Mastering Derivatives: Understanding Positive Theta in Deep ITM European Puts

Long option trades have negative theta and put option trades have positive theta. stated another way, decay of time Works against long options positions and benefits short options positions. But there is an exception. Long positions in deep in the money (ITM) trading European Positive theta puts. While such options may not form part of your typical trading repertoire, it is interesting to understand why these options are different. This week we discuss how asset price behavior explains why there is positive theta in deep European ITM positions.

Time benefits

Let’s say you have a deep European ITM situation; The underlying remains at current levels until the option expires. The position will carry positive theta as expiration approaches. This means that the option will gain value with each passing day. Why?

Asset prices can go up more than they can go down. This is because asset prices have (theoretically) an infinite rise, but cannot fall below zero (captured by the lognormal distribution). While upward and downward price movements may be limited to short periods of time, prices usually carry a bullish bias.

Now, if you buy a put option and the underlying value drops sharply, the option becomes ITM. The deeper the put option is ITM, the more willing you are to exercise the option and capture the intrinsic value. Note that selling an option helps you capture intrinsic value and time value while using an option helps you capture only intrinsic value.

Typically, traders are less inclined to deep ITM options, because such options require significant capital outlays. Thus, such options have low liquidity. Therefore, playing sports becomes a useful alternative to selling status. But you cannot exercise European status until expiration. The longer you wait to exercise the option, the greater the risk that the underlying asset can appreciate, eroding unrealized gains. Therefore, the faster the European deep sell date of ITM approaches, the better it is for the long position to capture gains from the intrinsic value. Hence, the increase in the value of time with each passing day or theta is positive. This argument does not apply to an American deep ITM offering, where you can exercise the option at any time before expiration and capture the intrinsic value.

Optional reading

The lognormal distribution of asset prices is also useful in explaining why there is no positive theta in deep ITM calls. Note that the time value of an option is made up of the time to expiry and the implied volatility. If asset prices are biased upwards, then traders who sell calls must price the risk of a continued rise in the asset, lest the call become an ITM and be exercised against them. This is true even if the trader shorts a deep ITM call, as the underlying can move further and make the call more ITM. This risk is priced into the call by its time value. This time value should decay as the option expiration approaches.

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