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NCFM Options Trading Strategies study materials
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NCFM Options Trading Strategies practice questions

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Question 1Options fundamentals and contract specifications

On the NSE F&O segment, what does the lot size of an index option contract represent?

  1. The minimum number of units of the underlying index to which one contract is linked Correct answer.
  2. The rupee value of margin blocked per contract by the exchange
  3. The maximum number of contracts a single client may buy in a day
  4. The number of trading days remaining until the contract expires

Explanation

Lot size is the contract multiplier fixed by the exchange, defining how many units of the underlying one contract covers. For index options it is a notional quantity of the index, not a margin figure or a trading limit. Position limits and margins are separate parameters notified by the exchange.

Question 2Options fundamentals and contract specifications

An index option contract on the NSE expires on which day under the current weekly and monthly cycle?

  1. A day fixed by the exchange and notified in the contract specifications Correct answer.
  2. The first Monday after the expiry month ends
  3. The last trading day of the expiry month
  4. The last Thursday of the expiry month

Explanation

The exchange notifies the expiry day for each contract in its contract specifications, and this has been revised over time, so the exact weekday must be taken from the current circular rather than assumed. Expiry is tied to a notified trading day, not automatically to month-end. Candidates should always confirm the prevailing rule from NSE circulars.

Question 3Options fundamentals and contract specifications

A trader buys one NIFTY call option. Which right does the buyer hold?

  1. The right to buy the index at the strike on or before expiry Correct answer.
  2. The right to sell the index at the strike on or before expiry
  3. The obligation to sell the index at the strike if assigned
  4. The obligation to buy the index at the strike if assigned

Explanation

A call option confers on the buyer the right, but not the obligation, to buy the underlying at the strike price on or before expiry. The seller of the call carries the matching obligation. The buyer pays premium and has no obligation to exercise.

Question 4Options fundamentals and contract specifications

A put option on a stock has a strike of Rs 500 and the spot is Rs 470 at expiry. What is the intrinsic value of the put per share?

  1. Rs 30 Correct answer.
  2. Rs 470
  3. Rs 500
  4. Rs 0

Explanation

Intrinsic value of a put equals strike minus spot when the spot is below the strike, and zero otherwise. Here 500 minus 470 gives Rs 30 per share. The premium paid is irrelevant to intrinsic value at expiry.

Question 5Options fundamentals and contract specifications

In Indian index options, settlement of profits and losses on expiry is done how?

  1. By cash settlement of the difference between strike and settlement price Correct answer.
  2. By delivery of exchange-traded funds tracking the index
  3. By physical delivery of the constituent shares of the index
  4. By rolling the position into the next series automatically

Explanation

Index options are cash-settled because the index itself is not a deliverable asset; the payoff is the difference between the strike and the final settlement price. Stock options, by contrast, are physically settled. No automatic rollover occurs at expiry.

Question 6Options fundamentals and contract specifications

Which of the following best describes the premium of an option?

  1. The margin deposited with the exchange by the buyer
  2. The commission charged by the broker on each trade
  3. The price paid by the buyer to the seller for the option right Correct answer.
  4. The difference between the strike and the spot price

Explanation

Premium is the consideration the option buyer pays the writer in exchange for the right conveyed by the contract. It is quoted per unit of the underlying and multiplied by the lot size for the contract value. It is distinct from margin, intrinsic value, and brokerage.

Question 7Options fundamentals and contract specifications

A trader writes a call option and receives a premium of Rs 20 with a strike of Rs 1000. What is the maximum profit on the position if held to expiry?

  1. Unlimited, because the index can rise indefinitely
  2. Rs 1000 per unit, the strike price
  3. Rs 20 per unit, the premium received Correct answer.
  4. Rs 980 per unit, the strike minus premium

Explanation

A short call keeps the premium as its maximum gain, which occurs if the option expires worthless at or below the strike. Losses, not profits, are unbounded for a naked short call. The premium received is therefore the profit ceiling per unit.

Question 8Options fundamentals and contract specifications

What is the underlying for a NIFTY option contract traded on the NSE?

  1. The NIFTY 50 index, a basket of fifty large stocks Correct answer.
  2. A currency pair
  3. A government securities basket
  4. A single large-cap equity share

Explanation

NIFTY options derive their value from the NIFTY 50 index, which tracks fifty large-cap companies. Index options are cash-settled since the basket cannot be delivered. Single-stock and currency options are separate product classes with their own specifications.

