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Ad-Hoc Black–Scholes vis-à-vis TSRV-based Black–Scholes: Evidence from Indian Options Market

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Abstract

This research paper examines one-day-ahead out-of-sample performance of the volatility smirk-based options pricing models, namely, Ad-Hoc-Black–Scholes (AHBS) models on the CNX Nifty index options of India. Further, we compare the performance of these models with that of a TSRV-based Black–Scholes (BS) model. For the purpose, the study uses tick-by-tick data. The results on the AHBS models are highly satisfactory and robust across all the subgroups considered in the study. Notably, a daily constant implied volatility based ad-hoc approach outperforms the TSRV-based BS model substantially. The performance of the ad-hoc approaches improves further when the smile/smirk effect is considered. For the estimation of the implied volatility smile, we apply three weighting schemes based on the Vega and liquidity of the options. All the schemes offer equally competing results. The major contribution of the study to the existing literature on options pricing is in terms of the ex-ante examination of the ad-hoc approaches to price the options by calibrating volatility smile/smirk on a daily basis.

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Notes

  1. From the preliminary analysis, we find that the AHBS models provide considerable improvements over the BS model, both in terms of the MAPE and the MPE. However, the SDs for the AHBS models are comparable to those of the BS; and in some cases, even higher. This indicates the presence of outliers in the data (especially, in the case of the AHBS models). However, in the case of the BS model, the SD fails to reflect the presence of outliers in the data. This may be traced to the considerably biased MPE. Further investigation of the data corroborates the presence of outliers (in some cases the MPE is as high as 10,000% or more). To remove the effect of such extreme outliers on the results, a 5% trimming scheme is applied on the overall mispricing data.

  2. A non-parametric test is applied in view of the stylised fact that the financial data, in general, is expected to show non-normality. The Jarque Bera test is conducted to confirm the non-normality of pricing errors. The test reveals that the data is not normally distributed since the null hypothesis of normality can be rejected with a very high level of confidence (p-value \(2.2\times 10^{-16})\). In view of this, it is appropriate to use a non-parametric test. The Wilcoxon Rank-Sum test is also known as the Mann-Whitney U test/Mann–Whitney–Wilcoxon test.

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Authors and Affiliations

  1. # 217, Faculty Block, Faculty of Finance and Accounting, Indian Institute of Management, Prabandh Nagar, IIM Road, Lucknow, 226013, India

    Alok Dixit

  2. Finance and Accounting, Indian Institute of Management, Lucknow, India

    Shivam Singh

Authors
  1. Alok Dixit
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  2. Shivam Singh
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Corresponding author

Correspondence to Alok Dixit.

Appendices

Appendix A

Fig. 1
figure 1

NIFTY call—volume vs time to expiry

Full size image
Fig. 2
figure 2

NIFTY put—volume vs time to expiry

Full size image

Appendix B

The Kruskal-Wallis multiple comparison test for AS\(_1\) in the case of call options, p value: 0.05

Comparisons

Obs. dif

Critical dif

diff

DOTM-OTM

108,403.590

2412.981

TRUE

DOTM-ATM

370,232.951

2372.076

TRUE

DOTM-ITM

520,651.343

6490.112

TRUE

DOTM-DITM

519,609.229

18,971.560

TRUE

OTM-ATM

261,829.361

2060.493

TRUE

OTM-ITM

412,247.752

6382.823

TRUE

OTM-DITM

411,205.639

18,935.125

TRUE

ATM-ITM

150,418.392

6367.472

TRUE

ATM-DITM

149,376.278

18,929.956

TRUE

ITM-DITM

1042.114

19,870.532

FALSE

  1. For the other categories, the results of the KW test are available on request

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Dixit, A., Singh, S. Ad-Hoc Black–Scholes vis-à-vis TSRV-based Black–Scholes: Evidence from Indian Options Market. J. Quant. Econ. 16, 57–88 (2018). https://doi.org/10.1007/s40953-017-0078-3

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  • DOI: https://doi.org/10.1007/s40953-017-0078-3

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