What is option delta time-decay?

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The delta of an option will tend to be affected by the passing of time. This is characterised by the option Greek sometimes known as charm or DdeltaDtime or just as delta decay. Let’s go with delta decay for now. Delta decay is a higher-order Greek, meaning it tells us the risk relating to the change in another Greek (i.e. delta) rather than telling us the direct impact of a change in circumstances on the value of our options. So delta decay shows us how much our option delta changes when time passes and typically this is normalized to show the change in delta for a 1 day change in the time to expiry.

A simple example of delta time-decay

Let’s take a simple example. Suppose we have an out-of-the-money call with a delta of 15%. Suppose this call has a normalized delta decay of 1. Then, other things being equal, when we look at the call tomorrow, we can expect it to have a delta of 14%. Why is the delta diminishing? Well, remember that delta can be understand as the probability of expiring in-the-money. For out-of-the-money options (such as this call), their chances of expiring in-the-money must fall over time, assuming nothing else is happening. This is simply because they have less time left to go in-the-money. Less optionality!

Why option delta decay matters

Delta decay is particularly relevant for option traders in two instances. Firstly with respect to the weekend (and even more so with respect to ‘long’ weekends).  And secondly with respect to expiration. Considering the weekend, this is important because the market will be closed for 2 whole days rather than just over-night which means the effect of delta decay is magnified. If a trader’s market closes at 5pm and re-opens the following morning at say 8am, there is only half a day or so of delta decay. But a weekend can mean the option loses 2 and a half days of life without the underlying product trading. So option traders (especially those managing delta-hedged positions) will pay particular attention on Friday to their delta decay. Consider a call option with 15% delta that is delta-hedged (suppose the trader is short 15 lots of the spot product for every 100 calls he owns). Now suppose the calls have delta decay of 1; by Monday morning the call delta may have dropped to 12.5% (2.5 days have passed, multiplied by the delta decay of 1). In this case the trader’s delta hedge is no longer accurate; he is too short the underlying. If the spot market opens on Monday higher, the trader is unlikely to be amused when he has to buy back deltas to cover his position (in order to re-establish a delta-neutral stance).

There are different tactics to deal with this situation. Some traders will look to ‘average in’; by realising their portfolio delta will be different on Monday, they will start to re-hedge over the course of the Friday afternoon. Other traders will leave everything to chance and hope that on average this is p&l neutral. Other traders again will completely forget about delta decay and only remember on the close on Friday at which point they sometimes hastily re-hedge in part or in full!

An important point to note about delta decay is that special care is needed around expiration time. Remember that, in general, option Greeks rarely stay constant for long and at expiration they can become super-dynamic. So whilst delta decay for an option with 6 months still on the clock is unlikely to alter much over-night, the delta decay of a dying option can itself change dramatically over time. For example, imagine a call option with a day until it expires and a delta of 15%. This option may have a delta decay, theoretically, of say 6, meaning that other things being equal we would expect the delta to be 9% in 24 hours time. This would be a foolish assumption because in 24 hours the option will no longer exist and unless the spot moves to make it in-the-money, its delta will be zero. The point is that this close to expiration, the delta decay will itself change rapidly over the next 24 hours. So, as is always the case at option expiration, mathematical modelling must be served with a generous slice of common-sense.

Option positions particularly exposed to delta decay risk

Not all option positions are exposed to delta decay. Or rather, some portfolios are self-hedging with respect to delta decay. For example, if someone owns the 15% delta call and the (-)15% delta put, the delta decay on these options may offset, leaving them delta decay-neutral. This is because, since delta decay makes the option delta tend towards zero over time (for out-of-the-money options), the call delta will fall over time, but the put delta will rise (from minus 15% towards zero). This position is known as a strangle (long out-of-the-money call and put). Straddles similarly can be delta-decay neutral (because, by definition, they have zero delta so it cannot decay).  Positions with potentially high levels of delta decay include delta-hedged calls, puts and risk reversals. For example if someone is long the 15% delta call and short the -15% delta put, the delta decay is now doubling rather than offsetting. Tomorrow for instance the call may have 14% delta and the put -14%; but this means the risk reversal delta has altered from 30% to 28%.

It is because of these facts that delta decay (or charm or dDelt; the lack of a standardised name indicates the lack of attention some people pay to this Greek!), is closely related to vanna (or dDelv), which is the change in delta for a change in implied volatility. Remember that time passing has a similar effect to a reduction in implied volatility as far as options are concerned; hence positions usually exhibit both vanna and delta decay or they exhibit neither.

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