Foundation — Calls, puts, moneyness and the four payoffs

16.1 Why options exist

"forward/futures contract is a COMMITMENT to buy/sell the underlying and has a **LINEAR payoff, which indicates UNLIMITED LOSSES AND PROFITS. However, some market participants desire to RIDE THE UPSIDE BUT RESTRICT THE DOWNSIDE. Accordingly, options have emerged as a financial instrument, as they allow UNLIMITED PROFITS on buying or selling of the underlying asset WITH A PROVISION OF RESTRICTING THE LOSSES."

"An option is a contract that gives the holder of the option THE RIGHT, BUT NOT AN OBLIGATION, to buy or sell the underlying asset ON OR BEFORE A STATED DATE/DAY, AT A PREDETERMINED PRICE. This right can be bought for a price known as the OPTION PREMIUM."

"The party taking a LONG position i.e., BUYING the option is called BUYER/HOLDER and the party taking a SHORT position i.e., SELLING the option is called the SELLER/WRITER. THE OPTION BUYER MUST PAY THE PREMIUM TO THE OPTION SELLER UPFRONT, i.e., AT THE TIME OF BUYING THE OPTION."

The asymmetry that defines the instrument: "the option buyer or holder has the RIGHT BUT NO OBLIGATION..., while the option writer HAS THE OBLIGATION... Therefore, the option buyer will EXERCISE HIS OPTION ONLY WHEN THE SITUATION IS FAVOURABLE TO HIM. On the other hand, the option writer is LEGALLY BOUND TO HONOUR THE CONTRACT WHENEVER THE OPTION BUYER DECIDES TO EXERCISE."

"An option, which gives the buyer/holder a RIGHT TO BUY the underlying asset, is called a CALL OPTION; and an option which gives the buyer/holder a RIGHT TO SELL the underlying asset, is called a PUT OPTION."

Option terminology

The chapter's two quotes as on 10 May 20XX, both with strike 18400, expiry 25 May 20XX, and underlying value 18315.10:

• Index option — "These options have a STOCK INDEX as the underlying asset. For example, options on Nifty, Sensex."
• Stock option — "These options have INDIVIDUAL STOCKS as the underlying. For example, option on ONGC, NTPC."
• Buyer — "one who has a RIGHT BUT NOT THE OBLIGATION... he pays a price called 'option premium'... He has a right to BUY the underlying asset in case of a CALL option and the right to SELL the underlying asset in case of a PUT option."
• Writer — "one who RECEIVES the option premium and is thereby OBLIGED to sell/buy the asset if the buyer exercises his right. He has a SELL obligation in case of a CALL option and a BUY obligation in case of a PUT option."
• American option — "can exercise his right AT ANY TIME ON OR BEFORE the expiry date/day."
• European option — "can exercise his right ONLY ON THE EXPIRY DATE/DAY of the contract. IN INDIA, ALL INDEX AND STOCK OPTIONS ARE EUROPEAN STYLE OPTIONS."
• Option premium — "the price which the option BUYER PAYS to the option SELLER... The premium mentioned here is for a SINGLE UNIT and to arrive at the TOTAL premium for the contract, we must MULTIPLY THIS PREMIUM WITH THE LOT SIZE."
• Spot price (S) — "the price at which the underlying asset is trading in the spot market."
• Strike price or Exercise price (X) — "the price per share for which the underlying security may be PURCHASED by the CALL option holder (or SOLD by the PUT option holder)."
• Exercise of options — "Option contracts traded on Indian exchanges are European style... buyers can exercise their options only at the time of MATURITY... All these options are exercised with respect to the SETTLEMENT VALUE/CLOSING PRICE of the stock on the day of exercise."
• Assignment of options — "the ALLOCATION OF EXERCISED OPTIONS TO ONE OR MORE OPTION SELLERS."

Opening and closing. An opening transaction "ADDS TO OR CREATES a new trading position" — an opening purchase is going long, an opening sale is going short. A closing transaction "REDUCES OR ELIMINATES an existing position by an appropriate OFFSETTING purchase or sale", also called "squaring off": a closing purchase reduces a short position ("frequently referred to as covering"), a closing sale reduces a long position.

