Time Decay Curve
The non-linear relationship between time to expiry and the time value (extrinsic value) of an option, characterised by slow decay in the early portion of the contract's life and rapidly accelerating decay in the final weeks and days before expiry.
Time value — the component of an option's premium attributable to the possibility of a favourable move before expiry — erodes continuously as expiry approaches. This erosion, measured by the Greek theta, does not occur at a constant daily rate. Instead, the rate of time decay follows a convex curve, accelerating as expiry nears.
In the first several weeks of an option contract's life, time decay is relatively gradual. An option with forty-five days to expiry loses time value slowly from day to day. The option buyer has ample time for the trade to play out, and the seller collects theta at a modest daily rate. As the contract enters the final two weeks, theta erosion picks up pace. In the last week, and especially in the final two or three days, time decay becomes severe for at-the-money options. An ATM option that was worth Rs 100 three weeks before expiry might retain only Rs 20 in the final two days — three-quarters of its time value having eroded in the last week.
The mathematical basis for this non-linearity was rooted in the Black-Scholes model. Theta — the first derivative of option price with respect to time — was proportional to the option's gamma and to the square root of time remaining. As time to expiry approached zero, the square root of time collapsed rapidly, driving an exponential acceleration in theta.
This shape of the time decay curve had significant strategic implications. Option sellers — who benefited from theta decay — preferred to sell options with relatively short time to expiry (typically weekly or monthly contracts) because the daily theta earned per unit of vega risk was highest near expiry. Option buyers, conversely, preferred longer-dated options that decayed slowly in percentage terms per day, giving the underlying more time to make the requisite move.
In India's F&O market, the introduction of weekly Nifty and Bank Nifty expiries in 2016 dramatically increased the prevalence of theta-decay-focused strategies. Traders who sold weekly ATM straddles or strangles on Nifty were deliberately harvesting the accelerated time decay of short-dated options, while managing the attendant gamma risk (sensitivity to sharp moves).