Statistical Models for Pricing Efficiency in Indian Derivatives Markets

Introduction

The Indian derivatives market, centered on the National Stock Exchange (NSE), has grown to become one of the largest in the world by contract volume. Despite this scale, academic research on the microstructure and pricing efficiency of Indian derivatives remains limited compared to the extensive literature on US and European markets.

This paper contributes to the literature by conducting a systematic analysis of pricing efficiency in Indian index and stock options, using a dataset spanning 36 months of tick-level options data.

Methodology

Data Collection

Our analysis utilizes tick-level options data from the NSE for the period January 2024 to December 2026, covering:

• NIFTY 50 index options (weekly and monthly expiries)
• BANKNIFTY index options (weekly and monthly expiries)
• Top 50 single-stock options by volume

Statistical Framework

We employ a multi-layer statistical framework:

1. Put-Call Parity Tests: Measuring deviations from the no-arbitrage put-call parity relationship across different strike prices and expiration horizons
2. Implied Volatility Surface Analysis: Constructing and analyzing the volatility surface for systematic patterns (skew, term structure, smile dynamics)
3. Model Comparison: Evaluating the performance of Black-Scholes, Heston stochastic volatility, and SABR models against observed market prices
4. Predictive Regressions: Testing whether options-implied metrics (IV rank, skew, term structure slope) predict future realized volatility and returns

Key Findings

Put-Call Parity Deviations

We find statistically significant put-call parity deviations in Indian markets, averaging 0.3-0.7% for index options and 0.8-1.5% for stock options. These deviations are:

• Persistent: Surviving for 2-15 minutes on average, compared to seconds in US markets
• Asymmetric: Calls are more frequently overpriced relative to puts in trending markets
• Time-varying: Deviations increase significantly around expiry week and during high-volatility periods
• Size-dependent: Larger deviations in less liquid stock options compared to index options

Volatility Surface Characteristics

The Indian options market exhibits a distinctive volatility surface topology:

• Steeper negative skew in index options compared to US markets, reflecting higher demand for downside protection
• Mean-reverting term structure with significant variations around budget announcements and RBI policy meetings
• Asymmetric smile in stock options, with the degree of asymmetry correlating with the stock’s beta and sectoral factors

Model Performance

Among the pricing models tested:

• The SABR model provides the best fit for index options across all moneyness levels
• Heston stochastic volatility outperforms Black-Scholes by 40-60% in out-of-sample pricing accuracy
• Local volatility models show superior performance during high-volatility regimes

Predictive Power

Options-derived metrics show meaningful predictive ability:

• IV Rank predicts 30-day realized volatility with R² = 0.42, suggesting options markets efficiently price future volatility
• Skew changes lead underlying returns by 1-3 days for index options
• Volume-weighted IV provides a superior variance forecast compared to historical volatility estimators

Implications

Our findings have several practical implications:

1. For traders: The persistence of put-call parity deviations suggests exploitable inefficiencies, particularly in stock options during high-volatility periods
2. For risk managers: Standard Black-Scholes Greeks underestimate tail risk in Indian markets; stochastic volatility models provide more accurate risk estimates
3. For platform builders: AI systems designed for the Indian market should incorporate market-specific volatility dynamics rather than relying on models calibrated to Western markets

Limitations and Future Work

This study is limited by the availability of intraday order book data, which would enable more granular analysis of price formation. Future work will extend the analysis to include:

• Cross-market arbitrage dynamics between NSE and BSE
• The impact of regulatory changes on pricing efficiency
• Machine learning approaches to volatility surface modeling

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This working paper is part of TRW’s ongoing research into Indian financial market structure and quantitative trading methods.