And a warning worth underlining: "A trader does NOT close out a LONG CALL position by PURCHASING A PUT (or any other similar transaction). A closing transaction for an option involves the sale or purchase of an option contract WITH THE SAME TERMS, i.e., an option with the SAME STRIKE PRICE AND SAME EXPIRY DATE."

16.2 Contract specifications

"the exchange decides all terms and conditions (EXCEPT THE OPTION PREMIUM) for all exchange-traded index and stock options."

Contract size. "the number of units of the underlying asset in a contract... different for option contracts on different stocks and indices." With a Nifty lot of 50, the total premium is 124.50 × 50 = Rs 6,225 for the call and 177.60 × 50 = Rs 8,880 for the put.

Contract trading cycle. "Index options in India are available for a WIDER RANGE of expiration dates as compared to STOCK options. Option contracts on INDIVIDUAL STOCKS traded on the NSE follow a THREE-MONTH trading cycle."

For index options: "available for trading with WEEKLY AS WELL AS MONTHLY maturities. Index options can be traded for 4 SERIAL WEEKLY CYCLES, excluding the monthly near-, mid- and far-month expiries... Index options are also available for THREE QUARTERLY EXPIRIES (March, June, September and December cycle). The exchanges also make available LONG-TERM index options having 8 HALF-YEARLY EXPIRIES (following the June-December cycle) after the three quarterly expiries."

Expiration date. "The Nifty and Bank Nifty option contracts expire on the LAST TUESDAY of the expiry month (or, on the PREVIOUS TRADING DAY, if the last Tuesday is a trading holiday)." And the recent restriction: "As per recent SEBI Circular dated Oct 01, 2024, exchanges may provide derivatives contracts for ONLY ONE OF ITS BENCHMARK INDICES WITH WEEKLY EXPIRY. This will be effective from NOV 20, 2024. For ex. BSE can only offer weekly Index derivative contract EITHER on Sensex 30 OR Bankex."

Tick size. "the tick size for index contracts is 5 PAISA." For stocks: "NSE: The tick size for stocks trading BELOW ₹250 is 0.01 paisa and for stocks trading ABOVE ₹250 is 0.05 paisa... BSE: The usual tick size is 0.05 paisa but tick size is 0.01 for stocks trading BELOW ₹100." And why it matters: "A SMALL tick size allows for BETTER RISK MANAGEMENT because positions can be adjusted with small price movements. A LARGE tick size may require HIGHER MARGINS due to the potential for larger price fluctuations."

Final settlement price. "Unlike the futures contracts, THERE IS NO DAILY SETTLEMENT OF OPTIONS CONTRACTS. Also, since all exchange-traded index and stock options in India are European style, the exercise and assignment... is permitted ONLY ON THE EXPIRATION DATE. The final settlement price... is the CLOSING PRICE OF THE RELEVANT INDEX OR STOCK IN THE CASH SEGMENT on the last trading day."

Trading hours. "between 9.15 am and 3.30 pm from Monday to Friday."

BSE Sensex options

16.3 Moneyness

The ATM practicality: "because the strike prices are at FIXED INTERVALS of say, Rs 5, Rs 10 or Rs 50, while the spot price moves in MUCH SMALLER INCREMENTS, the two prices MAY RARELY BE EQUAL." The illustration: "if the index is at 18415 and three options... with strike prices of 18350, 18400 and 18450 are available, the option with the strike price of 18400 is an ATM option."

In the chapter's own quotes, with spot 18315.10 and strike 18400: "the PUT option is IN-THE-MONEY" and "the CALL option is OUT-OF-THE-MONEY."

16.4 Intrinsic value and time value

"The option premium... consists of TWO COMPONENTS - INTRINSIC VALUE and TIME VALUE."

"The INTRINSIC VALUE of an option refers to the amount by which the option is IN-THE-MONEY i.e., the amount an option buyer will realize, BEFORE ADJUSTING FOR PREMIUM PAID, if he exercises the option instantly. Therefore, ONLY IN-THE-MONEY OPTIONS HAVE INTRINSIC VALUE whereas at-the-money and out-of-the-money options have ZERO intrinsic value. THE INTRINSIC VALUE OF AN OPTION CAN NEVER BE NEGATIVE because an option holder is NOT BOUND TO EXERCISE an option if such exercise will result in a loss to him."

The chapter's figures: the put has an intrinsic value of 18400 − 18315.10 = Rs 84.90; the call has an intrinsic value of zero.

