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SEC CO/AP practice questions

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Question 1Options Fundamentals and Contract Specifications

Under the SEC Options/AP regulatory framework, which characteristic distinguishes an option contract from a forward contract?

  1. The option premium is paid by the seller to the buyer at expiration rather than at trade inception
  2. The option contract always settles in cash, while a forward contract always settles by physical delivery
  3. The option contract must be traded on an exchange, while a forward contract must be traded over the counter
  4. The option buyer has a right but not an obligation to perform, while the forward party is obligated to perform Correct answer.

Explanation

An option confers a right on the holder, who may choose whether to exercise, whereas both parties to a forward are bound to settle at the agreed future date. This asymmetry of rights and obligations is the defining legal distinction between the two instruments. Premium timing and settlement method are contractual details, not defining features.

Question 2Options Fundamentals and Contract Specifications

A customer buys one listed equity call option contract. What does the buyer acquire, and what is the maximum loss?

  1. An obligation to buy 100 shares at the strike, with unlimited maximum loss
  2. A right to buy 100 shares at the strike, with maximum loss limited to the premium paid Correct answer.
  3. A right to buy 100 shares at the strike, with maximum loss equal to the strike price
  4. A right to sell 100 shares at the strike, with maximum loss limited to the premium paid

Explanation

A call gives the holder the right to buy the underlying at the strike price during the exercise window. Because the buyer pays a premium and has no further obligation, the most that can be lost is that premium. The strike price itself is never at risk for a long call holder.

Question 3Options Fundamentals and Contract Specifications

Which statement correctly describes the position of an investor who writes (sells) an uncovered equity call?

  1. The writer pays the premium and has a right to deliver shares if assigned
  2. The writer receives the premium and has a right to buy shares if assigned
  3. The writer pays the premium and has an obligation to sell shares if assigned
  4. The writer receives the premium and has an obligation to deliver shares if assigned Correct answer.

Explanation

The call writer collects the premium up front and, in exchange, assumes the obligation to deliver the underlying at the strike if the holder exercises. Because the position is uncovered, the writer's potential loss is theoretically unlimited as the stock rises. The writer has no right to choose performance.

Question 4Options Fundamentals and Contract Specifications

An investor purchases a put with a strike of 50 when the underlying trades at 55. What is the option's intrinsic value at that moment?

  1. 0 Correct answer.
  2. 55
  3. 5
  4. 50

Explanation

A put is in the money only when the strike exceeds the market price of the underlying. Here the strike of 50 is below the market price of 55, so the put is out of the money and has zero intrinsic value. Any premium paid above zero reflects time value, not intrinsic value.

Question 5Options Fundamentals and Contract Specifications

In listed options terminology, what does the exercise price (strike price) of a contract specify?

  1. The price the buyer pays for the option itself
  2. The maximum price the underlying may reach before the option expires
  3. The price at which the clearinghouse marks the contract to market daily
  4. The price at which the underlying may be bought or sold upon exercise Correct answer.

Explanation

The exercise or strike price is the fixed price at which the option holder may buy (call) or sell (put) the underlying. It is distinct from the premium, which is the price of the option contract itself. Clearinghouse margin and market price movements do not alter the strike.

Question 6Options Fundamentals and Contract Specifications

Which contract specification identifies the last day on which an option holder may exercise the contract?

  1. The settlement date
  2. The expiration date Correct answer.
  3. The trade date
  4. The record date

Explanation

The expiration date is the final date on which the holder may exercise the option, after which the contract ceases to exist. Settlement date concerns delivery and payment, while record and trade dates relate to ownership and execution timing. Confusing expiration with settlement is a common source of error.

Question 7Options Fundamentals and Contract Specifications

An equity call has a premium of 3 and a strike of 40. If the underlying is at 44 at expiration, what is the buyer's profit per share?

  1. 4
  2. 3
  3. 7
  4. 1 Correct answer.

Explanation

At expiration the call is worth its intrinsic value of 4 (44 minus 40). Subtracting the 3 premium paid leaves a profit of 1 per share. The premium must always be recovered before the buyer profits.

