Maximum likelihood estimation of stochastic volatility models

Journal of Financial Economics

Volumn 83, Issue 2, 2007, Pages 413-452

  Aït Sahalia, Yacine ^a   Kimmel, Robert ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

CEV model; Closed form likelihood expansions; GARCH model; Heston model; Volatility proxies

Indexed keywords

EID: 33846486684     PISSN: 0304405X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfineco.2005.10.006     Document Type: Article

References (51)

1. Ai{dotless}̈t-Sahalia Y. Transition densities for interest rate and other nonlinear diffusions. Journal of Finance 54 (1999) 1361-1395
2. Ai{dotless}̈t-Sahalia, Y., 2001. Closed-form likelihood expansions for multivariate diffusions. Working Paper, Princeton University.
3. Ai{dotless}̈t-Sahalia Y. Maximum-likelihood estimation of discretely-sampled diffusions: a closed-form approximation approach. Econometrica 70 (2002) 223-262
4. Ai{dotless}̈t-Sahalia Y., and Lo A. Nonparametric estimation of state-price-densities implicit in financial asset prices. Journal of Finance 53 (1998) 499-547
5. Ai{dotless}̈t-Sahalia Y., and Mykland P.A. The effects of random and discrete sampling when estimating continuous-time diffusions. Econometrica 71 (2003) 483-549
6. Andersen T.G., and Lund J. Estimating continuous time stochastic volatility models of the short term interest rate. Journal of Econometrics 77 (1997) 343-378
7. Bakshi G., Cao C., and Chen Z. Empirical performance of alternative option pricing models. Journal of Finance 52 (1997) 2003-2049
8. Bakshi G., Cao C., and Chen Z. Do call prices and the underlying stock always move in the same direction?. Review of Financial Studies 13 (2000) 549-584
9. Bates D.S. Post-'87 crash fears in the S&P 500 futures option market. Journal of Econometrics 94 (2000) 181-238
10. Bates, D.S., 2002. Maximum likelihood estimation of latent affine processes. Working Paper, University of Iowa.
11. Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the American Statistical Association, pp. 171-181.
12. Black F., and Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy 81 (1973) 637-654
13. Bollerslev T., and Zhou H. Estimating stochastic volatility diffusions using conditional moments of integrated volatility. Journal of Econometrics 109 (2002) 33-65
14. Carr P., and Madan D.B. Option valuation using the fast Fourier transform. Journal of Computational Finance 2 (1998) 61-73
15. Chacko G., and Viceira L.M. Spectral GMM estimation of continuous-time processes. Journal of Econometrics 116 (2003) 259-292
16. Derman E., and Kani I. Riding on the smile. RISK 7 (1994) 32-39
17. Dumas B., Fleming J., and Whaley R.E. Implied volatility functions: empirical tests. Journal of Finance 53 (1998) 2059-2106
18. Dupire B. Pricing with a smile. RISK 7 (1994) 18-20
19. Eraker B. MCMC analysis of diffusion models with application to finance. Journal of Business and Economic Statistics 19 (2001) 177-191
20. Feller W. Two singular diffusion problems. Annals of Mathematics 54 (1951) 173-182
21. Gallant A.R., and Tauchen G. Which moments to match?. Econometric Theory 12 (1996) 657-681
22. Harrison M., and Kreps D. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20 (1979) 381-408
23. Harrison M., and Pliska S. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and Their Applications 11 (1981) 215-260
24. Heston S. A closed-form solution for options with stochastic volatility with applications to bonds and currency options. Review of Financial Studies 6 (1993) 327-343
25. Heston, S., Loewenstein, M., Willard, G.A., 2004. Options and bubbles. Technical Report, University of Maryland.
26. Hull J., and White A. The pricing of options on assets with stochastic volatilities. Journal of Finance 42 (1987) 281-300
27. Hurn, A.S., Jeisman, J., Lindsay, K., 2005. Seeing the wood for the trees: a critical evaluation of methods to estimate the parameters of stochastic differential equations. Working Paper, School of Economics and Finance, Queensland University of Technology.
28. Jacquier E., Polson N.G., and Rossi P.E. Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 14 (1994) 429-434
29. Jensen B., and Poulsen R. Transition densities of diffusion processes: numerical comparison of approximation techniques. Journal of Derivatives 9 (2002) 1-15
30. Jiang G.J., and Knight J. Estimation of continuous-time processes via empirical characteristic function. Journal of Business and Economic Statistics 20 (2002) 198-212
31. Jones C.S. The dynamics of stochastic volatility: evidence from underlying and options markets. Journal of Econometrics 116 (2003) 181-224
32. Kim S., Shephard N., and Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65 (1999) 361-393
33. Lamoureux, C.G., Paseka, A., 2004. Information in option prices and the underlying asset dynamics. Working Paper, University of Arizona.
34. Ledoit, O., Santa-Clara, P., Yan, S., 2002. Relative pricing of options with stochastic volatility. Working Paper, University of California at Los Angeles.
35. Lewis A.L. Option Valuation under Stochastic Volatility (2000), Finance Press, Newport Beach, CA
36. Li M., Pearson N.D., and Poteshman A.M. Conditional estimation of diffusion processes. Journal of Financial Economics 74 (2004) 31-66
37. Meddahi, N., 2001. An eigenfunction approach for volatility modeling. Technical Report, Université de Montréal.
38. Merton R.C. The theory of rational option pricing. Bell Journal of Economics and Management Science 4 (1973) 141-183
39. Nelson D.B. ARCH models as diffusion approximations. Journal of Econometrics 45 (1990) 7-38
40. Pan J. The jump-risk premia implicit in options: evidence from an integrated time-series study. Journal of Financial Economics 63 (2002) 3-50
41. Romano M., and Touzi N. Contingent claims and market completeness in a stochastic volatility model. Mathematical Finance 7 (1997) 399-412
42. Rubinstein M. As simple as one, two, three. RISK 8 (1995) 44-47
43. Ruiz E. Quasi-maximum likelihood estimation of stochastic volatility models. Journal of Econometrics 63 (1994) 289-306
44. Singleton K. Estimation of affine asset pricing models using the empirical characteristic function. Journal of Econometrics 102 (2001) 111-141
45. Stein E.M., and Stein J.C. Stock price distributions with stochastic volatility: an analytic approach. Review of Financial Studies 4 (1991) 727-752
46. Stein J.C. Overreactions in the options market. Journal of Finance 44 (1989) 1011-1023
47. Stramer, O., Yan, J., 2005. On simulated likelihood of discretely observed diffusion processes and comparison to closed-form approximation. Working Paper, University of Iowa.
48. Takamizawa H., and Shoji I. Modeling the term structure of interest rates with general short-rate models. Finance and Stochastics 7 (2003) 323-335
49. Taylor S.J. Modeling stochastic volatility: a review and comparative study. Mathematical Finance 4 (1994) 183-204
50. Whaley R.E. The investor fear gauge. The Journal of Portfolio Management 26 (2000) 12-17
51. Yu, J., 2003. Closed-form likelihood estimation of jump-diffusions with an application to the realignment risk premium of the Chinese yuan. Ph.D. Thesis, Princeton University.