Abstract
This paper presents a framework for using high frequency derivative prices to estimate the drift of generalized security price processes. This work may be seen more generally as a quasi-likelihood approach to estimating continuous-time parameters of derivative pricing models using discrete option data. We develop a generalized derivative-based estimator for the drift where the underlying security price process follows any arbitrary state-time separable diffusion process (including arithmetic and geometric Brownian motion as special cases). The framework provides a method to measure premia in derivative prices, test for risk-neutral pricing and leads to a new empirical approach to pricing derivative contingent claims. A sufficient condition for the asymptotic consistency of the generalized estimator is also obtained. A study based on generating the S&P500 index and calls shows that the estimator can correctly estimate the drift parameter.
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Pandher, G.S. Drift Estimation of Generalized Security Price Processes from High Frequency Derivative Prices. Review of Derivatives Research 4, 263–284 (2000). https://doi.org/10.1023/A:1011383413977
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DOI: https://doi.org/10.1023/A:1011383413977