Quant Series: Profiting Off Stock Options Mispricings 💰💰💰

Article: https://summit.sfu.ca/item/733 

Basic Concept: The trading strategy is based on the belief that extreme levels of implied volatility and historical realized volatility will eventually return to their long-run averages. To identify mispriced options, they group them into deciles (See Definition below) using the Historic Volatility-Implied Volatility measure. Options with extremely positive Historic Volatility-Implied Volatility are considered cheap, while those with extremely negative Historic Volatility-Implied Volatility are seen as expensive. They then create a trading strategy by going long on portfolios with positive Historic Volatility-Implied Volatility (decile 10) and shorting portfolios with negative Historic Volatility-Implied Volatility (decile 1). They are primarily focused on verifying this method of identifying mispriced options and determining its profitability, rather than understanding the reasons for the mispricing.

Granger and Poon concluded that option implied volatility provides more accurate forecasts of future volatility compared to the other three-time series methods.

Explanation of their calculations:

The calculations involve determining the call option price by taking the average of the best bid and best ask prices, which represents the midpoint of the bid-ask spread. This is done to estimate a fair value for the call option.

In a risk-neutral environment, the forward price of the stock is calculated using the formula F = Serτ, where S is the current stock price, r is the risk-free interest rate, and τ is the time to expiry of the option. This forward price represents the expected future price of the stock at the option's expiration.

To ensure consistency in the data, the strike price (X) of each option is divided by 1000. This rescaling is necessary because OptionMetrics, the data provider, presents the strike price as 1000 times its actual value.

The second data screening process involves filtering out options that do not meet certain criteria. If the call option price falls outside the no-arbitrage interval (S - Xe-rτ, S), it is considered outside of a fair range and is removed from the analysis. Additionally, only at-the-money (ATM) options are desired, so options where the strike price (X) does not satisfy the condition .95 < X/F < 1.05 are also excluded.

Returns are then calculated for both the options and the underlying stocks. The returns are matched based on the option issue date, expiry date, and Security ID. This matching allows for analysis and comparison of the returns for each option. The calculated returns are reported as holding period rates of return (HPRR), which represent the percentage change in value over the holding period.

Their Results:

The passage discusses the construction of portfolios consisting of call options, stocks, and delta-hedged calls based on the ranking of options according to the difference between historical realized volatility (HV) and implied volatility (IV). The portfolios are divided into deciles for each month over a specific investment horizon.

The ranking is determined by evaluating the log difference between HV and IV for all options in each month. Decile 10 represents options with the highest positive difference (indicating they are considered cheap), while decile 1 contains options with the lowest negative difference (considered expensive).

Summary statistics are provided for IV and HV in Table 2. Average HV and IV values are obtained by calculating the time-series average for each decile and then computing the cross-sectional average of these decile averages.

Table 3 presents statistics for HV, IV, call prices scaled by stock price (C/S), and delta for each decile and option type. HV generally increases from decile 1 to decile 10, while IV tends to decrease. The scaled call price (C/S) generally decreases from decile 1 to decile 10, supporting the notion that decile 1 options are expensive and decile 10 options are cheap.

Holding period rates of return are computed for each decile and month for equally weighted portfolios of call options, stocks, and delta-hedged calls. The average returns for each decile are reported in Tables 4, 5, 6, and 7.

For 1-month-to-expiry call options, the observed returns decrease from decile 1 to decile 10, which is contrary to expectations and previous findings. Stock returns exhibit a similar pattern, deviating from the constant cross-sectional stock returns assumption of the Black-Scholes model.

The passage suggests a possible explanation based on the option-like features of a firm's equity and debt, where increasing volatility leads to a decrease in expected returns on call options. However, further research and evidence are needed to validate this hypothesis and explore the relationship between option returns and volatility.

The results for delta-hedged call returns differ from previous findings, potentially due to differences in data sets and filtering criteria. The passage highlights the need for additional research to refine the volatility measure, compare it to a benchmark, and investigate the relationship between option returns and volatility.

Similar patterns are observed for 2-month stock returns and delta-hedged call returns. However, for 2-month-to-expiry call options, the returns increase from decile 1 to decile 10. The passage suggests examining mean reversion as a possible explanation for these conflicting results.

The passage concludes by discussing the influence of short-term option implied volatilities and the suitability of the long-short strategy for different expiry periods. It suggests conducting additional tests on longer-term options to confirm the validity of the strategy.