8.1 Options: contracts, payoffs and moneyness

Motivation

A future gives you a linear exposure to the index (M07). An option gives you a convex exposure: you participate in one direction and are protected in the other, for a price paid up front. Every option trade is a trade on that price. Before we can say whether a price is rich or cheap, we need to know what it should be under stated assumptions.

Setup

A call option gives its holder the right, not the obligation, to buy the underlying (the asset the option is written on) at a fixed strike price $K$ on (or before) the expiry date $T$ . A put option gives the right to sell at $K$ . The buyer (the holder, or "long") pays a premium to the seller (the writer, or "short"). A European option can be exercised only at expiry; an American option can be exercised at any time up to expiry. On NSE an option contract covers a fixed lot of the underlying: as of 5 Nov 2026, one Nifty 50 option or future covers 65 units of the index and one Bank Nifty contract covers 30 (NSE F&O bhavcopy of 5 Nov 2026).

Payoffs, intrinsic and time value#

Write $S_t$ for the underlying price at time $t$ . At expiry the holder exercises only if it pays, so the payoffs are

C_T = (S_T-K)^+ = \max(S_T-K,0), \qquad P_T = (K-S_T)^+ . \tag{8.1}

The writer's payoffs are the negatives. Before expiry the intrinsic value is the payoff if exercised now, $(S_t-K)^+$ for a call, and the time value is premium minus intrinsic value:

\text{premium} = \text{intrinsic value} + \text{time value}. \tag{8.2}

Moneyness#

Moneyness compares spot with strike. A call is in the money (ITM) if $S>K$ , at the money (ATM) if $S\approx K$ and out of the money (OTM) if $S<K$ ; for puts the inequalities reverse. Desks often measure moneyness against the forward instead, by $\ln(F/K)$ or by delta (8.9), because the forward is the risk-neutral mean of $S_T$ (8.7).

Three facts follow directly from (8.1):

A long call plus a short put at the same strike pays $S_T-K$ in every state. That is a forward contract (8.2).
The payoffs are convex in $S_T$ . Jensen's inequality then makes option value increase with uncertainty, which is why volatility is the central input of everything that follows.
Payoffs are homogeneous of degree one in $(S,K)$ : doubling both doubles the payoff. Prices inherit this (Problem 8.4).

A Nifty call on settlement prices#

Worked example 8.1a Nifty call, real settlement prices

On 5 Nov 2026 the Nifty Dec-2026 24,500 call (expiry Tue 29 Dec 2026) settled at ₹587.65 and the 24,500 put at ₹370.90, with Nifty spot at 24,536.60 (NSE bhavcopy, 5 Nov 2026). Buying one lot of the call costs $587.65\times 65 = \text{₹}38{,}197.25$ . Intrinsic value is $24{,}536.60-24{,}500=36.60$ points; time value is $587.65-36.60=551.05$ points, so 94% of the premium is time value. At expiry the long call's profit per lot is $65\,[(S_T-24{,}500)^+-587.65]$ . Breakeven is $S_T=25{,}087.65$ , a rise of 2.25% in 54 days. If Nifty settles at 25,500 the profit is $65\times(1{,}000-587.65)=\text{₹}26{,}802.75$ ; if it settles anywhere at or below 24,500 the loss is the whole ₹38,197.25 (before costs, 8.11).

Practitioner notes

Quote and think in index points, then multiply by the lot size. Lot sizes change (Nifty went from 75 to 65 for contracts expiring after 30 Dec 2025), so read the lot from the bhavcopy column NewBrdLotQty of the date you trade, not from memory.
The premium is the most you can lose as a buyer. As a writer your loss is unbounded for calls and up to $K$ per unit for puts, which is why exchanges charge writers SPAN plus exposure margin (M07 · 7.4).
About 97% of individual F&O traders were option buyers in FY26, and options were about 92% of individual losses (SEBI FY26 study; M01 · 1.11 Case 1). The rest of this module explains what an option should cost; M09 explains why buyers in aggregate pay more than that.