In options markets, skew is the relative richness of put options vs call options, expressed in terms of implied volatility. For options on the same underlying and with the same expiry T, 25d skew focuses on puts with a delta of -25% and calls with a delta of 25% to demonstrate this difference in the market’s perception of implied volatility.

Figure 1: BTC 25d skew

The 25d skew is calculated as the difference between a 25-delta put’s implied volatility and a 25-delta call’s implied volatility, normalized by the at-the-money implied volatility:

$$skew^{25d}_{T} = {{\sigma^{25d}_{Put} (\,T)\, - \sigma^{25d}_{Call} (\,T)\,} \over {\sigma^{atm} (\,T)\,}}.$$

Where:

- \(\sigma^{25d}_{Put} (\,T)\,\): implied volatility of the 25-delta put with expiry \(T\)
- \(\sigma^{25d}_{Call} (\,T)\,\): implied volatility of the 25-delta call with expiry \(T\)
- \(\sigma^{atm} (\,T)\,\): at-the-money implied volatility with expiry \(T\)