Call option
Also written Call option (on a bond) · Call · Long call · Call contract · Right to buy
A contract giving its buyer the right, but never the obligation, to buy the underlying at a fixed strike price — so the loss is capped at the premium and the gain is not.
In plain language
A call option is a booking, not a purchase.
You pay a fee today for the right to buy something at an agreed price on an agreed date. If the thing turns out to be worth more than the agreed price, you take it and pocket the difference. If it is worth less, you walk away and lose only the fee.
The NISM workbook opens Chapter 4 with exactly this picture: Mr X pays Rs 50,000 today for the right — three months from now — to buy a piece of land at Rs 10,00,000. If the infrastructure project arrives and the land is worth Rs 15 lakh, he pays Rs 10 lakh and takes it. If the news was a rumour, he walks; Mr Y keeps the Rs 50,000.
That asymmetry is the whole instrument. The buyer has a right with no obligation. The seller — the writer — has an obligation with no right, and the premium is what he is paid to accept it.
How it works
On a government security the call buyer is taking a view that prices will rise, which on a bond means a view that yields will fall. Get the direction of that translation wrong and every answer in the chapter comes out backwards.
At expiry only one comparison matters. If the spot price of the underlying bond is above the strike, the call is in the money and is exercised. If it is at or below the strike, it lapses and the buyer loses the premium — nothing more.
Before expiry the premium is two things added together: intrinsic value, the amount by which the option is already in the money, and time value, the market's price for the chance that it gets further in. Time value only ever falls, which is why an option is called a wasting asset and why, in the workbook's words, the option seller is at a fundamental advantage.
Exchange-traded interest rate options in India are European and premium-style: the premium is paid up front, and the right can only be exercised on the expiry day. A buyer who wants out earlier sells the contract back into the market instead.
The formula
Intrinsic value of a call = max(Spot − Strike, 0)
Time value = Premium − Intrinsic value
Buyer pay-off at expiry = max(S − X, 0) − P
Writer pay-off at expiry = P − max(S − X, 0)
Break-even at expiry = X + P (same for buyer and writer)
One lot of an exchange-traded interest rate option is notional bonds of face value Rs 2,00,000 — 2,000 units — so every per-100 figure above becomes rupees when multiplied by 2,000.
A worked example
The workbook's own trade. On 1 October 2021, 6.10% GOI 2031 is trading at Rs 98.40. You buy the 98.50 call at a premium of Rs 0.20, expiring 28 October 2021. One lot = 2,000 units.
Cash out on day one: 0.20 × 2,000 = Rs 400. That is the entire risk of the position.
Break-even = 98.50 + 0.20 = Rs 98.70.
| Bond price at expiry | Intrinsic (B) | Buyer pay-off per 100 | Buyer per lot | Writer per lot |
|---|---|---|---|---|
| 98.20 | 0.00 | −0.20 | −Rs 400 | +Rs 400 |
| 98.50 | 0.00 | −0.20 | −Rs 400 | +Rs 400 |
| 98.60 | 0.10 | −0.10 | −Rs 200 | +Rs 200 |
| 98.70 | 0.20 | 0.00 | Rs 0 | Rs 0 |
| 98.90 | 0.40 | +0.20 | +Rs 400 | −Rs 400 |
| 99.50 | 1.00 | +0.80 | +Rs 1,600 | −Rs 1,600 |
| 100.00 | 1.50 | +1.30 | +Rs 2,600 | −Rs 2,600 |
Read the last two columns together: they are the same number with opposite signs. The buyer's maximum loss is Rs 400 and his gain has no ceiling; the writer's maximum gain is Rs 400 and his loss has no ceiling. Options are a zero-sum transfer between the two.
On cash settlement the buyer receives only the profit amount. At Rs 98.90 he is paid the intrinsic value of 0.40 × 2,000 = Rs 800, against the Rs 400 already spent — a net Rs 400.
Intraday, using delta. The workbook's second call: 6.10% GOI 2031 at Rs 98.80 at 9:30 a.m., the 98.50 call quoted at Rs 0.45 with a delta of +0.55. If the bond reaches Rs 99.00 by 3 p.m., the bond has moved 0.20, so the premium is expected to move 0.20 × 0.55 = 0.11, to Rs 0.56. If it falls to Rs 98.60 instead, the premium falls by the same 0.11, to Rs 0.34.
Why NISM asks about it
Chapter 4 (Exchange Traded Interest Rate Options) builds the whole paper on this contract: section 4.1 for the terminology, 4.4 for moneyness, 4.5 for the five pricing factors and the Greeks, 4.8.1 and 4.8.2 for the long and short call pay-off tables the example above reproduces.
The questions that come from it are mechanical and they recur: compute the break-even, state the maximum loss per lot rather than per unit, fill in the moneyness table, and read the direction table — spot up, call up; strike up, call down; volatility up, call up; time longer, call up; interest rates up, call up.
Common exam traps
- A call is in the money when the strike is below the spot. The workbook's table is worth memorising in that direction, because the put is the mirror and candidates routinely swap them under time pressure.
- Maximum loss is per lot, not per unit. Rs 0.20 of premium is Rs 400 of money, because the lot is 2,000 units of Rs 100 face value.
- Break-even is a property of the instrument, not of the side. Both the buyer and the writer break even at X + P; only the sign of the pay-off differs.
- Buying a call on a G-sec is a bet that yields fall. Bond prices and yields move in opposite directions, so "bullish" on the bond means "bearish" on the rate.