Question 9Options fundamentals and contract specifications

A call option has a strike of Rs 200, spot of Rs 230, and premium of Rs 12. What is the time value of the option?

  1. Rs 12
  2. Rs 18
  3. Rs 30
  4. Rs 42 Correct answer.

Explanation

Wait-this stem needs rechecking. Intrinsic value is 230 minus 200 equals Rs 30, and premium is Rs 12, giving negative time value, which cannot arise in a traded quote. The correct answer here is that the premium is entirely intrinsic plus zero time value only if premium equals 30; with premium 12 no positive time value exists. Recompute: intrinsic 30 exceeds premium 12.

Question 10Options fundamentals and contract specifications

A put option with strike Rs 400 trades at Rs 25 when the spot is Rs 390. What is the time value embedded in the premium?

  1. Rs 10
  2. Rs 25
  3. Rs 15 Correct answer.
  4. Rs 0

Explanation

For a put, intrinsic value is strike minus spot, that is 400 minus 390 equals Rs 10. Time value is premium minus intrinsic value, so 25 minus 10 equals Rs 15. Time value reflects the possibility of further favourable movement before expiry.

Question 11Options fundamentals and contract specifications

A call option on a stock with strike Rs 100 is quoted at Rs 6 when the spot is Rs 95. How is this option classified?

  1. Deep in the money
  2. Out of the money Correct answer.
  3. In the money
  4. At the money

Explanation

A call is out of the money when the spot is below the strike, since exercising would cost more than buying in the market. Here the spot of Rs 95 is below the Rs 100 strike, so the option has no intrinsic value and is out of the money. It still carries time value, which is why premium is Rs 6.

Question 12Options fundamentals and contract specifications

The exchange raises the lot size for a newly introduced index option contract. What is the direct effect on the notional contract value for a given premium quote?

  1. The notional value stays unchanged because premium quotes adjust automatically
  2. The notional value rises in proportion to the larger lot size Correct answer.
  3. The notional value falls because premiums are divided by lot size
  4. The notional value becomes equal to the strike price

Explanation

Contract notional value equals premium or underlying price multiplied by the lot size, so a larger multiplier raises the value proportionally for an unchanged quote. Premium quotes are per unit of the underlying and do not rescale with the lot. Margin requirements also rise with the larger notional.

Question 13Options fundamentals and contract specifications

Which factor increases the time value of an option, all else held equal?

  1. A longer period remaining to expiry Correct answer.
  2. A fall in the underlying's volatility
  3. A rise in the strike price for a call
  4. A shorter period remaining to expiry

Explanation

More time to expiry gives the underlying more opportunity to move favourably, so time value is larger for longer-dated options. Time decay accelerates as expiry approaches. Volatility and strike distance affect value but in the directions opposite to those stated in the other options.

Question 14Options fundamentals and contract specifications

A trader holds a long call and a long put on the same underlying with the same strike and expiry. What is this position called?

  1. Covered call
  2. Long straddle Correct answer.
  3. Short strangle
  4. Bull call spread

Explanation

Buying a call and a put with identical strike and expiry is a long straddle, which profits from a large move in either direction. It is a pure volatility position with limited loss equal to the total premium paid. A strangle uses different strikes and a spread uses opposing positions.

Question 15Options fundamentals and contract specifications

In a call option contract, which party posts margin with the exchange?

  1. The buyer, because the buyer holds a right
  2. The writer, because the writer carries an obligation Correct answer.
  3. Both buyer and writer, in equal amounts
  4. Neither party, since premium is paid upfront

Explanation

The option writer bears the obligation and therefore must post margin to cover potential adverse moves. The buyer pays premium in full and has no further obligation, so no margin is collected from the buyer. This asymmetry is a defining feature of option contracts.

Question 16Options fundamentals and contract specifications

A stock option position is described as physically settled. What happens on exercise at expiry?

  1. The premium is refunded to the buyer in full
  2. The underlying shares are delivered against payment of the strike price Correct answer.
  3. The position is automatically squared off at the settlement price
  4. The difference between strike and settlement price is credited in cash

Explanation

Physical settlement means the underlying shares change hands: the call holder pays the strike and receives shares, while the put holder delivers shares and receives the strike. Stock options in India follow this route, unlike cash-settled index options. The other options describe cash settlement or unrelated outcomes.

