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Unit study guide · NISM Series IV

Exchange Traded Interest Rate Options

22 questions in this unit

What this unit covers

Key ideas

From the practice bank · 1

A European put is written on a government bond’s price with strike 100. What right does the put buyer obtain under the contract’s exercise and settlement terms?

A put gives its holder a sale right at the , or the equivalent cash payoff for a cash-settled contract. For a bond-price put, at is max(strike − bond price, 0). The premium purchases that right. It is separate from the exercise value. Remember: A put’s direction is determined by the specified underlying price.

Hint Common mistake: Mixing option ownership with ownership of the referenced bond.

IV-061

From the practice bank · 2

An exchange-traded bond option is European style. Which statement is correct?

European describes when an option may be exercised. It does not mean the holder must keep the position until expiry: an offsetting sale may close it earlier if the market allows execution. Trading and exercise style must therefore be analysed separately. Remember: Exercise, closing a position and expiry are not interchangeable concepts.

Hint Common mistake: Treating European style as a prohibition on selling the option.

IV-062

From the practice bank · 3

A bond-price call has strike 101 and the underlying bond price is 102. The buyer originally paid premium 1.50. How is the call classified by moneyness?

The call’s intrinsic value is 102 − 101 = 1, so it is . If these were expiry values, the buyer would still lose 0.50 after the 1.50 premium. An option can be in the money without its buyer earning a net profit. Remember: Moneyness describes intrinsic value, not the owner’s realised profitability.

Hint Common mistake: Including the original premium in the moneyness test.

IV-063

From the practice bank · 4

A bond trades at 99.20. A put with strike 100 has a premium of 1.10 per unit. Its intrinsic value and residual time value are:

Put intrinsic value = max(K − S, 0) = 0.80. Residual = premium − intrinsic = 1.10 − 0.80 = 0.30. Time value reflects the value of future possibilities and other model inputs before expiry. It is not an additional exercise receipt on top of the full premium. Remember: Decompose premium into intrinsic value and the residual rather than double-counting them.

Hint Common mistake: Assuming an in-the-money option has no time value.

IV-064

From the practice bank · 5

A bond-price call has strike 100 and premium 0.60 per unit. The expiry settlement price is 101.40 and the contract multiplier is 2,000. Ignoring costs, what is the buyer’s net profit on one contract?

Call exercise payoff = max(101.40 − 100, 0) × 2,000 = ₹2,800. Premium outflow = 0.60 × 2,000 = ₹1,200. Net profit = ₹1,600. Premium financing and transaction charges are excluded explicitly, so they must not be invented in the calculation. Remember: An option payoff is not the same as profit after premium.

Hint Common mistake: Reporting gross exercise proceeds as the buyer’s net gain.

IV-065

From the practice bank · 6

A writer sells a bond-price put with strike 100 and receives premium 0.90 per unit. The bond settles at 98 at expiry. What is the writer’s net result per unit, excluding costs?

For the put writer, net P/L = premium − max(K − S_T, 0). Here 0.90 − max(100 − 98, 0) = −1.10. The writer’s maximum premium income is earned only when the option expires without an exercise liability. Collecting premium is not evidence that the position is safe. Remember: Writer profit reverses the buyer’s payoff and includes the premium received.

Hint Common mistake: Treating premium received as profit before accounting for the exercise obligation.

IV-066

From the practice bank · 7

A bond-price call has delta +0.60. The bond price rises by 0.20. Holding other inputs constant and using only the delta approximation, what premium change is expected?

Locally, Δoption value ≈ × Δunderlying price. The expected change is +0.60 × 0.20 = +0.12 per quoted unit. Delta itself can change as the market moves, and changes in volatility, time and other inputs can also affect the actual premium. Remember: Delta is a local slope, not a fixed lifetime hedge ratio.

Hint Common mistake: Treating a first-order estimate as an exact repricing for any market move.

IV-067

From the practice bank · 8

A call’s delta is 0.45 and gamma is 0.08 per one-unit change in underlying bond price. If the bond price rises by 0.50, what is the approximate new delta, using constant gamma?

measures the local change in delta for a change in the underlying. New delta ≈ 0.45 + 0.08 × 0.50 = 0.49. This is another local approximation: gamma need not remain constant over a large move, so a position hedged at the original delta can require rebalancing. Remember: Gamma explains why a delta-neutral option position need not stay delta-neutral.

Hint Common mistake: Using gamma as a direct premium change rather than a change in delta.

