Introduction to Equity Options

1What an option is

Futures have linear payoffs with unlimited gains and losses. Options let you keep the upside while capping the downside. An option gives the holder (buyer) the right but not the obligation to buy or sell the underlying at a set price on or before a date. The buyer pays a premium upfront to the writer (seller), who takes on the obligation if the buyer exercises.

• Call: right to buy. The call writer must sell if exercised.
• Put: right to sell. The put writer must buy if exercised.

Key terms:

• Index options (on Nifty, Sensex) and stock options (on individual shares).
• American options can be exercised any time up to expiry; European options only on expiry. All index and stock options in India are European.
• Premium: quoted per unit; multiply by the lot size for the contract.
• Spot price (S) and strike or exercise price (X).
• Exercise: in India, only at expiry, against the closing price that day. Assignment: allocating exercised options to sellers.
• Opening purchase / opening sale create or increase a long / short position. Closing purchase (covering) reduces a short; closing sale reduces a long. You close an option only with the same option (same strike and expiry), not by buying a put against a long call.

Remember

• Buyer: right, pays premium. Seller: obligation, receives premium.
• Indian options are European.

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2Option contract specifications

The exchange sets every term except the premium.

• Lot size: varies by underlying. Total premium = premium × lot size (for example ₹124.50 × 50 = ₹6,225).
• Trading cycle: stock options follow a three-month cycle (near, next, far). Index options also have weekly expiries, plus quarterly and longer half-yearly expiries. Since November 2024, each exchange can offer weekly contracts on only one benchmark index.
• Expiry: Nifty and Bank Nifty monthly options expire on the last Tuesday (previous trading day if a holiday); BSE contracts on Thursday.
• Tick size: ₹0.05 for index options; stock tick sizes vary with the share price and exchange.
• Settlement: there is no daily settlement of options. The final settlement price is the closing price of the underlying in the cash market on expiry day.
• Hours: 9:15 a.m. to 3:30 p.m. Sensex options have a lot of 20, European style, cash settled.

Remember

• No daily MTM on option buyers; settlement uses the underlying's close on expiry.

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3Moneyness

• In the money (ITM): exercising now would give a positive cash flow. Call: S > X. Put: S < X.
• At the money (ATM): S = X; in practice, the strike closest to the spot price.
• Out of the money (OTM): exercising now would give a negative cash flow. Call: S < X. Put: S > X.

Example Nifty at 18,315.10. The 18,400 call is OTM; the 18,400 put is ITM. With Nifty at 18,415 and strikes 18,350, 18,400 and 18,450, the ATM strike is 18,400.

Remember

• Call ITM when spot is above strike; put ITM when spot is below strike.

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4Intrinsic value and time value

Premium = intrinsic value + time value.

• Intrinsic value is the amount the option is in the money: call = max(S − X, 0), put = max(X − S, 0). It is never negative. Only ITM options have it.
• Time value = premium − intrinsic value. ATM and OTM options are all time value.

Example Spot 18,315.10, put strike 18,400 at ₹177.60: intrinsic = 84.90, time value = 92.70. The 18,400 call at ₹124.50 is all time value.

Example Stock at ₹286; ₹260 call at ₹45. Intrinsic = 286 − 260 = ₹26; time value = ₹19.

Remember

• OTM and ATM options have zero intrinsic value.

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5Payoffs of the four basic positions

Long call (bullish): maximum loss = premium; profit unlimited; break-even = X + P. Index options are cash settled. Buyers pay no margin, since the premium is their whole risk.

Example Strike 17,500, premium ₹95. At 17,400 the loss is ₹95; at 17,595 (break-even) zero; at 18,000 profit = 500 − 95 = ₹405. With a lot of 50, the most you can lose is ₹4,750.

Short call: the mirror image. Maximum profit = premium; loss unlimited as prices rise; break-even X + P. The seller pays margin.

Long put (bearish): maximum loss = premium; maximum profit = X − P (if the price falls to zero); break-even = X − P.

Example Strike 17,500, premium ₹150: break-even 17,350; maximum profit 17,350.