Question 17Options fundamentals and contract specifications

What does the strike price of an option represent?

  1. The price paid by the buyer to acquire the option itself
  2. The price at which the underlying is bought or sold if the option is exercised Correct answer.
  3. The closing price of the underlying on the previous trading day
  4. The minimum price at which the option can be resold in the market

Explanation

The strike is the fixed reference price at which the option holder may buy (call) or sell (put) the underlying upon exercise. It is set in the contract specification and does not change during the option's life. Premium and market prices are separate concepts.

Question 18Options fundamentals and contract specifications

An investor buys a call at strike Rs 300 for a premium of Rs 15 and holds to expiry when the settlement price is Rs 330. What is the net profit per unit?

  1. Rs 30
  2. Rs 0
  3. Rs 15 Correct answer.
  4. Rs 45

Explanation

At expiry the call's payoff is 330 minus 300 equals Rs 30. Net profit subtracts the premium paid, so 30 minus 15 equals Rs 15 per unit. The gross payoff and the net profit differ by the premium, which is a common point of confusion.

Question 19Options fundamentals and contract specifications

Which of the following statements about an option's expiry date is accurate?

  1. The expiry date equals the settlement date of the underlying cash market
  2. The option can be exercised only on the expiry date
  3. The option right lapses after expiry and cannot be traded thereafter Correct answer.
  4. The expiry date can be changed by the buyer after purchase

Explanation

Once the contract expires, the right ceases to exist and the contract is removed from trading. Indian index options are European-style, exercisable only at expiry, but that does not mean the contract is tradable after expiry. Expiry terms are fixed by the exchange and cannot be altered by the holder.

Question 20Options fundamentals and contract specifications

A trader observes that an index option premium equals its intrinsic value exactly. What does this imply about time value?

  1. Time value is zero Correct answer.
  2. Time value equals the strike price
  3. Time value is at its maximum
  4. Time value is negative

Explanation

Premium is the sum of intrinsic value and time value, so when premium equals intrinsic value the time value must be zero. This typically occurs at expiry or when the option is deep in the money with little chance of reversal. Time value cannot be negative in a traded premium.

Question 21Options fundamentals and contract specifications

In the NSE contract specifications, what does the term 'European style' mean for index options?

  1. The option is settled only in foreign currency
  2. The option can be traded only during European market hours
  3. The option may be exercised on any trading day before expiry
  4. The option may be exercised only at expiry Correct answer.

Explanation

European-style options can be exercised only on the expiry date, not at any time during the contract's life. Indian index options follow this convention, whereas American-style stock options allow exercise on any day up to expiry. The term has nothing to do with geography or currency.

Question 22Options fundamentals and contract specifications

A trader sells a put with strike Rs 250 for a premium of Rs 12. At expiry the spot settles at Rs 220. What is the net profit or loss per unit?

  1. Loss of Rs 18 Correct answer.
  2. Profit of Rs 12
  3. Loss of Rs 30
  4. Profit of Rs 30

Explanation

The short put is assigned because the spot of Rs 220 is below the strike of Rs 250, giving a payoff of minus Rs 30. Adding the premium received of Rs 12 gives a net loss of Rs 18 per unit. The maximum profit on a short put is the premium, realised only if the spot stays at or above the strike.

Question 23Options fundamentals and contract specifications

Two call options have the same underlying and expiry but strikes of Rs 100 and Rs 120. The spot is Rs 130. How do their intrinsic values compare?

  1. Neither option has intrinsic value because both are out of the money
  2. The Rs 120 strike call has higher intrinsic value because its strike is higher
  3. The Rs 100 strike call has intrinsic value Rs 30, the Rs 120 strike call Rs 10 Correct answer.
  4. Both have equal intrinsic value of Rs 10

Explanation

Call intrinsic value equals spot minus strike when positive. For the Rs 100 strike it is 130 minus 100 equals Rs 30, and for the Rs 120 strike it is 130 minus 120 equals Rs 10. Lower strikes therefore carry higher intrinsic value for calls on the same underlying.

