Extremes of stochastic volatility models

Annals of Applied Probability

Volumn 8, Issue 3, 1998, Pages 664-675

  Breidt, F Jay ^a   Davis, Richard A ^b  

^a Department of Statistics Center for Statistics and Applications in Forensic Evidence Iowa State University 2438 Osborn Dr Ames   (United States)

^b Department of Environmental and Radiological Health Sciences   (United States)

Author keywords

Double exponential; Normal comparison lemma; Point process convergence; Stochastic variance; Tail behavior

Indexed keywords

EID: 0032147537     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903446     Document Type: Article

References (22)

1. ABRAMOWITZ, M. and STEGUN, I. A. (1965). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Washington, D.C.
2. ADLER, R. J. (1978). Weak convergence results for extremal processes generated by dependent random variables. Ann. Probab. 6 660-667.
3. BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31 307-327.
4. BOLLERSLEV, T., CHOU, R. Y. and KRONER, K. F. (1992). ARCH modeling in finance. J. Econometrics 52 5-59.
5. BREIDT, F. J., CRATO, N. and DE LIMA, P. (1995). On the detection and estimation of long memory in stochastic volatility. J. Econometrics. To appear.
6. BROCKWELL, P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York.
7. CLARK, P. K. (1973). A subordinated stochastic process model with finite variances for speculative prices. Econometrica 41 135-156.
8. DAVIS, R. A. and RESNICK, S. I. (1991). Extremes of moving averages of random variables with finite endpoint. Ann. Probab. 19 312-328.
9. DE HAAN, L., RESNICK, S. I., ROOTZÉN, H. and DE VRIES, C. G. (1989). Extremal behaviour of solutions to a stochastic difference equation with applications to ARCH processes. Stochastic Process. Appl. 32 213-224.
10. ENGLE, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 987-1007.
11. FEIGIN, P. D. and YASHCHIN, E. (1983). On a strong Tauberian result. Z. Wahrsch. Verw. Gebiete 65 35-48.
12. GEWEKE, J. (1994). Comment on "Bayesian analysis of stochastic volatility models" by E. Jacquier, N. G. Polson and P. E. Rossi. J. Bus. Econom. Statist. 12 397-399.
13. HULL, J. and WHITE, A. (1987). The pricing of options on assets with stochastic volatilities. J. Finance 42 281-300.
14. JACQUIER, E., POLSON, N. G. and ROSSI, P. E. (1994). Bayesian analysis of stochastic volatility models (with discussion). J. Bus. Econom. Statist. 12 371-417.
15. LEADBETTER, M. R., LINDGREN, G. and ROOTZÉN, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York.
16. MANDELBROT, B. (1963). The variation of certain speculative prices. J. Business 36 394-419.
17. MELINO, A. and TURNBULL, S. M. (1990). Pricing foreign currency options with stochastic volatility. J. Econometrics 45 239-265.
18. RESNICK, S. (1975). Weak convergence to extremal processes. Ann. Probab. 3 951-960.
19. RESNICK, S. (1987). Extreme Values, Regular Variation and Point Processes. Springer, New York.
20. TAUCHEN, G. and PITTS, M. (1983). The price variability-volume relationship on speculative markets. Econometrica 51 485-505.
21. TAYLOR, S. (1986). Modelling Financial Time Series. Wiley, New York.
22. 2 and t distributions. Biometrika 34 170-178.