Options
Calls and puts, moneyness, intrinsic and time value, payoff diagrams with breakeven, the Greeks and put-call parity.
Options give an SIF strategy the ability to shape its risk: to buy protection against a fall, to earn income by selling calls, or to take a short view with a loss capped at the premium. The exam tests payoffs at expiry, breakeven points, and which Greek measures what. This chapter works through each with Nifty-sized numbers.
Calls, puts, buyers and sellers
A call option gives the buyer the right to buy the underlying at the strike price on or before expiry. A put option gives the right to sell. The buyer pays a premium up front and can never lose more than that premium. The seller (writer) receives the premium and takes on the obligation to deliver if the buyer exercises; the writer must post margin because the potential loss is large, and for an uncovered call it is unlimited.
Index options in India are European: they can be exercised only at expiry, and in practice are cash settled automatically if in the money. American options can be exercised any time. Premiums are quoted per unit; multiply by the lot size for the cash amount.
Moneyness, intrinsic value and time value
An option is in the money (ITM) when exercising it now would be profitable: a call with strike below spot, a put with strike above spot. At the money (ATM) means strike equals spot. Out of the money (OTM) is the reverse. The premium has two parts:
Intrinsic value can never be negative. Time value is what the buyer pays for the chance that the option moves further into the money before expiry; it is highest for ATM options and decays to zero at expiry. With Nifty at 24,300, a 24,000 call trading at 450 has intrinsic value 300 and time value 150. A 24,500 call at 120 has zero intrinsic value; the entire 120 is time value.
Payoffs and breakeven
At expiry the option is worth exactly its intrinsic value. The buyer's profit is intrinsic value minus the premium paid; the seller's profit is the mirror image.
| Buy Nifty 24,000 call at premium 150; lot 75 | Cost ₹11,250 |
| Breakeven = 24,000 + 150 | 24,150 |
| Nifty at expiry 23,800: intrinsic 0; profit = (0 − 150) × 75 | −₹11,250 (max loss) |
| Nifty at expiry 24,150: intrinsic 150; profit = (150 − 150) × 75 | ₹0 |
| Nifty at expiry 24,400: intrinsic 400; profit = (400 − 150) × 75 | +₹18,750 |
| Nifty at expiry 25,000: intrinsic 1,000; profit = (1,000 − 150) × 75 | +₹63,750 |
The seller of the same call earns ₹11,250 if Nifty stays at or below 24,000, breaks even at 24,150, and loses ₹18,750 at 24,400 and ₹63,750 at 25,000, with no ceiling on the loss. For a put the picture flips: buying a 24,000 put at 120 breaks even at 23,880, has maximum loss ₹9,000 (120 × 75), and gains (24,000 − S − 120) × 75 below that, with maximum profit if the index went to zero.
What drives the premium
Six inputs move an option's price: spot price, strike, time to expiry, volatility, the risk-free rate and expected dividends. Higher spot raises calls and lowers puts. More time raises both (more chance to finish in the money). Higher volatility raises both, because the possible payoff grows while the loss stays capped. Higher interest rates raise calls slightly and lower puts. Dividends lower calls and raise puts. The Black-Scholes model combines these into a theoretical price; traders quote the implied volatility that makes the model match the market premium, and India VIX is the implied volatility of near-month Nifty options.
The Greeks
- Delta: change in premium per one-unit change in spot. Calls have delta between 0 and +1, puts between −1 and 0; ATM is about 0.5. Delta is also a rough probability of finishing ITM and the hedge ratio: a short 0.4-delta call is hedged by 0.4 lots of futures.
- Gamma: change in delta per unit change in spot. Highest for ATM options near expiry.
- Theta: change in premium per day as time passes; negative for buyers (time decay), positive for sellers.
- Vega: change in premium per 1% change in implied volatility; positive for both calls and puts.
- Rho: change in premium per 1% change in interest rates; small for short-dated equity options.
A long-short SIF strategy that sells options to earn premium is "short gamma and short vega": it profits from quiet markets and time decay but suffers when volatility spikes. That trade-off is what the risk-band and scenario analysis are meant to show the investor.
Put-call parity
A call and a put with the same strike and expiry are linked to the underlying by a no-arbitrage relation:
Buying a call and selling a put at the same strike replicates a long forward at K. If the relation breaks, an arbitrageur trades the cheap side against the expensive one. With S = 24,300, K = 24,000, r = 6%, T = one month (0.0833): K × e^(−rT) = 24,000 × 0.99501 = 23,880. So C − P should be about 420; if the call is 450, the put should be near 30. The exam uses parity to make you compute the missing premium.
Remember
- Call = right to buy, put = right to sell; the buyer's loss is capped at the premium, the writer of an uncovered call has unlimited loss.
- Intrinsic value = max(S − K, 0) for calls and max(K − S, 0) for puts, never negative; time value = premium − intrinsic.
- Long call breakeven = strike + premium; long put breakeven = strike − premium; multiply per-unit results by lot size for rupees.
- Index options in India are European and cash settled; premiums rise with time to expiry and volatility.
- Delta (direction), gamma (change in delta), theta (time decay), vega (volatility), rho (rates); option sellers are short gamma and vega.
- Put-call parity: C − P = S − K·e^(−rT); use it to back out a missing premium or spot an arbitrage.