This study attempts to analyse one-day-ahead out-of-sample performance of the stochastic volatility model of Heston (SVH) in the Indian context. Also, the study compares the ex-ante performance of the SVH with that of a Two-Scale-Realised-Volatility (TSRV)-based Black-Scholes model (BS) using the liquidity-weighted performance metrics. For the purpose, we utilise the tick-by-tick data of the CNX Nifty index and options thereon, the most liquid equity options in the world in terms of the number of contracts traded 1. Additionally, the study compares the two models across subgroups based on the moneyness, volatility of the underlying and time-to-expiration of the options. The results establish that the SVH model is better than the BS model in pricing equity index options. Further, the SVH model appears to be superior across all the subgroups, for both call options and put options.
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.
This study provides new insights into certain recent developments in derivatives trading in India. Specifically, it examines the implications of introduction of short‐selling for pricing efficiency of the Nifty 50 index derivative contracts of National Stock Exchange of India. The empirical results suggest that the introduction of short‐selling, supported by a well‐functioning security lending and borrowing market, has significantly reduced the overpricing of Nifty 50 index put options. Moreover, the introduction of this short‐selling mechanism has lessened the underpricing of Nifty 50 index futures.
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