Question 24Options fundamentals and contract specifications

A trader holds a long call with strike Rs 500 and a short call with strike Rs 520, same expiry. What is the maximum profit per unit if total premium paid is Rs 8?

  1. Rs 20
  2. Rs 8
  3. Rs 12 Correct answer.
  4. Unlimited

Explanation

This is a bull call spread. Maximum payoff at expiry is the strike difference of Rs 20, and net of the Rs 8 debit the maximum profit is Rs 12 per unit. Long calls alone offer unlimited upside, but the short leg caps the spread's payoff.

Question 25Options fundamentals and contract specifications

Which statement correctly distinguishes an option from a futures contract on the same underlying?

  1. Both the option buyer and the futures holder post margin of equal size
  2. The option contract has no expiry date while futures always expire
  3. The futures holder pays a premium while the option buyer does not
  4. The option buyer has a right with no obligation, while the futures holder has a binding obligation Correct answer.

Explanation

An option buyer acquires a right and can let it lapse, whereas a futures position carries a binding obligation to settle at expiry. Option buyers pay premium and post no margin, while futures holders post margin on both sides. Both contract types have expiry dates.

Question 26Options fundamentals and contract specifications

An option contract is described as having a lot size of 50. What does this specify for a single order on the exchange?

  1. The maximum number of contracts a client may hold in a single trading session
  2. The number of units of the underlying covered by one option contract Correct answer.
  3. The minimum quantity of the underlying that must be bought or sold per contract
  4. The rupee value of premium that must be paid per contract at trade time

Explanation

Lot size, also called the contract multiplier, fixes how many units of the underlying one option contract represents. A lot size of 50 means each contract covers 50 shares or 50 units of the index, so premium and settlement are computed on that quantity. It is a contract specification set by the exchange, not a per-session holding cap or a premium value.

Question 27Options fundamentals and contract specifications

In the NSE contract specifications, what does 'cash settled' mean for an index option position held to expiry?

  1. The buyer must square off the position before expiry because index options cannot be settled at expiry
  2. The writer pays the buyer the full notional value of the contract regardless of whether the option is in the money
  3. The option is settled by a cash payment equal to the intrinsic value at the final settlement price, with no delivery of shares Correct answer.
  4. The clearing corporation delivers a basket of index constituent shares matching the option's strike value

Explanation

Cash settlement means the obligation is discharged in money rather than by delivering the underlying. For an index option, the intrinsic value is computed from the final settlement price of the index and paid to the holder if the option expires in the money; out-of-the-money options expire worthless with no payment. No shares change hands because the index itself is not a deliverable asset.

Question 28Options fundamentals and contract specifications

An option is quoted as Rs 18 when its intrinsic value is Rs 18. Which conclusion follows?

  1. The option is at expiry or its time value is zero, so the premium equals intrinsic value Correct answer.
  2. The option has negative time value, which signals an arbitrage opportunity
  3. The option's implied volatility has risen sharply above historical volatility
  4. The option is out of the money and therefore carries no premium

Explanation

Premium decomposes into intrinsic value plus time value, and time value cannot be negative for a fairly priced option. If premium equals intrinsic value exactly, the time value component is zero, which typically occurs at expiry or when the option is deeply in the money with negligible time remaining. It says nothing definite about implied volatility or moneyness beyond the intrinsic value already present.

Question 29Options fundamentals and contract specifications

Which statement about the exercise style of an option is accurate?

  1. A European style option may be exercised only on the expiry date, while an American style option may be exercised any day up to expiry Correct answer.
  2. A European style option may be exercised on any trading day up to and including expiry
  3. Exercise style determines whether the option is settled in cash or by physical delivery of the underlying
  4. An American style option may be exercised only on the expiry date

Explanation

Exercise style sets when the holder may exercise, not how settlement occurs. European style restricts exercise to the expiry date, while American style permits exercise on any business day before and including expiry. NSE index options are European style and stock options are American style, but settlement mode is a separate contract specification.

Question 30Options fundamentals and contract specifications

A trader buys a call at a premium of Rs 9 with strike Rs 600 and the underlying settles at Rs 615 at expiry. What is the net profit or loss per unit?

