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.

Options pricing and short‐selling in the underlying: Evidence from India

“…But, the underpricing of Nifty 50 call options is a rare phenomenon. The empirical evidence suggests that call options are generally overpriced due to volatility risk premium in the Indian market (Garg & Vipul, ; Singh & Vipul, , among others). Therefore, the introduction of short‐selling facility is unlikely to have much impact on the pricing of Nifty 50 call options.…”

Performance of the Heston’s Stochastic Volatility Model: A Study in Indian Index Options Market

“…Risk-free rate: NSE provides the daily "zero-coupon yield curve" rates, based on the prices of the traded Treasury bills and bonds, on a weekly basis. In line with the approach followed by Vipul [26] and Singh and Vipul [23], these rates are used as a proxy for the risk-free rate. For each day over the period of the study, the required risk-free rates for 7,14,21,28,35,42,49,56 and 63 days are extracted from the data.…”

“…The former is primarily used for getting the estimate of the realised volatility, while the latter is used to remove the microstructure noise inherent in the price process. Singh and Vipul [23] provide more details of the estimation procedure and the issues involved with it.…”

“…Based on the literature reviewed, it appears that only a few studies have been conducted in the Indian market using high-frequency data. In this regard, Singh and Vipul [23], in their analysis of a Two-Scale Realised Volatility (TSRV)-based BS, found that the BS model failed to capture the pricing dynamics of the Indian index options market. However, they documented that the TSRV-based estimates of volatility improved the performance of the BS model.…”

An Open Innovation Intraday Implied Volatility for Pricing Australian Dollar Options

“…Using the Merton [15] version of the BS model (BSM) to calculate prices of European currency options, all components are observable except the volatility of the underlying currency. Errors in the estimation of volatility result in the options mispricing [16][17][18]. The improvement of volatility estimation leads to lower errors of option prices [19].…”