Pricing and Greeks

Futures price = Spot × (1 + r×t) − dividends, where r is risk-free rate and t is time to expiry. This is "cost-of-carry": the futures price reflects what it would cost to buy the underlying today and hold it until the future date. Options pricing is more complex (Black-Scholes), involving spot, strike, time, volatility, and rate.

Greeks are sensitivities of an option's price to inputs. Delta — change in option price per unit change in underlying (calls: 0 to +1; puts: 0 to −1; ATM around ±0.5). Gamma — rate of change of Delta (peaks ATM, near-zero deep ITM/OTM). Theta — daily price decay due to time passing (negative for both calls and puts, accelerates near expiry). Vega — sensitivity to volatility (positive for both calls and puts; matters most for longer-dated options). For a hedger, Delta is the position-sizing tool. For a speculator on volatility, Vega is the key Greek.

Practical insight: India's implied volatility (IV) tends to be higher than realised volatility on average — meaning option sellers (writers) have a structural edge over option buyers, before transaction costs. This is why "selling premium" strategies (covered calls, cash-secured puts, iron condors) are popular among institutional traders. But the tail risk on the seller side is unbounded for naked positions — the 2020 March crash wiped out many naked option sellers. The Greek that captures this tail risk is "Speed" (third derivative of price w.r.t. underlying); not exam-required at NISM 8 but important practitioner-level.