Theta Differences in Out-of-the-Money Put Debit Spreads

Summary

The note addresses a claim that time decay can favor a seller of a debit spread. Its answer considers a put spread in which the position is short the higher-strike put and long the lower-strike put, with both options out of the money. In that setup, the short option is said to have greater theta than the long option, so time decay on the short leg can outweigh time decay on the long leg.

This is a narrow, conditional explanation of net theta, not a general rule for all debit spreads or market conditions. The excerpt does not specify the underlying, time to expiry, volatility surface, or whether theta signs are quoted from the holder’s or writer’s perspective. Those details matter when assessing an actual position; the stated comparison should be checked for the spread’s precise structure and inputs.

Key ideas

• A spread’s net theta depends on the relative theta of its short and long legs.
• For the described out-of-the-money put spread, the short higher-strike put is said to have greater theta than the long lower-strike put.
• Under that stated condition, decay on the short leg can exceed decay on the long leg.
• The claim is position-specific and does not establish that sellers of every debit spread benefit from time decay.

Tags

# How does Theta benefit sellers of debit spreads?


# How does Theta benefit sellers of debit spreads?












John Hull. Options, Futures, and Other Derivatives (2017 10 edn). p 408.

> Theta is usually negative for an option.7 This is because, as time passes with all else remaining the same, the option tends to become less valuable. 7 An exception to this could be an in-the-money European put option on a non-dividend-paying stock or an in-the-money European call option on a currency with a very high interest rate.

u/BANG_BANG_SHRIMP alleges

> Theta works in your favor if you are selling debit spreads.

Why? I know that Option writers benefit from time decay because the options that were written become less valuable as the time to expiration approaches. Consequently, it is cheaper for option writers to buy back the options to close out the short position.

## Answer by Lliane (score 2)

https://quant.stackexchange.com/a/54206

If both options are out of the money, your higher strike put (of which you are short) has a higher theta than your lower strike put (of which you are long). Thus earn more theta than you lose.

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