| By: |
Peter Christoffersen (McGill University and CREATES);
Steven Heston (R.H. Smith School of Business, University of Maryland);
Kris Jacobs (McGill University and Tilburg University) |
| Abstract: |
State-of-the-art stochastic volatility models generate a "volatility smirk"
that explains why out-of-the-money index puts have high prices relative to the
Black-Scholes benchmark. These models also adequately explain how the
volatility smirk moves up and down in response to changes in risk. However,
the data indicate that the slope and the level of the smirk fluctuate largely
independently. While single-factor stochastic volatility models can capture
the slope of the smirk, they cannot explain such largely independent
fluctuations in its level and slope over time. We propose to model these
movements using a two-factor stochastic volatility model. Because the factors
have distinct correlations with market returns, and because the weights of the
factors vary over time, the model generates stochastic correlation between
volatility and stock returns. Besides providing more flexible modeling of the
time variation in the smirk, the model also provides more flexible modeling of
the volatility term structure. Our empirical results indicate that the model
improves on the benchmark Heston model by 24% in-sample and 23% out-of-sample.
The better fit results from improvements in the modeling of the term structure
dimension as well as the moneyness dimension. |
| Keywords: |
Stochastic correlation, stochastic volatility, equity index options, multifactor model, persistence, affine, out-of-sample |
| JEL: |
G12 |
| Date: |
2009–06–17 |
| URL: |
http://d.repec.org/n?u=RePEc:aah:create:2009-34&r=fmk |