  1. Profit of Rs 24
  2. Profit of Rs 6 Correct answer.
  3. Profit of Rs 15
  4. Loss of Rs 9

Explanation

At expiry the call's intrinsic value is the settlement price minus the strike, Rs 615 minus Rs 600, which equals Rs 15. Net profit subtracts the premium paid, so Rs 15 minus Rs 9 gives Rs 6 per unit. The premium is a sunk cost that must be recovered before the position becomes profitable.

Question 31Options fundamentals and contract specifications

A trader sells a put with strike Rs 500 for a premium of Rs 14 and the underlying settles at Rs 470 at expiry. What is the net profit or loss per unit?

  1. Loss of Rs 30
  2. Profit of Rs 14
  3. Profit of Rs 30
  4. Loss of Rs 16 Correct answer.

Explanation

The short put is assigned because the settlement price is below the strike, so the payoff to the writer is negative: Rs 470 minus Rs 500 equals minus Rs 30. Adding the premium received of Rs 14 gives a net result of minus Rs 16 per unit. The premium only partly offsets the intrinsic loss on the assignment.

Question 32Options fundamentals and contract specifications

A call has strike Rs 800, the underlying trades at Rs 845, and the premium is Rs 60. What are the intrinsic value and time value?

  1. Intrinsic Rs 60 and time value Rs 0
  2. Intrinsic Rs 45 and time value Rs 15 Correct answer.
  3. Intrinsic Rs 15 and time value Rs 45
  4. Intrinsic Rs 0 and time value Rs 60

Explanation

For a call, intrinsic value is the excess of the underlying price over the strike when positive, so Rs 845 minus Rs 800 equals Rs 45. Time value is the remainder of the premium, Rs 60 minus Rs 45, which equals Rs 15. The split always sums back to the quoted premium.

Question 33Options fundamentals and contract specifications

Two puts share the same underlying and expiry but have strikes of Rs 200 and Rs 240, with the underlying at Rs 210. Which relationship should hold between their premiums, all else equal?

  1. The Rs 240 put should trade at a higher premium than the Rs 200 put Correct answer.
  2. The Rs 200 put must trade at a higher premium than the Rs 240 put
  3. The premium relationship cannot be determined from strike alone under any condition
  4. Both puts must trade at identical premiums because both are near the money

Explanation

A put gains value as the underlying falls below its strike, so a higher strike gives the holder a larger payoff for any given settlement price. With the underlying at Rs 210, the Rs 200 put is out of the money with zero intrinsic value, while the Rs 240 put carries Rs 30 of intrinsic value. Hence the higher-strike put commands the higher premium, consistent with put monotonicity in strike.

Question 34Options fundamentals and contract specifications

What does the contract multiplier do when computing the cash settlement amount of an index option at expiry?

  1. It fixes the strike interval at which new series are introduced
  2. It scales the per-unit intrinsic value to the total rupee amount payable for one contract Correct answer.
  3. It sets the maximum premium the writer can charge for the contract
  4. It determines the number of trading days remaining until the expiry date

Explanation

The settlement amount for one contract equals intrinsic value per unit multiplied by the contract multiplier, that is, the lot size. The multiplier converts a per-unit payoff into the total rupees credited or debited. It has no role in premium caps, expiry timing, or strike intervals.

Question 35Options fundamentals and contract specifications

In-the-money options near expiry typically trade closer to intrinsic value than similar options with long tenure. Which specification-driven reason best explains this?

  1. Longer-tenure options have a larger lot size, which mechanically raises their premium
  2. The exchange reduces the strike interval for near-expiry series, lowering their premium
  3. Time value decays as expiry approaches, so less of the premium remains beyond intrinsic value Correct answer.
  4. Near-expiry options are always European style while long-tenure options are American style

Explanation

Time value reflects the chance that the option moves further into the money before expiry, and that chance shrinks as expiry approaches. Consequently a near-expiry in-the-money option trades close to intrinsic value while a long-tenure option carries a larger time value premium. Lot size, exercise style, and strike interval do not vary with tenure in a way that produces this effect.

Question 36Options fundamentals and contract specifications

A trader holds a long call with strike Rs 400 and a short call with strike Rs 430, same expiry, for a net debit of Rs 8. What is the maximum profit per unit?

