pricing kernels / the time-varying risk preference of investors

引用本文

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周海林 , 吴鑫育 , 丁忠明. 不完全市场中的期权定价:一种基于动态经验投影定价核的期权定价方法. 系统工程理论与实践, 2014, 34(s1): 120-130 https://doi.org/10.12011/1000-6788(2014)s1-120
ZHOU Hai-lin , WU Xin-yu , DING Zhong-ming. Option pricing based on dynamic empirical projected pricing kernels in incomplete asset markets. Systems Engineering - Theory & Practice, 2014, 34(s1): 120-130 https://doi.org/10.12011/1000-6788(2014)s1-120
中图分类号: F224   

参考文献

[1] Black F, Scholes M S. The pricing of options and corporate liabilities[J]. Journal of Political Economy,1973, 81: 637-654.
[2] Merton R. The theory of rational option pricing[J]. Bell Journal of Economics and Management Science, 1973, 4: 141-184.
[3] Ross S. Neoclassical finance[M]. Princeton: Princeton University Press, 2005.
[4] 吴鑫育, 周海林, 汪寿阳, 等. 权证定价: B-S vs. CEV[J]. 系统工程理论与实践, 2013, 33(5): 1126-1134.Wu Xinyu, Zhou Hailin, Wang Shouyang, et al. Warrant pricing: B-S vs. CEV[J]. Systems Engineering——Theory & Practice, 2013, 33(5): 1126-1134.
[5] Harrison J M, Kreps D M. Martingales and arbitrage in multiperiod securities markets[J]. Journal of Economic Theory, 1979, 20: 381-408.
[6] Harrison J M, Pliska S R. Martingales and stochastic integrals in the theory of continuous trading[J]. Stochastic Processes and their Applications, 1981, 11: 215-260.
[7] Delbaen F, Schachermayer W. A general version of the fundamental theorem of asset pricing[J]. Mathematische Annalen, 1994, 300: 463-520.
[8] Eberlein E, Jacod J. On the range of options prices[J]. Finance and Stochastics, 1997, 1: 131-140.
[9] Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1-2): 125-144.
[10] Hull J, White A. The pricing of options on asset with stochastic volatilities[J]. Journal of Finance, 1987, 42(2): 281-300.
[11] Kramkov D. Optional decomposition of super martingales and hedging contingent claims in incomplete security markets[J]. Probability Theory and Related Fields, 1996, 105: 459-479.
[12] Follmer H, Kramkov D. Optional decompositions under constraints[J]. Probability Theory and Related Fields, 1997, 109: 1-25.
[13] Hodges S, Neuberger. An optimal replication of contingent claims under transactions costs[J]. Review of Futures Markets, 1989, 8: 222-239.
[14] Delbaen F, Grandits P, Rheinlander T, et al. Exponential hedging and entropic penalties[J]. Mathematical Finance, 2002, 12: 99-123.
[15] Follmer H, Sondermann D. Hedging of non-redundant contingent claims[C]//Hildenbrand W, Mas-Colell A. Contributions to Mathematical Economics, 1986: 205-223.
[16] Bouleau N, Lamberton D. Residual risks and hedging strategies in markovian markets[J]. Stochastic Processes Application, 1989, 33: 131-150.
[17] Xia J M, Yan J A. Markowitz's portfolio optimization in an incomplete market[J]. Mathematical Finance, 2006, 16(1): 203-216.
[18] Miyahara Y. Canonical martingale measures of incomplete assets markets[C]//Watanabe S, et al. Probability Theory and Mathematical Statistics: Proceedings of the Seventh Japan-Russia Symposium, Tokyo, 1996: 343-352.
[19] Frittelli M. The minimal entropy martingale measure and the valuation problem in incomplete markets[J]. Mathematical Finance, 2000, 10(1): 39-52.
[20] Breeden D. An intertemporal asset pricing model with stochastic consumption and investment opportunities[J]. Journal of Financial Economics, 1979, 7: 265-296.
[21] Abel A. Asset prices under habit formation and catching up with the Joneses[J]. American Economic Review, 1990, 80: 38-42.
[22] Constantinides G M. Habit formation: A resolution of the equity premium puzzle[J]. Journal of Political Economy, 1990, 98: 519-543.
[23] Campbell J, Cochrane J. By force of habit: A consumption based explanation of aggregate stock market behavior[J]. Journal of Political Economy, 1999, 107: 205-251.
[24] Eichenbaum M S, Hansen L P, Singleton K J. A time series analysis of representative agent models of consumption and leisure choice under uncertainty[J]. Quarterly Journal of Economics, 1988, 103: 51-78.
[25] Startz R. The stochastic behavior of durable and non-durable consumption[J]. Review of Economics and Statistics, 1989, 71: 356-363.
[26] Bansal R, Viswanathan S. No arbitrage and arbitrage pricing: A new approach[J]. Journal of Finance, 1993, 48: 1231-1262.
[27] Hansen L P, Singleton K J. Generalized instrumental variables estimation of nonlinear rational expectations models[J]. Econometrica, 1982, 50: 1269-1286.
[28] Ermini L. Some new evidence on the timing of consumption decisions and their generating process[J]. Review of Economics and Statistics, 1989, 71: 643-650.
[29] Wilcox D. The construction of U.S. consumption data: Some facts and their implications for empirical work[J]. American Economic Review, 1992, 82: 922-941.
[30] Slesnick D T. Are our data relevant to the theory? The case of aggregate consumption[J]. Journal of the American Statistical Association, 1998, 16: 52-61.
[31] Ross S A. Neoclassical finance[M]. Princeton: Princeton University Press, 2005.
[32] Breeden D T, Litzenberger R H. Prices of state-contingent claims implicit in option prices[J]. Journal of Business, 1978, 51(4): 621-651.
[33] Melick W R, Thomas C P. Using options prices to infer PDF'S for asset prices: an application to oil prices during the gulf crisis[J]. Journal of Financial and Quantitative Analysis, 1997, 32(1): 91-115.
[34] Ait-Sahalia Y, Lo A W. Nonparametric estimation of state-price density implicit in financial asset pricing[J]. Journal of Finance, 1998, 53: 499-547.
[35] Figlewski S. Estimating the implied risk neutral density for the U.S. market portfolio[C]//Bollerslev T, Russell J R, Watson M. Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle. Oxford, UK: Oxford University Press, 2008.
[36] Hardle W, Hlavka Z. Dynamics of state price densities[J]. Journal of Econometrics, 2009, 150(1): 1-15.
[37] Rosenberg J, Engle R. Empirical pricing kernels[J]. Journal of Financial Economics, 2002, 64: 341-372.
[38] Cochrane J. Asset pricing[M]. Princeton: Princeton University Press, 2001.
[39] Glosten L R, Jagannathan R, Runkle D E. On the relation between the expected value and the volatility of the nominal excess return on stocks[J]. The Journal of Finance, 1993, 48(5): 1779-1801.
[40] Botev Z I, Grotowski J F, Kroese D P. Kernel density estimation via diffusion[J]. Annals of Statistics, 2010, 38(5): 2916-2957.
[41] Galai D, Schneller M. Pricing of warrants and the value of the firm[J]. Journal of Finance, 1978, 33(5): 1333-1342.

基金

国家自然科学基金(71101001)
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