"TIME VALUE: It is the DIFFERENCE BETWEEN THE PREMIUM AND INTRINSIC VALUE, if any, of an option. ATM AND OTM OPTIONS HAVE ONLY TIME VALUE because the intrinsic value of such options is zero." So the put's time value is 177.60 − 84.90 = Rs 92.70, and "in the case of the call option, the ENTIRE option premium of Rs 124.50 represents TIME VALUE."

16.5 The four payoffs

Long option. "You have the RIGHT to exercise that option"; "Your potential loss is LIMITED TO THE PREMIUM AMOUNT you paid"; "Profit would depend on the LEVEL OF UNDERLYING ASSET PRICE at the time of exercise/expiry."

Short option. "Your MAXIMUM PROFIT is the PREMIUM RECEIVED"; "You can be ASSIGNED an exercised option any time during the life of option contract (in case of AMERICAN options). All option writers should be aware that ASSIGNMENT IS A DISTINCT POSSIBILITY"; "Your potential loss is THEORETICALLY UNLIMITED."

Long call — strike 17500, premium 95, index at 17562

"If the index closes at 17400, you will NOT exercise... Why will you buy something at 17500 when you can have the same thing at 17400?... your loss will be equal to the premium."

"If the index were to close at 17595, the option will expire in-the-money... you will receive a payoff of Rs 95... but you have already paid an equal amount..., making your net gain equal to ZERO. Hence, 17595 is the BREAK-EVEN POINT (BEP)... A general formula for calculating BEP for CALL options is STRIKE PRICE PLUS PREMIUM (X + P)."

At 18000: "you will receive a payoff of Rs 500... But since you have already paid Rs 95..., your actual profit would be Rs 500 – Rs 95 = Rs 405."

"The contract value for an index option with lot size of 50 and strike of 17500 is Rs 8,75,000. The MAXIMUM LOSS for such an option buyer would be equal to Rs 95 × 50 = Rs 4,750... A long call position helps you to LIMIT YOUR LOSS to a maximum of Rs 4,750 WITH POTENTIALLY UNLIMITED PROFIT."

And on margin: "As a call option buyer, you NEED NOT PAY ANY MARGIN to the Exchange because your PAYMENT OBLIGATION IS RESTRICTED TO THE OPTION PREMIUM that you have already paid."

Short call — the mirror image

"if the maximum loss for a long call position is equal to the premium paid, it automatically means that the MAXIMUM GAIN FOR THE SHORT CALL POSITION WILL BE EQUAL TO THE PREMIUM RECEIVED. Similarly, if maximum gain for long call position is unlimited, then the MAXIMUM LOSS FOR THE SHORT CALL POSITION MUST BE UNLIMITED."

"BEP for a short call position will ALSO be equal to X + P. BEP IS INDEPENDENT OF POSITION (LONG OR SHORT), IT IS INSTRUMENT SPECIFIC (CALL OPTION)."

And the margin asymmetry: "Although the call seller receives a premium initially..., HE MUST PAY A MARGIN to the Exchange on the short position. This is because the option seller HAS AN OBLIGATION and since his LOSSES CAN BE UNLIMITED, HE CAN BE A POTENTIAL RISK FOR THE STABILITY OF THE SYSTEM."

Long put — strike 17500, premium 150

"You hold the right to SELL the index at 17500... You will do so ONLY WHEN THE INDEX IS AT A LEVEL LOWER THAN THE STRIKE PRICE... The maximum loss... will be equal to the premium already paid i.e., Rs 150."

"What can be the maximum profit? Theoretically, THE INDEX CAN FALL ONLY TILL ZERO. So, the maximum profit will be achieved when the index closes at zero... The profit in this case will be Rs 17,500, but since you have already paid Rs 150..., your net profit will be Rs 17,350."

"A margin is paid ONLY IF THERE IS ANY OBLIGATION. An option buyer (either buyer of a call option or a put option) HAS NO OBLIGATION."

Short put

"the gain of the put seller is FIXED at Rs 150, the premium received initially. However, the short put position starts making losses as the index dips below 17350, which is the break-even point. The seller of the put option receives the premium but HE IS REQUIRED TO PAY A MARGIN on his position as he has an OBLIGATION to deliver the underlying asset and HIS LOSSES CAN BE HUGE."

The risk and return table