Option premium

In plain language

How it works

Premium = Intrinsic value + Time value

The formula

Premium = Intrinsic value + Time value

Intrinsic value of a call = max(Spot - Strike, 0)
Intrinsic value of a put  = max(Strike - Spot, 0)
Time value                = Premium - Intrinsic value

A worked example

Intrinsic value = 1,280 - 1,170 = Rs 110
Time value      = 200 - 110     = Rs  90

Why NISM asks about it

Common exam traps

Check yourself

1. 1.A commodity call option has a strike price of Rs 1,000, the current market price of the underlying commodity futures is Rs 1,150, and the option premium is Rs 200. What is its time value?

   1. a)Rs 150
   2. b)Rs 100
   3. c)Rs 50
   4. d)Rs 200
   Show the answer

   Answer: (c) Rs 50

   (This is a sample question from the NISM workbook.)

   Premium = Intrinsic Value + Time Value

   • Intrinsic value of a call = S − X = 1,150 − 1,000 = Rs 150
   • ⚠️ Time value = Premium − Intrinsic value = 200 − 150 = Rs 50

   Option (a) Rs 150 is the intrinsic value offered as if it were the answer, and option (d) Rs 200 is the whole premium — so read carefully which of the three quantities the question wants.

   The rules that constrain these two components:

   • Only in-the-money options have intrinsic value; at-the-money and out-of-the-money options have zero intrinsic value
   • The intrinsic value of an option cannot be negative — because no one would like to exercise his right under a no-advantage condition
   • ATM and OTM options will have only time value

   And the deeper split worth remembering: of the five pricing determinants, underlying price and strike price create intrinsic value, while volatility, time to expiry and interest rate create time value.

2. 2.Assuming all other factors remain constant, which statement is TRUE regarding the relation between interest rates and option premium?

   1. a)Higher interest rates will decrease the value of both call and put options
   2. b)Higher interest rates will increase the value of both call and put options
   3. c)Higher interest rates will increase the value of a call option and decrease the value of a put option
   4. d)Higher interest rates will decrease the value of a call option and increase the value of a put option
   Show the answer

   Answer: (c) Higher interest rates will increase the value of a call option and decrease the value of a put option

   (This is a sample question from the NISM workbook.)

   "High interest rates will increase the value of a call option and a decrease in the value of a put option."

   This sensitivity is measured by Rho — the change in option price given a one percentage point change in the risk-free interest rate. An increase in interest rate increases the call option price but reduces the put option price. Similarly, a reduction in interest rate increases the put option price but reduces the call option price.

   This is the row of the determinants table most often guessed wrong, so it is worth having a reason rather than a memory. A call buyer has locked in a purchase price he will pay later — the higher the interest rate, the more that deferral is worth. A put buyer has locked in a sale price he will receive later — the higher the rate, the more that delay costs him.

   The full table:

   Factor rises	Call	Put
   Price of underlying	Rises	Falls
   Strike price	Falls	Rises
   Time to expiry	Rises	Rises
   Volatility	Rises	Rises
   Interest rate	Rises	Falls

   Only volatility and time move both premiums the same way — which is what makes options (a) and (b) tempting.

3. 3.Silver futures at Rs 60,000 with the Rs 60,000-strike call at Rs 3,500; at Rs 63,000 the premium is Rs 6,100 and at Rs 66,000 it is Rs 8,800. What are Delta at these two moves and Gamma between them?

   1. a)Delta 0.867 and 0.90; Gamma 0.00001
   2. b)Delta 0.90 and 0.867; Gamma 0.001
   3. c)Delta 2,600 and 2,700; Gamma 0.033
   4. d)Delta 0.05 and 0.10; Gamma 0.00001
   Show the answer

   Answer: (a) Delta 0.867 and 0.90; Gamma 0.00001

   • At Rs 63,000: (6,100 − 3,500) / 3,000 = 2600/3000 = ⚠️ 0.867
   • At Rs 66,000: (8,800 − 6,100) / 3,000 = 2700/3000 = ⚠️ 0.90

   ⚠️ Gamma = (0.867 − 0.900) / (−3000) = 0.00001, i.e. 0.001%

   Read what the two deltas are telling you. As the call moved deeper into the money, delta rose from 0.867 towards 1 — the option began behaving more and more like the underlying itself. Gamma is the speed of that transition: it "signifies the speed with which an option will go either in-the-money or out-of-the-money due to a change in price of the underlying asset." It is "the second derivative option with regard to price of the underlying asset."

   Option (c) is the trap for anyone who forgets to divide — Rs 2,600 and Rs 2,700 are the raw premium changes, not deltas. Option (b) reverses the order, which matters because delta rises as a call goes deeper ITM.

   Delta signs to carry into the exam: call buyer POSITIVE (like a long or bull position), call seller NEGATIVE, put buyer NEGATIVE (like a short or bear position), put seller POSITIVE — the seller's figure always the same magnitude with the opposite sign.