Short put: maximum profit = premium; maximum loss = X − P; break-even X − P; the seller pays margin.

Example Sold a put with strike ₹245 for ₹49. Maximum loss = 245 − 49 = ₹196 (if the share falls to zero).

Remember

• Call break-even = X + P; put break-even = X − P (same for buyer and seller).
• Option buyers pay no margin; sellers do.

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6Options versus futures

Options have asymmetric payoffs; futures have symmetric payoffs. Options give leverage: a small premium controls a large contract value, which magnifies both percentage gains and, if the option expires worthless, the loss of the whole premium.

Remember

• Futures: symmetric. Options: asymmetric.

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7What drives option prices

Prices are set by the market, not by exchanges or SEBI. Five factors:

1. Spot price: a rise lifts calls and lowers puts.
2. Strike price: a higher strike lowers calls and raises puts.
3. Volatility: higher volatility raises both calls and puts.
4. Time to expiry: more time generally raises both. Time value falls as expiry nears (time decay), so options are wasting assets and the passage of time favours sellers.
5. Interest rates: higher rates raise calls and lower puts.

Remember

• Volatility and time push both calls and puts up.

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8The Greeks

• Delta = change in premium ÷ change in underlying price. Long call positive, long put negative (sellers have the opposite sign). Delta 0.60 means a ₹1 move changes the premium by 60 paise. Delta is the hedge ratio: shares held ÷ delta = calls to write for a delta-neutral hedge.
• Gamma = change in delta ÷ change in underlying price (the "acceleration" of delta). Delta 0.50 with gamma 0.08 becomes 0.58 after a ₹1 rise.
• Theta = change in premium for one day less to expiry (time decay), usually negative for long options. Theta 1.2 means the premium falls about ₹1.20 a day.
• Vega = change in premium for a 1% change in volatility; positive for long calls and long puts.
• Rho = change in premium for a 1 percentage point change in interest rates.

Remember

• Delta: price. Gamma: change in delta. Theta: time. Vega: volatility. Rho: interest.

9Option pricing models

• Binomial model (William Sharpe, 1978): builds a tree of possible up and down price moves at equal time steps. Flexible and accurate, but iterative and time-consuming.
• Black–Scholes model (Fischer Black and Myron Scholes, 1973): a fast, non-iterative formula using the five inputs (stock price, strike, volatility, time, risk-free rate), ignoring dividends.

Formula Call C = S·N(d1) − X·e^(−rt)·N(d2); Put P = X·e^(−rt)·N(−d2) − S·N(−d1); d1 = [ln(S/X) + (r + v²/2)t] ÷ (v√t); d2 = d1 − v√t

Remember

• Black–Scholes is non-iterative; binomial is iterative.

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10Historical and implied volatility

Historical volatility is the standard deviation of past price changes. Traders care more about expected volatility over the option's life. Implied volatility is worked out by running Black–Scholes backwards from the option's market price.

Traders tend to sell options when implied volatility is high (premiums are rich) and buy when it is low. Before a big event, such as a court verdict, implied volatility can far exceed historical volatility; writers price that in through high premiums.

Remember

• Implied volatility comes from the option price, not past prices.

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11Choosing strikes as buyer or seller

Deep ITM options cost more (intrinsic plus time value); ATM and OTM options are cheaper (time value only). ATM options have the most uncertainty, because small moves tip them ITM or OTM, so their time value is highest.

Example Index at 17,562. The 17,300 call at ₹327 has intrinsic value 262 and time value 65; the 17,600 call at ₹130 is all time value. If the index ends at 17,800, the returns on premium are 53%, 60%, 62% and 54% for the 17,300, 17,400, 17,500 and 17,600 calls.

• Call sellers are neutral to bearish; put sellers are neutral to bullish.
• For put buyers, deep OTM puts give the highest percentage return if the index falls sharply (for example 362% on the 17,300 put if the index falls to 17,000), but are most likely to expire worthless.
• Selling deep ITM puts earns more premium but carries more risk; selling deep OTM puts earns less but is safer.

Remember

• ITM = expensive; OTM = cheap; ATM = most time value.

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