How Delta, Vega, and Theta Change Long Option Values

Summary

This note explains why long put options can lose much of a recent gain even when the underlying futures price remains below an earlier level. It uses the option Greeks to separate the effects: delta reflects changes in the underlying, vega reflects changes in implied volatility, and theta reflects the passage of time. A fall in volatility can reduce the value of a long option, while time decay lowers its remaining extrinsic value.

The example concerns puts on WTI futures and describes a situation in which oil has stopped falling after a sharp decline. It offers a qualitative explanation rather than a calculation or a full option valuation. The relative contribution of each Greek depends on the contracts and market conditions; the note does not give the strikes’ moneyness, implied volatility changes, interest rates, or option prices needed to quantify the move.

Key ideas

• Delta links underlying price changes to option value.
• Vega makes long options sensitive to changes in implied volatility.
• Theta represents time decay and generally weighs on long option value.
• A flat underlying price does not prevent an option from losing value.

Tags

# Options Pricing


# Options Pricing












I bought Sep and Oct '18 puts on WTI futures strike price 58, two weeks ago. They increased in value on both recent 4% down moves. Today, the price of Oil is roughly flat. Why have the value of my options retraced almost completely the gains from yesterday when Oil remains 4% below it's open price yesterday?

## Answer by Joshua Kalina (score 1)

https://quant.stackexchange.com/a/40813

With Options, the Greeks will help you understand the story. You have a few factors working either for you or against you: delta, gamma, theta, vega. The price movement that worked in your favor will be reflected in the delta (Delta is the effect of the price movement to the underlying on the price of the option).

Vega is likely working against you too. Vega is the effect of volatility on your option price. If Oil is staying flat at 4% down, volatility is likely being crushed. Higher volatility is good for long options.

Most importantly, Theta is working against you. That is the effect of time decay on the price of your option. Your option is now two weeks older and there is less extrinsic value to the option than when you bought it.

Try a good google-fu for "Option Greeks" to understand it more succinctly.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.