Where this is taught

• Series XXI-B · Chapter 5: Derivativesintroduced here
• Series XVI · Chapter 1: Introduction to Commodity Marketsintroduced here
• Series XII · Chapter 6: Derivative Marketsintroduced here
• Series IV · Chapter 4: Exchange Traded Interest Rate Optionsintroduced here
• Series VIII · Chapter 4: Introduction to Optionsintroduced here
• Series V-D · Chapter 21: Exchange Traded Interest Rate Optionsintroduced here
• Series XVI · Chapter 4: Commodity 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.
• Call optionA 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.
• 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.
• 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.
• 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.
• Off-Balance Sheet ExposureExposure a fund takes through leverage and derivative contracts to assets that are not its direct obligation — only margin and premium show in the books, but the fund bears the full risk and return.
• 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 FloorA series of interest rate put options that pays the buyer at the end of each period in which the underlying interest rate is below the strike rate — protection against falling rates.
• 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.
• 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.
• Commodity Transaction TaxA transaction tax on non-agricultural commodity derivatives — 0.01% on the sale of a futures contract, paid by the seller, with separate rates for options.
• Pay-offThe profit or loss on a position at expiry, stated as a function of the settlement price — positive when the trade makes money, negative when it loses.
• Short Option Minimum MarginThe SPAN-computed margin charged to the writer of a commodity option, floored by SEBI-prescribed minimum volatility scan ranges so that a cheap option cannot be written on a trivial margin.
• Black-76 modelThe variant of the Black-Scholes model used to price Options on Futures, which substitutes the futures price F for the spot price and discounts the whole payoff at e^(-rT).
• Covered short putWriting a put option while holding enough funds to buy the commodity if the put is exercised — a premium-earning strategy, as opposed to a naked short put written without the funds.
• 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.
• 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.
• At-the-moneyAn option whose strike price is closest to the spot price, so exercising it immediately would produce neither a gain nor a loss — the strike where the whole premium is time value and uncertainty peaks.
• Out-of-the-moneyAn option that would produce a negative cash flow if exercised immediately — a call with the spot below the strike, or a put with the spot above it. Its intrinsic value is zero and its premium is all time value.
• Time decayThe steady loss of an option's time value as expiry approaches — the reason options are called wasting assets and the reason the workbook says option sellers hold a structural advantage.
• RhoThe option Greek that measures interest rate sensitivity — the change in an option premium for a one percentage point change in the risk-free rate. It is positive for calls and negative for puts.
• Historical volatilityVolatility measured backwards — the standard deviation of the underlying's past percentage price changes, as against implied volatility, which is worked out forwards from the option price.
• 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.
• Short speculatorA speculator who sells a commodity futures contract first, expecting to buy it back later at a lower price — profiting from a price fall with no intention of ever taking or giving physical delivery.
• Swap exposure ruleThe workbook's mapping of directional commodity price exposure in a fixed-for-floating swap — fixed price payer long, fixed price receiver short, floating price payer short, floating price receiver long.
• Futures carry effectThe reason a call on futures carries more intrinsic value than a call on goods, while a put on goods carries more than a put on futures — because before expiry the futures price sits above the spot price.
• InsuranceThe risk-management approach that pays an explicit upfront premium to remove the downside while keeping the upside — which in derivatives means buying an option rather than selling a future.
• 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.
• Horizontal spreadTwo options of the same type and the same strike but different expiries — a position whose entire value is the difference between the two legs' time values, not a view on direction.
• Diagonal spreadTwo options of the same type on the same underlying with both a different strike and a different expiry — the most complicated of the three spread families, and the only one that varies on both axes.
• Black-Scholes modelA 1973 closed-form option pricing model using spot, strike, volatility, time to expiry and the risk-free rate; Indian exchanges use it for the theoretical price of exchange-traded currency options.
• Margin on consolidated crystallized obligationPart of initial margin that blocks a client's net payable from closed-out futures profit or loss and option premium intraday, and all settlement obligations at end of day, until settlement.
• 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.
• Contingent cash flowA foreign currency receipt or payment that may not happen at all — an unconfirmed order or an unsuccessful bid — for which the workbook prefers bought options to futures, because the loss is capped at the premium.
• 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.
• Index futures and options horizonsThe workbook comparison of how long an index derivative can be held against how long an index fund can be held: a few days to a maximum of 3 months, against a lifetime.
• 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.
• LeverageControl of a large contract value for a small upfront outlay — premium for an option buyer, margin for a futures position — which multiplies percentage gains and percentage losses by the same factor.
• Securities Transaction TaxA central government tax collected by the exchange on the sell side of every futures and option trade — 0.05% of futures traded value, 0.15% of option premium, and 0.15% of settlement price on exercise.
• American optionAn option whose holder may exercise it at any time on or before expiry. All exchange-traded index and stock options in India are European style instead — exercisable only on expiry.
• 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.
• Premium marginA margin charged at client level on option buyers equal to the premium they owe the clearing corporation, levied until the premium settlement pay-in is complete.
• 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.
• 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.