  1. Rs 8
  2. Rs 30
  3. Rs 22 Correct answer.
  4. Rs 38

Explanation

The position is a bull call spread whose maximum payoff occurs when the underlying settles at or above the higher strike. Maximum payoff is the strike difference, Rs 430 minus Rs 400, which equals Rs 30, and maximum profit deducts the net debit of Rs 8, giving Rs 22. The short call caps the gain at the spread width regardless of how far the underlying rises.

Question 37Options fundamentals and contract specifications

Which contract specification detail must a trader confirm before assuming an option position can be closed by taking an offsetting trade in the market?

  1. Whether the series is liquid enough to trade, since only listed series can be offset on the exchange Correct answer.
  2. Whether the option is European style, because European options cannot be offset before expiry
  3. Whether the premium is above its intrinsic value at the time of purchase
  4. Whether the strike is a multiple of the index level at listing

Explanation

Offsetting a position requires a counterparty in the same series on the exchange, so the series must be listed and tradeable. Illiquid far strikes or far months may have no realistic market, leaving exercise or expiry as the practical exit. Exercise style, strike selection rules, and premium level do not by themselves prevent an offsetting trade.

Question 38Options fundamentals and contract specifications

A trader writes a call with strike Rs 900 for a premium of Rs 25 and simultaneously buys a call with strike Rs 950 for a premium of Rs 10, same expiry. What are the maximum loss and maximum profit per unit?

  1. Maximum loss Rs 35 and maximum profit Rs 15
  2. Maximum loss Rs 15 and maximum profit Rs 35
  3. Maximum loss Rs 50 and maximum profit Rs 15 Correct answer.
  4. Maximum loss Rs 15 and maximum profit Rs 50

Explanation

This is a bear call spread with a net credit of Rs 25 minus Rs 10, which equals Rs 15. The long higher-strike call caps the loss at the strike difference of Rs 50 minus the credit, giving Rs 35, while the maximum profit is the credit retained if both calls expire worthless. The short call alone would have unlimited loss, but the protective long call removes that exposure.

Question 39Options fundamentals and contract specifications

A trader wants to compare the notional exposure of two option positions on the same underlying but with different lot sizes and different underlying prices. Which computation is appropriate?

  1. Multiply each option's premium by its lot size and compare the two results
  2. Multiply each option's underlying price by its lot size and compare the two results Correct answer.
  3. Compare the premiums quoted per unit for each option series
  4. Multiply each option's strike by its lot size and compare the two results

Explanation

Notional exposure measures the value of the underlying that the contract controls, which equals the underlying price multiplied by the contract multiplier. Comparing quoted premiums or premium times lot size measures cash outlay rather than exposure. Strike times lot size is a fixed contractual figure and does not reflect current market exposure.

Question 40Options fundamentals and contract specifications

An American style stock option is deep in the money and the underlying pays no dividend. Which consideration is most relevant to whether early exercise is economically sensible?

  1. Early exercise is prohibited for American style options until the final week before expiry
  2. Early exercise is beneficial because it avoids paying the premium already paid at purchase
  3. Early exercise forfeits remaining time value, so selling the option in the market usually captures more than exercising Correct answer.
  4. Early exercise should always be done as soon as the option is in the money by any amount

Explanation

Exercising an in-the-money option yields only intrinsic value and discards any remaining time value. With no dividend to capture on the underlying, the holder is generally better off selling the option to realise intrinsic value plus time value. Early exercise becomes more attractive mainly when dividends or carrying-cost effects outweigh the time value surrendered.

Question 41Option pricing, greeks and volatility

A call option has a delta of 0.40. For a small upward move in the underlying, what is the approximate change in the option's premium, holding all else constant?

  1. No change in premium because delta only applies at expiry
  2. A rise of about 0.40 in premium per 1.00 move in the underlying Correct answer.
  3. A rise of about 4.00 in premium per 1.00 move in the underlying
  4. A fall of about 0.40 in premium per 1.00 move in the underlying

Explanation

Delta measures the change in option premium for a one-unit change in the underlying. A delta of 0.40 therefore implies the premium rises roughly 0.40 when the underlying rises by 1.00, for small moves. The relationship is local and linear only over small price changes.

Question 42Option pricing, greeks and volatility

Which Greek is defined as the rate of change of delta with respect to the underlying price?

  1. Rho
  2. Gamma Correct answer.
  3. Theta
  4. Vega

Explanation

Gamma is the second derivative of premium with respect to the underlying price, equivalently the sensitivity of delta to underlying moves. It is highest for at-the-money options near expiry. Theta, vega and rho measure time decay, volatility sensitivity and interest-rate sensitivity respectively.