- Higher interest rates raise a call's value and lower a put's — the one pricing factor that pushes the two in opposite directions. Volatility and time to expiry raise both.
- Indian exchange-traded interest rate options are European and cash settled. There is no early exercise to consider; you square off instead, as in the workbook's 4.8.5 illustration.
- The writer posts margin; the buyer does not, having paid the premium up front. That is why "premium style" appears in the contract specification.
Where this is taught
- Series XII · Chapter 6: Derivative Marketsintroduced here
- Series IV · Chapter 1: Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Marketsintroduced here
- Series XVI · Chapter 4: Commodity Optionsintroduced here
- Series XXI-B · Chapter 5: Derivativesintroduced here
- Series VI · Chapter 11: Special Services - Debt Instruments & Government Securitiesintroduced here
- Series V-D · Chapter 21: Exchange Traded Interest Rate Optionsintroduced here
- Series XXI-A · Chapter 5: Derivativesintroduced here
- Series VIII · Chapter 4: Introduction to Optionsintroduced here
- Series IV · Chapter 4: Exchange Traded Interest Rate Options
Related terms
- Intrinsic valueWhat an asset is actually worth — the present value of the cash it will generate over its remaining life, as against whatever price the market is quoting today.
- Break-even pointThe level of the underlying at which a position makes neither profit nor loss — for a bought call, strike plus premium; for a bought put, strike minus premium.
- DeltaThe change in an option's premium for a one-rupee change in the underlying — the first and most used Greek, and the hedge ratio that says how much underlying to hold against an option position.
- Implied volatilityThe volatility figure that, put into an option pricing model, reproduces the option's actual market price — the market's consensus forecast of how much the underlying will move.
- MoneynessWhether exercising an option right now would give the buyer a positive, zero or negative cash flow — classifying it as in the money, at the money or out of the money.
- OptionA contract giving the buyer the right, but not the obligation, to buy or sell the underlying at a stated price on or before a stated date, in exchange for a premium paid to the writer.
- Strike priceThe price fixed in an option contract at which the buyer may buy (call) or sell (put) the underlying if he chooses to exercise — fixed for the life of the contract, unlike the premium.
- Time valueThe part of an option premium that is not intrinsic value — what the buyer pays for the possibility that the underlying moves further in his favour before expiry. It falls to zero on expiry day.
- Option premiumThe price an option buyer pays the seller for the right the contract carries — non-refundable, and made up of intrinsic value plus time value.
- Put optionA contract giving its buyer the right, but never the obligation, to sell the underlying at a fixed strike price — insurance against a fall, bought for a premium.
- Wasting assetAn option, whose time value shrinks towards zero every day it is held and is worth nothing at expiry — so an option buyer loses money simply from the passage of time.
- SwaptionAn option on a swap — the right, not the obligation, to enter an interest rate swap at a predetermined strike rate on a future date, bought for a premium.
- Interest Rate CapA series of interest rate call options, called caplets, that pays the buyer at the end of each period in which the underlying interest rate is above the strike rate agreed in advance.
- Bermudan optionAn option that can be exercised only on specific dates named in the contract, usually near expiry — more flexible than a European option, less flexible than an American one.
- Asymmetric risk exposureThe defining pay-off feature of options: gains when the underlying moves one way differ sharply from losses when it moves the other way. Futures, by contrast, have symmetric exposure.
- ExercisePutting an option's right into effect: a call holder buys the underlying at the strike, a put holder sells at the strike. In cash settled IRD options the holder simply receives the difference.
- Intrinsic and time valueThe two components of an option's premium — intrinsic value, the amount the option is currently in the money by, and time value, the extra a buyer pays for the chance the option becomes more valuable before expiry.
- Vertical spreadTwo options of the same type and the same expiry but different strikes, one bought and one sold — a limited-profit, limited-loss position that trades away part of the upside to cut the cost or cap the risk.
- Covered callHolding the underlying in the cash market and writing a call against it — a way of earning premium income from a holding, at the cost of capping the gain above the strike.
- Put-call parityThe arbitrage-free relationship binding a European call and put of the same strike and expiry to the spot and the discounted strike: c + X·e^(−rt) = p + S. Deviations create risk-free profit.
- Put-Call RatioPut open interest (or volume) divided by call open interest on the same underlying, read as a contrarian sentiment gauge: below 1 is taken as bearish, above 1 as bullish.
- Currency optionAn option giving the buyer the right, but not the obligation, to buy or sell an agreed amount of one currency against another at a specified exchange rate, on or before a specified future date.
- Protective callBuying a call option to hedge a foreign currency payable: it caps the purchase rate at strike plus premium, while leaving the importer free to benefit if the currency falls.
- CollarAn options strategy extending a covered call: hold the stock, sell a call above the price and buy a put below it, putting a floor under losses in exchange for a lower cap on profits.
- Asymmetric payoffA payoff where gains when the underlying moves one way differ sharply from losses when it moves the other — the defining feature of options, as against the symmetric, linear payoff of futures.
- Delta hedgingOffsetting an option position's delta with the underlying or futures so the combined delta is zero, then buying or selling as delta changes to keep it there — the option trader's way of managing risk.
- WarrantAn option issued by a company giving the holder the right, not the obligation, to subscribe to its shares at a fixed price on or after a set date. SEBI requires 25 per cent of the price upfront.
- European optionAn option that can be exercised only on its expiry date. Indian equity options are European — coded CE for calls and PE for puts — unlike American options, exercisable any time up to expiry.