Implied and Historical Volatility

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Abstract

This TradingView indicator visualizes implied volatility (IV) derived from the VIX index and historical volatility (HV) computed from past price data of the S&P 500 (or any selected asset). It enables users to compare market participants' forward-looking volatility expectations (via VIX) with realized past volatility (via historical returns). Such comparisons are pivotal in identifying risk sentiment, volatility regimes, and potential mispricing in derivatives.
Functionality

Implied Volatility (IV):

The implied volatility is extracted from the VIX index, often referred to as the "fear gauge." The VIX represents the market's expectation of 30-day forward volatility, derived from options pricing on the S&P 500. Higher values of VIX indicate increased uncertainty and risk aversion (Whaley, 2000).

Historical Volatility (HV):

The historical volatility is calculated using the standard deviation of logarithmic returns over a user-defined period (default: 20 trading days). The result is annualized using a scaling factor (default: 252 trading days). Historical volatility represents the asset's past price fluctuation intensity, often used as a benchmark for realized risk (Hull, 2018).

Dynamic Background Visualization:

A dynamic background is used to highlight the relationship between IV and HV:

Yellow background: Implied volatility exceeds historical volatility, signaling elevated market expectations relative to past realized risk.

Blue background: Historical volatility exceeds implied volatility, suggesting the market might be underestimating future uncertainty.

Use Cases

Options Pricing and Trading:

The disparity between IV and HV provides insights into whether options are over- or underpriced. For example, when IV is significantly higher than HV, options traders might consider selling volatility-based derivatives to capitalize on elevated premiums (Natenberg, 1994).

Market Sentiment Analysis:

Implied volatility is often used as a proxy for market sentiment. Comparing IV to HV can help identify whether the market is overly optimistic or pessimistic about future risks.

Risk Management:

Institutional and retail investors alike use volatility measures to adjust portfolio risk exposure. Periods of high implied or historical volatility might necessitate rebalancing strategies to mitigate potential drawdowns (Campbell et al., 2001).

Volatility Trading Strategies:

Traders employing volatility arbitrage can benefit from understanding the IV/HV relationship. Strategies such as "long gamma" positions (buying options when IV < HV) or "short gamma" (selling options when IV > HV) are directly informed by these metrics.

Scientific Basis

The indicator leverages established financial principles:

Implied Volatility: Derived from the Black-Scholes-Merton model, implied volatility reflects the market's aggregate expectation of future price fluctuations (Black & Scholes, 1973).

Historical Volatility: Computed as the realized standard deviation of asset returns, historical volatility measures the intensity of past price movements, forming the basis for risk quantification (Jorion, 2007).

Behavioral Implications: IV often deviates from HV due to behavioral biases such as risk aversion and herding, creating opportunities for arbitrage (Baker & Wurgler, 2007).

Practical Considerations

Input Flexibility: Users can modify the length of the HV calculation and the annualization factor to suit specific markets or instruments.

Market Selection: The default ticker for implied volatility is the VIX (CBOE:VIX), but other volatility indices can be substituted for assets outside the S&P 500.

Data Frequency: This indicator is most effective on daily charts, as VIX data typically updates at a daily frequency.

Limitations

Implied volatility reflects the market's consensus but does not guarantee future accuracy, as it is subject to rapid adjustments based on news or events.

Historical volatility assumes a stationary distribution of returns, which might not hold during structural breaks or crises (Engle, 1982).

References

Black, F., & Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 81(3), 637-654.

Whaley, R. E. (2000). "The Investor Fear Gauge." The Journal of Portfolio Management, 26(3), 12-17.

Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson Education.

Natenberg, S. (1994). Option Volatility and Pricing: Advanced Trading Strategies and Techniques. McGraw-Hill.

Campbell, J. Y., Lo, A. W., & MacKinlay, A. C. (2001). The Econometrics of Financial Markets. Princeton University Press.

Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill.

Baker, M., & Wurgler, J. (2007). "Investor Sentiment in the Stock Market." Journal of Economic Perspectives, 21(2), 129-151.