A semiparametric factor model for implied volatility surface dynamics

We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.

[1]  Bent E. Sørensen,et al.  GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study , 1996 .

[2]  David S. Bates,et al.  Maximum Likelihood Estimation of Latent Affine Processes , 2003 .

[3]  E. Ghysels,et al.  A Semiparametric Factor Model of Interest Rates and Tests of the Affine Term Structure , 1998, Review of Economics and Statistics.

[4]  S. Pastorello,et al.  Iterative and Recursive Estimation in Structural Non-Adaptive Models * , 2003 .

[5]  Wolfgang K. Härdle,et al.  The Dynamics of Implied Volatilities: A Common Principal Components Approach , 2003 .

[6]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[7]  N. Touzi,et al.  Option Hedging And Implied Volatilities In A Stochastic Volatility Model , 1996 .

[8]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

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

[10]  N. Shephard,et al.  Multivariate stochastic variance models , 1994 .

[11]  Jianwei Zhu,et al.  Stochastic Volatility With an Ornstein-Uhlenbeck Process: An Extension , 1998 .

[12]  R. Hafner,et al.  The Dynamics of DAX Implied Volatilities , 2000 .

[13]  Nicholas G. Polson,et al.  The Impact of Jumps in Volatility and Returns , 2000 .

[14]  Les Clewlow,et al.  The Dynamics of the S&P 500 Implied Volatility Surface , 2000 .

[15]  M. Rubinstein. Nonparametric tests of alternative option pricing models using all reported trades and quotes on the , 1985 .

[16]  Oliver Linton,et al.  The Common and Specific Components of Dynamic Volatility , 2003 .

[17]  E. Ghysels,et al.  A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation , 2000 .

[18]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[19]  O. Barndorff-Nielsen Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling , 1997 .

[20]  P. Phillips,et al.  Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach , 2001 .

[21]  L. Clewlow,et al.  The Dynamics of Implied Volatility Surfaces , 1998 .

[22]  Mark Britten-Jones,et al.  Option Prices, Implied Price Processes, and Stochastic Volatility , 2000 .

[23]  Bent E. Sørensen,et al.  Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study , 1999 .

[24]  C. Alexander,et al.  Model-free hedge ratios and scale-invariant models , 2007 .

[25]  L. Harris,et al.  A maximum likelihood approach for non-Gaussian stochastic volatility models , 1998 .

[26]  Eric Renault,et al.  A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models , 1998 .

[27]  S. Turnbull,et al.  Pricing foreign currency options with stochastic volatility , 1990 .

[28]  Gregory Connor,et al.  Semiparametric Estimation of a Characteristic-Based Factor Model of Stock Returns , 2000 .

[29]  Wolfgang Härdle,et al.  On extracting information implied in options , 2007, Comput. Stat..

[30]  M. Avellaneda,et al.  An E-Arch Model for the Term Structure of Implied Volatility of FX Options , 1997 .

[31]  Szymon Borak,et al.  DSFM fitting of implied volatility surfaces , 2005, 5th International Conference on Intelligent Systems Design and Applications (ISDA'05).

[32]  Yacine Ait-Sahalia,et al.  Nonparametric Option Pricing Under Shape Restrictions , 2002 .

[33]  Yu Zhu,et al.  Scenario Simulation: Theory and methodology , 1996, Finance Stochastics.

[34]  S. Heston A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[35]  Luis M. Viceira,et al.  Spectral GMM Estimation of Continuous-Time Processes , 1999 .

[36]  Yacine Aït-Sahalia,et al.  Do option markets correctly price the probabilities of movement of the underlying asset , 2001 .

[37]  Peter E. Rossi,et al.  Bayesian Analysis of Stochastic Volatility Models , 1994 .

[38]  David S. Bates Post-'87 crash fears in the S&P 500 futures option market , 2000 .

[39]  D. Duffie,et al.  Transform Analysis and Asset Pricing for Affine Jump-Diffusions , 1999 .

[40]  David S. Bates Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[41]  D. Duffie,et al.  Simulated Moments Estimation of Markov Models of Asset Prices , 1990 .

[42]  M. Broadie,et al.  Série Scientifique Scientific Series Nonparametric Estimation of American Options Exercise Boundaries and Call Prices Nonparametric Estimation of American Options Exercise Boundaries and Call Prices * , 2022 .

[43]  R. Tompkins Implied volatility surfaces: uncovering regularities for options on financial futures , 2001 .

[44]  E. Mammen,et al.  Yield Curve Estimation by Kernel Smoothing , 2004 .

[45]  B. Dumas,et al.  Implied volatility functions: empirical tests , 1996, IEEE Conference on Computational Intelligence for Financial Engineering & Economics.

[46]  Zongwu Cai,et al.  Adaptive varying‐coefficient linear models , 2000 .

[47]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[48]  Jianqing Fan,et al.  Functional-Coefficient Regression Models for Nonlinear Time Series , 2000 .

[49]  A. Gallant,et al.  Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions , 1998 .

[50]  Gerhard Tutz,et al.  The survival of newly founded firms: a case-study into varying-coefficient models , 2005 .

[51]  Jun Pan The jump-risk premia implicit in options: evidence from an integrated time-series study $ , 2002 .

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

[53]  C. J. Stone,et al.  The Dimensionality Reduction Principle for Generalized Additive Models , 1986 .

[54]  Enno Mammen,et al.  The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions , 1999 .

[55]  H. Akaike Statistical predictor identification , 1970 .