Question 8Options Fundamentals and Contract Specifications

Which party to a listed option contract is exposed to margin calls and performance-bond requirements?

  1. Both the buyer and the writer equally
  2. Neither party, because the clearinghouse absorbs all losses
  3. The writer only Correct answer.
  4. The buyer only

Explanation

The buyer's maximum loss is the premium already paid, so no margin is required from the buyer. The writer bears an ongoing obligation that can become costly, so the writer must post and maintain margin. The clearinghouse guarantees performance but does not eliminate the writer's obligation.

Question 9Options Fundamentals and Contract Specifications

An investor buys a put with a strike of 60 and pays a premium of 4. At expiration the underlying is at 48. What is the profit per share?

  1. 16
  2. 12
  3. 8 Correct answer.
  4. 4

Explanation

The put's intrinsic value at expiration is 12 (60 minus 48). Deducting the 4 premium paid gives a profit of 8 per share. The premium must be subtracted from the intrinsic value, not added to it.

Question 10Options Fundamentals and Contract Specifications

What does the term 'American-style' mean when applied to an exchange-listed option?

  1. The option may be exercised only if the holder gives five business days' notice
  2. The option may be exercised at any time up to and including the expiration date Correct answer.
  3. The option may be exercised only on the expiration date
  4. The option may be exercised only at the close of each calendar quarter

Explanation

American-style exercise permits the holder to exercise on any business day before expiration. European-style options, by contrast, may be exercised only on the expiration date. The label describes exercise timing and has nothing to do with the option's geographic listing.

Question 11Options Fundamentals and Contract Specifications

A stock trades at 32. Which of the following listed calls is in the money?

  1. A call with a strike of 30 Correct answer.
  2. A call with a strike of 40
  3. A call with a strike of 45
  4. A call with a strike of 35

Explanation

A call is in the money when the market price of the underlying exceeds the strike. With the stock at 32, only the 30 strike is below the market price, so that call carries intrinsic value of 2. Strikes above 32 leave the call out of the money.

Question 12Options Fundamentals and Contract Specifications

What is the effect of a stock split on the terms of outstanding listed option contracts?

  1. The strike price and number of deliverable shares are adjusted so the contract's aggregate value is preserved Correct answer.
  2. The contracts are cancelled and holders are refunded their premiums
  3. The contracts are converted into contracts on the post-split shares with the original strike and original deliverable quantity
  4. The number of contracts held is doubled while strikes remain unchanged

Explanation

When the underlying splits, the options exchange adjusts the strike and the deliverable quantity so that the economic terms of the contract are preserved. The aggregate exercise value before and after the adjustment is intended to be equivalent. The contract is not cancelled, and leaving both strike and quantity unchanged would transfer value between parties.

Question 13Options Fundamentals and Contract Specifications

An investor writes a put with a strike of 45 and receives a premium of 2. What is the maximum profit on the position?

  1. 43 per share
  2. 45 per share
  3. Unlimited
  4. 2 per share Correct answer.

Explanation

A put writer keeps the entire premium if the put expires worthless, which happens when the underlying stays at or above the strike. That premium of 2 per share is therefore the maximum profit. The maximum loss, not the maximum profit, is the large figure for a short put.

Question 14Options Fundamentals and Contract Specifications

Which pairing correctly matches a position with its maximum loss?

  1. Short call - loss limited to the premium received
  2. Short put - loss limited to the premium received
  3. Long call - loss limited to the premium paid Correct answer.
  4. Long put - loss limited to the strike price

Explanation

The long call holder can lose no more than the premium, since the option can always be allowed to expire unused. Short positions carry the larger exposure, and a long put's maximum loss is likewise the premium rather than the strike. Matching each position to its true risk profile is essential for suitability analysis.

Question 15Options Fundamentals and Contract Specifications

A customer holds a long call that is deep in the money as expiration approaches. Which consideration bears most directly on whether to exercise early?

  1. The original premium paid for the contract
  2. The trading volume in the underlying on the prior day
  3. The number of contracts held in the account
  4. The remaining time value that would be forfeited by exercising now Correct answer.

