How Forward Prices and Volatility Skew Affect Option Delta
Summary
The document explains option delta as sensitivity to changes in the underlying price and as a model-based estimate related to the chance of expiring in the money. It emphasizes that delta depends on the pricing model and the quality of its inputs. In crypto markets, futures can diverge from a theoretical spot forward because of sentiment, liquidity, and differing funding costs. Using a market futures price instead can therefore change calculated call and put deltas, so traders may report different deltas for the same option.
The article also describes how implied volatility varies by strike to represent supply and demand that a constant-volatility lognormal model cannot capture. A volatility smile or skew reflects the market’s pricing of tail moves and directional demand. Higher implied volatility generally increases the absolute delta of an out-of-the-money option while reducing that of an in-the-money option. These are model interpretations rather than guarantees about actual probabilities; delta shifts as prices and volatility inputs change.
Key ideas
- Option delta depends on the pricing model and its inputs, including the assumed forward price and implied volatility.
- Crypto futures may diverge from theoretical forwards because of sentiment, liquidity, and funding differences.
- Using a higher forward price raises call delta and makes put delta less negative, all else equal.
- Strike-specific implied volatility captures market pricing that a constant-volatility lognormal model misses.
- Higher implied volatility tends to raise the absolute delta of out-of-the-money options and lower it for in-the-money options.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.