IV-068

From the practice bank · 9

An option has vega 0.12 per one percentage-point change in implied volatility. If implied volatility rises from 10% to 12%, what is the vega-only premium change?

The volatility change is 12% − 10% = 2 percentage points. With vega quoted per point, the estimated premium change is 0.12 × 2 = 0.24. The wording of vega’s unit matters. Multiplying by 0.02 would understate the result by a factor of 100. Remember: Always inspect whether volatility sensitivities use decimal volatility or percentage points.

Hint Common mistake: Confusing a two-percentage-point increase with a 2% relative change.

IV-069

From the practice bank · 10

A long bond option’s theta is quoted as −0.03 premium units for each calendar day elapsed. With all other inputs unchanged and constant theta, what is the three-day estimated premium change?

The question defines theta as value change per day elapsed, so Δpremium ≈ −0.03 × 3 = −0.09. Some texts use different mathematical time variables, which can reverse a derivative’s displayed sign. The explicit convention here governs. Actual theta changes as expiry approaches, so the estimate is local. Remember: Time-decay calculations require a stated sign and day convention.

Hint Common mistake: Assuming every text defines theta with the same time variable.

IV-070

From the practice bank · 11

An analyst solves an option-pricing model for the volatility input that reproduces the observed option premium. What is being estimated?

Implied volatility is inferred by matching a model to the observed premium while holding its other inputs specified. Historical volatility instead summarises past variation. Differences between them can reflect expectations, risk pricing and model assumptions. A fitted implied volatility is not a guaranteed realised path. Remember: Identify whether volatility is measured from returns or inferred from option prices.

Hint Common mistake: Treating a volatility figure taken from option prices as a direct observation of the future.

IV-071

From the practice bank · 12

In a one-period model, a bond price is 100 and ends at either 110 or 90. A call has strike 100. The risk-free growth factor is 1.02 and there are no intervening payments. What is the no-arbitrage call value?

The replicating risk-neutral probability is q = (100×1.02 − 90)/(110 − 90) = 0.60. Terminal call payoffs are 10 and 0, so current value = [0.60×10 + 0.40×0]/1.02 = 5.88235. The probability is a pricing weight, not an asserted real-world likelihood of the up move. Remember: Risk-neutral valuation discounts a replicating expected payoff, not a subjective forecast.

Hint Common mistake: Using a 50–50 probability simply because the model has two states.

IV-072

From the practice bank · 13

For European options on a bond with no coupon before option expiry, the bond price is 100, present value of strike is 97 and call premium is 5. Assuming frictionless put–call parity, the matching put premium is:

For the stated no-interim-income European setting, C + PV(K) = P + S. Therefore P = C + PV(K) − S = 5 + 97 − 100 = 2. A coupon during the option’s life requires an income adjustment, so the no-coupon assumption is essential. Remember: Use a parity formula consistent with exercise style and interim cash flows.

Hint Common mistake: Applying a no-income parity formula to a coupon-paying period without adjustment.

IV-073

From the practice bank · 14

A non-coupon-paying bond over the option horizon has price 104. The present value of a European call’s strike is 100. Under frictionless no-arbitrage assumptions, which is the call’s lower bound?

A call plus enough risk-free cash to pay the strike cannot be worth less than the underlying in the stated no-income setting. Hence C ≥ S − PV(K), together with C ≥ 0. The lower bound is 4. It is not necessarily the actual premium because optionality may add value. Remember: A no-arbitrage bound is a constraint, not a complete pricing model.

Hint Common mistake: Reporting the lower bound as the exact option premium.

IV-074

From the practice bank · 15

A bond price rises modestly, yet a long call premium falls. Which explanation is consistent with option valuation?

Delta describes the effect of an underlying move with other inputs held constant. In actual trading, time passes and implied volatility can fall. Their negative effects may exceed the benefit from a small bond-price increase. This is especially important when an option is bought at an elevated implied volatility. Remember: Do not infer a Greek from total price movement while ignoring other changing inputs.

Hint Common mistake: Assuming a correct directional view guarantees a profitable option purchase.

IV-075

From the practice bank · 16

One bond option covers 2,000 units of ₹100 face value. Its premium is 0.35 per unit. What is the premium outlay for four contracts, excluding charges?

