Options pricing with time changed Lévy processes under imprecise information

This study evaluates a time changed Lévy model for European call options under a fuzzy environment. The proposed model is characterized by high frequency jumps, stochastic volatility, and stochastic volatility with the jumps, existing in the returns process of financial assets. Moreover, to consider imperfect and unpredictable accounting information, this study uses fuzzy logic to account for the impreciseness of the accounting information, which can not be described in extant models, and provides reasonable reference instruments for future research on option pricing under a jump diffusion model with imprecise market information. Our empirical results also show that the fuzzy time changed Lévy model has better fitting performance when compared with the time changed Lévy and the Black and Scholes model when using S&P 500 index option data.

[1]  Huibert Kwakernaak,et al.  Fuzzy random variables - I. definitions and theorems , 1978, Inf. Sci..

[2]  M. Carmen Garrido,et al.  Exact and heuristic procedures for solving the fuzzy portfolio selection problem , 2012, Fuzzy Optim. Decis. Mak..

[3]  Masami Yasuda,et al.  A Discrete-Time American Put Option Model with Fuzziness of Stock Prices , 2005, Fuzzy Optim. Decis. Mak..

[4]  P. Carr,et al.  The Finite Moment Log Stable Process and Option Pricing , 2003 .

[5]  Steven Kou,et al.  A Jump Diffusion Model for Option Pricing , 2001, Manag. Sci..

[6]  P. Carr,et al.  Time-Changed Levy Processes and Option Pricing ⁄ , 2002 .

[7]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[8]  R. Cont.  Empirical properties of asset returns: stylized facts and statistical issues , 2001 .

[9]  Wei-jun Xu,et al.  A jump-diffusion model for option pricing under fuzzy environments , 2009 .

[10]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[11]  Robert Fullér,et al.  On Weighted Possibilistic Mean and Variance of Fuzzy Numbers , 2002, Fuzzy Sets Syst..

[12]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[13]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[14]  Marc Yor,et al.  Time Changes for Lévy Processes , 2001 .

[15]  Masami Yasuda,et al.  A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty , 2006, Fuzzy Sets Syst..

[16]  R. Fullér.  On product-sum of triangular fuzzy numbers , 1991 .

[17]  Liuren Wu,et al.  Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes , 2003 .

[18]  Hongyi Li,et al.  A study of Greek letters of currency option under uncertainty environments , 2010, Math. Comput. Model..

[19]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[20]  C. R. Bector,et al.  Application of possibility theory to investment decisions , 2008, Fuzzy Optim. Decis. Mak..

[21]  Gurdip Bakshi,et al.  Equilibrium Valuation of Foreign Exchange Claims , 1997 .

[22]  A. Thavaneswaran,et al.  Fuzzy coefficient volatility (FCV) models with applications , 2007, Math. Comput. Model..

[23]  P. Carr,et al.  Option valuation using the fast Fourier transform , 1999 .

[24]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[25]  M. Rubinstein..  Implied Binomial Trees , 1994 .

[26]  M. Yor,et al.  Stochastic Volatility for Lévy Processes , 2003 .

[27]  Yuhan Liu,et al.  Uncertain stock model with periodic dividends , 2013, Fuzzy Optim. Decis. Mak..

[28]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[29]  M. Yor,et al.  The Fine Structure of Asset Retums : An Empirical Investigation ' , 2006 .

[30]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .