Performance of Black-Scholes model with TSRV estimates
Abstract
Purpose
The purpose of this paper is to test the pricing performance of Black-Scholes (B-S) model, with the volatility of the underlying estimated with the two-scale realised volatility measure (TSRV) proposed by Zhang et al. (2005).
Design/methodology/approach
The ex post TSRV is used as the volatility estimator to ensure efficient volatility estimation, without forecasting error. The B-S option prices, thus obtained, are compared with the market prices using four performance measures, for the options on NIFTY index, and three of its constituent stocks. The tick-by-tick data are used in this study for price comparisons.
Findings
The B-S model shows significantly negative pricing bias for all the options, which is dependent on the moneyness of the option and the volatility of the underlying.
Research limitations/implications
The negative pricing bias of B-S model, despite the use of the more efficient TSRV estimate, and post facto volatility values, confirms its inadequacy. It also points towards the possible existence of volatility risk premium in the Indian options market.
Originality/value
The use of tick-by-tick data obviates the nonsynchronous error. TSRV, used for estimating the volatility, is a significantly improved estimate (in terms of efficiency and bias), as compared to the estimates based on closing data. The use of ex post realised volatility ensures that the forecasting error does not vitiate the test results. The sample is selected to be large and varied to ensure the robustness of the results.
Keywords
Acknowledgements
JEL Classification — G10, G13
Citation
Singh, S. and ., V. (2015), "Performance of Black-Scholes model with TSRV estimates", Managerial Finance, Vol. 41 No. 8, pp. 857-870. https://doi.org/10.1108/MF-06-2014-0177
Publisher
:Emerald Group Publishing Limited
Copyright © 2015, Emerald Group Publishing Limited