Premium is quoted per unit, so multiply by the contract’s unit multiplier and quantity: 0.35 × 2,000 × 4 = ₹2,800. The corresponding face notional is ₹8,00,000, a different measure. Buying the option does not require paying full face notional simply because that amount determines exposure. Remember: Quote units determine the option cash premium.

Hint Common mistake: Confusing option premium, face notional and exercise cash flow.

IV-076

From the practice bank · 17

A purchased cash-settled call expires out of the money. It was held without any separate leveraged position, and all premium was paid upfront. Ignoring charges, what is the buyer’s loss on the option itself?

For a fully paid long call, net expiry P/L is max(S_T − K, 0) minus premium. If the option expires out of the money, the first term is zero, so the loss is the premium. This limited-loss statement applies to the option itself, not to an unrelated financed portfolio or an option writer. Remember: Limited loss still means the entire premium can be lost.

Hint Common mistake: Mistaking no exercise for a premium refund.

IV-077

From the practice bank · 18

A company needs protection for an unusual notional amount and an exact payment date unavailable in listed bond options. What is the central exchange-versus-OTC trade-off?

Exchange products pool trading in standard terms. Bespoke OTC products can align specific dates, amounts and references. The better contractual match must be weighed against pricing, liquidity, credit support and documentation. The question is about a trade-off, not a universal claim that either market is always superior. Remember: Compare economic fit and implementation risks together.

Hint Common mistake: Choosing an OTC or exchange label without analysing the actual exposure match.

IV-078

From the practice bank · 19

For plain vanilla bond-price options under conventional smooth pricing models, which position normally has positive gamma?

Gamma measures how delta changes as the underlying moves. Long vanilla calls and puts are convex in underlying price, so their gamma is normally positive. Their delta signs differ, but gamma signs do not. Shorting the options reverses gamma and creates an exposure that can become more adverse as the underlying moves. Remember: Delta direction and gamma sign describe different properties of an option.

Hint Common mistake: Assuming a negative-delta long put must also have negative gamma.

IV-079

From the practice bank · 20

CASE O: A European bond-price put has strike 101, premium 0.80 and multiplier 2,000. At expiry the settlement reference is 99.50. What is the gross exercise receipt for the buyer?

Put exercise value is max(K − S_T, 0) × multiplier. Here it is 1.50 × 2,000 = ₹3,000. The ₹1,600 premium was a separate acquisition cost, so the net profit would be ₹1,400, but that is not the measure requested. This distinction is important when reconciling settlement receipts and trade P/L. Remember: Label exercise cash flow and net P/L separately.

Hint Common mistake: Subtracting premium when the question asks specifically for gross settlement.

IV-080

From the practice bank · 21

CASE O: A European bond-price put has strike 101, premium 0.80 and multiplier 2,000. Ignoring costs and financing, at which expiry bond price does the buyer break even?

For an in-the-money put, net P/L per unit = K − S_T − premium. Set this to zero: S_T = 101 − 0.80 = 100.20. The multiplier scales both premium and payoff equally, so it does not change the break-even underlying price. Remember: A put buyer needs the underlying below strike minus premium to profit at expiry.

Hint Common mistake: Using the strike itself as the premium-inclusive break-even.

IV-081

From the practice bank · 22

CASE O2: A desk owns 20 bond puts. Each contract covers 2,000 units and each put’s delta is −0.35 per unit. What is the portfolio delta expressed in underlying bond units?

Aggregate delta = contracts × units per contract × option delta = 20 × 2,000 × (−0.35) = −14,000 underlying units. This is a local sensitivity equivalent, not legal ownership of negative 14,000 bonds. If bond-price delta changes, the equivalent exposure changes too. Remember: Aggregate option delta using both contract count and multiplier.

Hint Common mistake: Reporting contract count as though each contract represented only one underlying unit.

IV-082

Read the related lesson

Strike Price

The strike price is the level at which an option can be exercised.

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Intrinsic Value

Intrinsic value is the part of an option's premium that would survive if the contract expired at this instant.

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Expiry Day

Expiry day is the last day on which a derivative contract can be traded.

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Liquidity

Liquidity describes how easily a given quantity can be traded.

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Moneyness (ITM, ATM, OTM)

Moneyness describes where an option's strike sits relative to the current level of the underlying.

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Time Value

Time value is the part of an option's premium that is left after intrinsic value is taken out.

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Delta

Delta is the rate at which an option's premium changes for a one-unit change in the underlying.

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Gamma

Gamma is the rate at which an option's delta changes as the underlying moves.

Read more