Explanation

Exercising a call early surrenders any remaining time value, because exercise captures only intrinsic value. A rational holder therefore weighs the time value forfeited against the benefit of holding the shares sooner. The original premium and recent volume do not determine whether early exercise is economically sensible.

Question 16Options Fundamentals and Contract Specifications

What is the breakeven price for a buyer of a call with a strike of 25 and a premium of 3?

  1. 31
  2. 22
  3. 25
  4. 28 Correct answer.

Explanation

A long call breaks even where the underlying equals the strike plus the premium paid, which is 25 plus 3, or 28. Below that level the intrinsic value fails to recover the premium. Adding the premium to the strike, rather than subtracting it, is the key step.

Question 17Options Fundamentals and Contract Specifications

Which statement best describes the role of the Options Clearing Corporation in listed options trading?

  1. It sets the strike prices at which new series are issued
  2. It acts as issuer and guarantor of every listed option contract, standing between buyer and seller Correct answer.
  3. It determines the premium at which each contract trades on the exchange
  4. It lends shares to writers who must deliver on assigned calls

Explanation

The clearing corporation becomes the buyer to every seller and the seller to every buyer, guaranteeing performance and removing counterparty risk between the original parties. It does not set premiums or strikes, which are determined by the market and by listing rules respectively. This novation function is central to understanding listed options.

Question 18Options Fundamentals and Contract Specifications

An investor is short a call with a strike of 50 and has been assigned. What is the investor's obligation?

  1. To buy 100 shares at 50 per share
  2. To pay the call's current market premium in cash
  3. To buy back the option contract at its intrinsic value
  4. To sell 100 shares at 50 per share Correct answer.

Explanation

Assignment on a short call obligates the writer to deliver the underlying at the strike price, which here means selling 100 shares at 50. The writer does not choose whether to perform once assigned. Cash payment of premium or intrinsic value is not the deliverable for a physically settled equity call.

Question 19Options Fundamentals and Contract Specifications

Which of the following is a valid reason that a listed option series may be added by an exchange?

  1. The underlying company requests additional strikes for its employees
  2. The premium on existing series has risen above a regulatory ceiling
  3. A change in the underlying's market price creates a need for new strike prices Correct answer.
  4. The clearing corporation requires a minimum number of strikes per month

Explanation

Exchanges add new strike series as the underlying's price moves, so that investors have contracts available near the current market level. Strike availability is driven by price movement and listing standards, not by premium ceilings or issuer requests. This keeps the listed market usable as prices drift.

Question 20Options Fundamentals and Contract Specifications

An investor buys a call with a strike of 30 for a premium of 2 and simultaneously writes a call with a strike of 40 for a premium of 1. What is the maximum profit per share?

  1. 9 Correct answer.
  2. 8
  3. 11
  4. 10

Explanation

This is a bull call spread with a net debit of 1. At expiration above 40 the long call is worth 10 and the short call costs 10, giving a spread value of 10; subtracting the 1 debit leaves a maximum profit of 9. The maximum profit is capped because the short call offsets gains above its strike.

Question 21Options Fundamentals and Contract Specifications

A put has a strike of 80 and the underlying trades at 80. The option's premium is 5. What does the entire 5 represent?

  1. Intrinsic value
  2. Time value Correct answer.
  3. A combination of intrinsic value and time value in equal parts
  4. The clearinghouse's guarantee fee

Explanation

When the underlying equals the strike, the option is at the money and has no intrinsic value. Any premium is therefore entirely time value, reflecting the possibility that the underlying moves before expiration. Intrinsic value arises only when the option is in the money.

Question 22Options Fundamentals and Contract Specifications

A customer writes a naked call with a strike of 100 and receives a premium of 4. The underlying then rises to 130. What is the loss per share if the position is closed at expiration?

  1. Unlimited, so no finite loss can be stated
  2. 26 Correct answer.
  3. 30
  4. 34

Explanation

At expiration the short call's intrinsic value is 30 (130 minus 100). The writer received 4 in premium, so the net loss is 30 minus 4, or 26 per share. Although the theoretical loss on a naked call is unlimited, at a given settlement price the realized loss is a definite figure.

