Charm
Charm, also known as delta decay or DdeltaDtime, was a second-order options Greek measuring the rate of change of an option's delta with respect to the passage of time, indicating how much the delta was expected to change as each day passed, even if the underlying price remained constant.
Charm was the partial derivative of delta with respect to time, or equivalently the partial derivative of theta with respect to the underlying price. Its significance became most pronounced as options approached their expiry date. For an at-the-money option, charm caused the delta to drift toward 0.5 as time passed — or more precisely, as the option decayed, the delta of an ATM call remained near 0.5 while OTM and ITM options saw more dramatic delta shifts over time due to the accelerating effect of charm.
For options writers and delta hedgers in Indian markets, charm had a practical consequence that became particularly important during the final days of weekly NSE expiries. A delta-hedged short straddle on Nifty that was established on a Monday might have a delta close to zero based on Monday's Greeks. By Wednesday, even if Nifty had not moved, the passage of two days of theta would have changed the delta of each option component — and charm quantified exactly how much. A hedger who rebalanced only once at initiation without accounting for charm would find their position had drifted to a non-zero delta by expiry, potentially resulting in an unintended directional exposure at settlement.
Charm was larger in magnitude for options that were near the money and had short time to expiry — precisely the category of options most actively traded on NSE's weekly expiry schedule. OTM options with little time remaining had delta approaching zero and experienced charm pulling delta further toward zero. ITM options had delta approaching 1.0 and also experienced charm pulling delta closer to 1.0. The ATM options sat in the middle where charm's effect on absolute delta was smallest, though the relative change could still be significant.
The value of charm was typically measured in delta units per day. For practical hedgers, knowing the charm of their position allowed them to estimate how much the delta hedge ratio would need to change each day purely due to time passage, independent of any movement in the underlying. This was particularly relevant for market makers on NSE who maintained delta-neutral books overnight: even with zero overnight movement in Nifty futures, the book's delta changed by the charm multiplied by the time elapsed, requiring a hedge adjustment at the open.
Charm was rarely displayed on retail trading platforms in India, appearing instead in professional-grade risk management systems. Its relevance to retail options participants was mainly educational — understanding that delta was not a static number but evolved continuously with time, even in the absence of price changes, formed an important conceptual foundation for more advanced options risk management.