Variance Swap Premium under Stochastic Volatility and Self-Exciting Jumps

We introduce a stochastic volatility model with self-exciting jump intensity to capture the change in pricing dynamic triggered by big negative stock returns. The stochastic variance and jump intensity, and their risk premium are estimated jointly from daily stock returns and option data over 2007-2010. The model is calibrated to cumulants implied from option prices instead of option prices directly. We find evidence that the time varying jump intensity plays a very important role in the sub-prime crisis and explained most of the risk premium, while in other calmer periods, stochastic variance accounts for most of the risk premium.

[1]  R. Laeven.  Modeling financial contagion , 2010 .

[2]  Bjørn Eraker.  MCMC Analysis of Diffusion Models With Application to Finance , 2001 .

[3]  K. Demeterfi,et al.  More than You ever Wanted to Know about Volatility Swaps , 1999 .

[4]  L. Bergomi.  Smile Dynamics III , 2008 .

[5]  Jun Yu,et al.  Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility , 2012 .

[6]  Viktor Todorov,et al.  Variance Risk-Premium Dynamics: The Role of Jumps , 2010 .

[7]  P. Carr,et al.  Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions , 2011, Journal of Financial and Quantitative Analysis.

[8]  P. Carr,et al.  Option Pricing, Interest Rates and Risk Management: Towards a Theory of Volatility Trading , 2001 .

[9]  J. Duan.  THE GARCH OPTION PRICING MODEL , 1995 .

[10]  Yacine Ait-Sahalia,et al.  Modeling Financial Contagion Using Mutually Exciting Jump Processes , 2010 .

[11]  Peter Carr,et al.  Variance Risk Premiums , 2009 .

[12]  Rama Cont,et al.  Dynamics of implied volatility surfaces , 2002 .

[13]  Bjørn Eraker.  Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices , 2004 .

[14]  L. Bergomi.  Smile Dynamics II , 2005 .

[15]  Jun Pan.  The Jump-Risk Premia Implicit in Options : Evidence from an Integrated Time-Series Study , 2001 .

[16]  Thomas H. McCurdy,et al.  News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns , 2003 .

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

[18]  M. Pitt,et al.  Particle filters for continuous likelihood evaluation and maximisation , 2011 .

[19]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[20]  Gurdip Bakshi,et al.  A Theory of Volatility Spreads , 2006, Manag. Sci..

[21]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

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

[23]  A. Hawkes.  Spectra of some self-exciting and mutually exciting point processes , 1971 .

[24]  G. Peters,et al.  Monte Carlo Approximations for General State-Space Models , 1998 .

[25]  Jim Gatheral,et al.  A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives , 2004 .