Charm (which is not represented by a greek letter) is one of the options greeks which are collectively used to determine how closely an options or warrants contract will track its underlying market. Specifically, charm is the rate at which the delta (Δ) of an options or warrants contract will change over the passage of time (i.e. the delta time decay). Charm is a second order derivative, and is useful when a trader is making a delta hedged trade.
Calculation
Charm is the second derivative of the value (V) of an options or warrants contract, with respect to the price of the underlying market and to the passage of time. Charm is calculated as shown in the above calculation image. Charm is also mathematically equivalent to the negative derivative of theta with respect to the price of the underlying market (also shown in the calculation image).
Use In Trading
Charm is the rate that the delta of an options or warrants contract will change over the passage of one year, but is sometimes given as the charm for a shorter time frame (e.g. one month, one week, or one day). Charm is therefore useful for traders that want to make a delta hedged trade. In other words, traders that want to make an options or warrants trade where the delta does not change regardless of what happens in the underlying market, will need to use charm (along with vanna).
