The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well

Management Science - Tập 55 Số 12 - Trang 1914-1932 - 2009
Peter Christoffersen1, Steven L. Heston2, Kris Jacobs3
1Desautels Faculty of Management, McGill University, Montreal, Quebec H3A 1G5, Canada; Copenhagen Business School, 2000 Frederiksberg, Denmark; and CREATES, University of Aarhus, 8000 Aarhus, Denmark
2Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742
3Desautels Faculty of Management, McGill University, Montreal, Quebec H3A 1G5, Canada; and C. T. Bauer College of Business, University of Houston, Houston, Texas 77204

Tóm tắt

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. Although 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 stochastic volatility 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.

Từ khóa


Tài liệu tham khảo

10.1111/1540-6261.00454

10.1111/1540-6261.00460

10.1111/j.1540-6261.1997.tb02749.x

10.1093/rfs/9.1.69

10.1016/S0304-4076(99)00021-4

Black F., 1976, Proc. 1976 Meetings Bus. Econom. Statistics Section, 177

10.1086/260062

10.1111/j.1540-6261.2007.01241.x

10.1016/S0304-405X(03)00171-5

10.1016/j.jfineco.2006.03.010

10.1016/S0304-405X(00)00046-5

10.1016/S0304-4076(03)00108-8

10.1016/0304-405X(82)90018-6

10.1016/j.jfineco.2003.02.001

Christoffersen P., Jacobs K., Mimouni K. Models for S&P 500 dynamics: Evidence from realized volatility, daily returns, and option prices. (2008a) . Working paper, McGill University, Montreal, QC

10.1016/j.jfineco.2007.12.003

10.1111/0022-1082.00278

10.1016/S0304-405X(02)00067-3

10.1093/rfs/hhg010

10.1093/rfs/12.1.197

10.1111/j.1467-9965.1996.tb00123.x

10.1111/1468-0262.00164

10.1111/0022-1082.00083

10.1111/j.1540-6261.2004.00666.x

10.1111/1540-6261.00566

10.1002/fut.3990120202

Harvey C. R., 1992, J. Financial Econom., 30, 33

10.1093/rfs/6.2.327

10.1093/rfs/13.3.585

10.1111/j.1540-6261.2004.00667.x

10.1111/j.1540-6261.1987.tb02568.x

Hull J., 1988, Adv. Futures Options Res., 3, 29

10.1111/j.1540-6321.2004.00632.x

10.1093/rfs/hhn110

10.1016/S0304-4076(03)00107-6

Lewis A., 2000, Option Valuation under Stochastic Volatility

10.3905/jfi.1991.692347

10.1016/0304-4076(90)90100-8

10.1016/S0378-4266(98)00047-8

10.1016/S0304-405X(01)00088-5

10.1111/j.1540-6261.1994.tb02454.x

Santa-Clara P., 2009, Rev. Econom. Statist.

10.2307/2330793

10.1023/A:1009642705121

10.2307/2331190

Trolle A., 2009, Rev. Financial Stud.

10.1016/0304-405X(87)90009-2

Thông tin
Thông tin xuất bản

Management Science

Tập 55 Số 12

1914-1932

Thông tin tác giả