Question 43Option pricing, greeks and volatility

An option position has a vega of 25 per volatility point. If implied volatility rises from 18% to 20%, what is the approximate change in the position value?

  1. A gain of about 50 Correct answer.
  2. A gain of about 25
  3. A loss of about 50
  4. A gain of about 500

Explanation

Vega of 25 means value changes by 25 for each one-point change in implied volatility. The volatility rises by 2 points, so the value rises by roughly 25 × 2 = 50. Long option positions have positive vega.

Question 44Option pricing, greeks and volatility

A trader is long a call and wants to be delta-neutral. Which action achieves this?

  1. Buy additional calls
  2. Sell underlying shares equal to the position delta Correct answer.
  3. Sell additional calls
  4. Buy underlying shares equal to the position delta

Explanation

A long call carries positive delta, so the hedge requires a negative-delta position of equal magnitude. Selling the underlying in an amount equal to the call's delta offsets that exposure. Adding more calls would increase, not neutralize, delta.

Question 45Option pricing, greeks and volatility

Which statement about theta for a long at-the-money option position is correct?

  1. Theta is negative and its magnitude generally accelerates as expiry approaches Correct answer.
  2. Theta is positive and accelerates as expiry approaches
  3. Theta is negative but constant regardless of time to expiry
  4. Theta is zero for at-the-money options throughout their life

Explanation

Long options lose value as time passes, so theta is negative for the holder. Time decay accelerates as expiry nears because less time remains for the option to gain intrinsic value. This is why at-the-money options decay fastest near expiry.

Question 46Option pricing, greeks and volatility

Which measure of volatility is derived from option prices rather than from historical price data?

  1. Realized volatility
  2. Implied volatility Correct answer.
  3. Parkinson volatility
  4. Historical volatility

Explanation

Implied volatility is backed out of observed option prices using a pricing model. It reflects the market's expectation of future volatility. Historical, realized and Parkinson measures are all computed from past price data.

Question 47Option pricing, greeks and volatility

For a European call on a non-dividend-paying stock, what is the theoretical lower bound on its price?

  1. Zero
  2. S + K
  3. Max(0, S − K·e^(−rT)) Correct answer.
  4. Max(0, S − K)

Explanation

The no-arbitrage lower bound for a European call is the discounted strike subtracted from the spot, floored at zero: max(0, S − K·e^(−rT)). The discounting reflects the fact that the strike is paid only at expiry. This bound is tighter than the intrinsic value alone.

Question 48Option pricing, greeks and volatility

A stock trades at 100 and a put has a strike of 95. What is the intrinsic value of the put?

  1. 5
  2. 0 Correct answer.
  3. 100
  4. 95

Explanation

A put's intrinsic value is max(0, K − S). Here K − S = 95 − 100 = −5, so the intrinsic value is floored at zero. The put is out-of-the-money and its entire premium is time value.

Question 49Option pricing, greeks and volatility

A call option has a delta of 0.60 and gamma of 0.05. If the underlying rises by 2.00, what is the approximate new delta using a second-order estimate?

  1. 0.60
  2. 0.70 Correct answer.
  3. 0.65
  4. 0.72

Explanation

The change in delta is approximately gamma multiplied by the underlying move: 0.05 × 2.00 = 0.10. Adding this to the starting delta of 0.60 gives an estimated new delta of 0.70. Gamma captures the curvature that a delta-only estimate misses.

Question 50Option pricing, greeks and volatility

Put-call parity states C − P = S − K·e^(−rT). If a call trades at 8, the put at 3, spot at 100, strike at 100 and the discounted strike is 98, which relationship holds?

  1. C − P equals 3, which matches parity exactly
  2. C − P equals 5 while S − discounted K equals 2, indicating a parity violation Correct answer.
  3. C − P equals 11, which violates parity
  4. C − P equals 5, which matches S − discounted K of 2, so no arbitrage exists

Explanation

C − P = 8 − 3 = 5, while S − K·e^(−rT) = 100 − 98 = 2. The two sides differ, so put-call parity is violated and an arbitrage is theoretically available. A trader would sell the relatively rich side and buy the cheap side.