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Previously in this column, we discussed vanna, which is the change in option delta because of change in the option’s implied volatility. To recap, we saw that the vanna of an at-the-money (ATM) option is close to zero whereas out-of-the-money (OTM) and in-the-money (ITM) options have a large vanna. This week, we look at how delta changes with passage of time and its relevance to managing option positions.
Delta and time
The sensitivity of delta to passage of time is called charm. It is also referred to as delta decay or delta bleed. A positive charm means that the delta increases with passage of time, whereas a negative charm means that the delta decreases with passage of time. Note that delta is linked to time value. Therefore, the change in delta is linked to time decay. That is, the change in delta accelerates when time decays fast. Therefore, charm becomes more relevant when an option approaches expiry.
ITM calls have positive charm while OTM calls have negative charm. Why? An ITM call has a high probability of ending ITM as the option approaches expiry. Likewise, the probability of an OTM call ending ITM decreases as the option approaches expiry. Now, apply the probability interpretation of delta. ITM calls have higher delta because it has a higher probability of expiring ITM. The ITM call delta (positive charm) increases with passage of time. OTM calls have lower delta which decreases with passage of time (negative charm). Another interesting point is that option charm increases as strike decreases. That is, ITM calls and OTM puts have positive charm whereas OTM calls and ITM puts have negative charm. An ATM option has a charm closer to zero.
Charm is useful if you are setting up delta-neutral trades. This because delta changes with the change in underlying and with passage of time. The former is captured by gamma and the latter by charm. The point is that you may want to consider adjusting your position when the delta changes. Your decision to adjust the position to make it delta-neutral is function of associated costs.
Charm is also useful when you short options. In such cases, your primary gains come from time decay. As charm captures change in delta with passage of time, selecting an option (immediate OTM, for instance) will help you capture gains from time decay and hence, declining delta too.
Optional reading
An option price can change because of interaction of different variables. From a perspective of second-order effects, both charm and vanna effect an option’s delta. During stable markets, charm dominates as time decay becomes more important, whereas in volatile markets, vanna dominates because of sharp increase in implied volatility. These second-order effects only fine-tune your trading strategies. It goes without saying that the primary reason to trade must be your view on the underlying — uptrend, downtrend, or sideways movement of the underlying.
The author offers training programmes for individuals to manage their personal investments
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