Pricing Derivatives Securities with Prior Information on Long- Memory Volatility
This paper investigates the existence of long memory in the volatility of the Mexican stock market. We use a stochastic volatility (SV) model to derive statistical test for changes in volatility. In this case, estimation is carried out through the Kalman filter (KF) and the improved quasi-maximum likelihood (IQML). We also test for both persistence and long memory by using a long-memory stochastic volatility (LMSV) model, constructed by including an autoregressive fractionally integrated moving average (ARFIMA) process in a stochastic volatility scheme. Under this framework, we work up maximum likelihood spectral estimators and bootstraped confidence intervals. In the light of the empirical findings, we develop a Bayesian model for pricing derivative securities with prior information on long-memory volatility.
Volume (Year): XII (2003)
Issue (Month): 1 (January-June)
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- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
- Clewlow, Les & Hodges, Stewart, 1997. "Optimal delta-hedging under transactions costs," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1353-1376, June.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 69-87, January.
- Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
- Bollerslev, Tim & Ole Mikkelsen, Hans, 1996.
"Modeling and pricing long memory in stock market volatility,"
Journal of Econometrics,
Elsevier, vol. 73(1), pages 151-184, July.
- Tom Doan, . "RATS program to replicate Bollerslev-Mikkelson(1996) FIEGARCH models," Statistical Software Components RTZ00173, Boston College Department of Economics.
- Venegas-Martinez, Francisco, 2001. "Temporary stabilization: A stochastic analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 25(9), pages 1429-1449, September.
- Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
- Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996.
"Fractionally integrated generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 74(1), pages 3-30, September.
- Tom Doan, . "RATS programs to replicate Baillie, Bollerslev, Mikkelson FIGARCH results," Statistical Software Components RTZ00009, Boston College Department of Economics.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
- M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
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