How Does Duration Between Trades of Underlying Securities Affect Option Prices
We propose a model for stock price dynamics that explicitly incorporates random waiting times between trades, also known as duration, and show how option prices can be calculated using this model. We use ultra-high-frequency data for blue-chip companies to motivate a particular choice of waiting-time distribution and then calibrate risk-neutral parameters from options data. We also show that the convexity commonly observed in implied volatilities may be explained by the presence of duration between trades. Furthermore, we find that, ceteris paribus, implied volatility decreases in the presence of longer durations, a result consistent with the findings of Engle (2000) and Dufour and Engle (2000) which demonstrates the relationship between levels of activity and volatility for stock prices.
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- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2000.
"Fractional calculus and continuous-time finance,"
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- Robert F. Engle, 1996.
"The Econometrics of Ultra-High Frequency Data,"
NBER Working Papers
5816, National Bureau of Economic Research, Inc.
- Easley, David & O'Hara, Maureen, 1992. " Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
- Peter Carr & Liuren Wu, 2002.
"The Finite Moment Log Stable Process and Option Pricing,"
- Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004.
"Fractional calculus and continuous-time finance II: the waiting- time distribution,"
- Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
- Peter Carr & Liuren Wu, 2002.
"Time-Changed Levy Processes and Option Pricing,"
- Alfonso Dufour & Robert F. Engle, 2000.
"Time and the Price Impact of a Trade,"
Journal of Finance,
American Finance Association, vol. 55(6), pages 2467-2498, December.
- Dufour, Alfonso & Engle, Robert F, 1999. "Time and the Price Impact of a Trade," University of California at San Diego, Economics Working Paper Series qt62c0h04j, Department of Economics, UC San Diego.
- Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Yacine Ait-Sahalia & Per A. Mykland, 2002.
"The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions,"
NBER Technical Working Papers
0276, National Bureau of Economic Research, Inc.
- Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March.
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