Question 23Options Fundamentals and Contract Specifications

Which set of contract terms is fixed for a given listed option series?

  1. Underlying, premium, open interest, and expiration date
  2. Underlying, expiration month, strike price, and exercise style Correct answer.
  3. Premium, implied volatility, delta, and open interest
  4. Premium, strike price, bid-ask spread, and volume

Explanation

A series is defined by the underlying, the expiration, the strike, and the exercise style, all of which are set by the terms of the listing. Premium, implied volatility, delta, open interest, and volume are market-determined variables that change continuously. Distinguishing fixed terms from market variables is fundamental to contract specification.

Question 24Options Fundamentals and Contract Specifications

An investor holds a long put with a strike of 70 and the underlying falls to 55. Ignoring premium, what is the intrinsic value per share and what happens if the holder does nothing at expiration?

  1. Intrinsic value is 55, and the holder must deliver shares to realize it
  2. Intrinsic value is 15, and the holder automatically receives 15 in cash at expiration
  3. Intrinsic value is 15, and the option expires worthless unless exercised Correct answer.
  4. Intrinsic value is 0, and the option must be sold before expiration to realize value

Explanation

The put's intrinsic value is 15 (70 minus 55), but that value is captured only by exercising or selling the option. An unexercised option simply expires, and the holder forfeits the intrinsic value. Listed equity options are not automatically cash-settled at intrinsic value for retail holders in the manner described.

Question 25Options Fundamentals and Contract Specifications

Which adjustment to an outstanding option contract is consistent with preserving its economic terms after a special cash dividend on the underlying?

  1. Converting the contract into a cash-settled index option
  2. Cancelling the contract and returning the premium to the holder
  3. Reducing the strike price by the per-share dividend amount Correct answer.
  4. Increasing the number of deliverable shares while leaving the strike unchanged

Explanation

For a special cash dividend, exchanges commonly adjust the strike downward by the per-share amount so the option's economic value is preserved. Simply increasing the deliverable quantity would not offset the value transferred by the distribution. Cancellation and conversion are not standard adjustments for a special dividend.

Question 26Options Fundamentals and Contract Specifications

A listed option contract has a multiplier of 100. An investor buys one call at a premium of 1.75. What total amount does the investor pay, excluding commissions?

  1. $1,750
  2. $175 Correct answer.
  3. $1.75
  4. $17.50

Explanation

The quoted premium is per share of the underlying, and the standard listed contract covers 100 shares. The cash outlay is therefore 1.75 multiplied by 100, or $175. Commissions and fees would be added to that figure.

Question 27Options Fundamentals and Contract Specifications

Which strike price increment applies to a newly listed equity option series quoted at $2.50 or higher when the underlying stock trades below $25 per share?

  1. $5 Correct answer.
  2. $2.50
  3. $10
  4. $1

Explanation

Exchange strike-price rules scale the increment to the price of the underlying and the level of the strike. For stocks trading under $25, strikes at $2.50 and above are listed in $5 increments, while lower strikes use $2.50 increments. The finer $1 and $2.50 spacing is used for higher-priced strikes or higher-priced underlying stocks.

Question 28Options Fundamentals and Contract Specifications

An investor buys a call and a put on the same underlying with the same strike and the same expiration. Which statement describes the position?

  1. It is a short straddle with unlimited loss potential.
  2. It is a long straddle, and the maximum loss is the combined premiums paid. Correct answer.
  3. It is a long strangle, because the strikes differ.
  4. It is a covered call, because the put protects the call.

Explanation

Buying a call and a put with identical strike and expiration is a long straddle, a position that profits from a large move in either direction. The most the investor can lose is the total premium paid for both options, which occurs if the underlying finishes exactly at the strike.

Question 29Options Fundamentals and Contract Specifications

A customer owns 100 shares of a stock trading at $58 and writes one call on that stock with a strike of $60, receiving a premium of $2. What is the maximum profit on the combined stock-and-option position?

  1. $400 Correct answer.
  2. $6,200
  3. $200
  4. $600

Explanation

In a covered call, maximum profit equals the appreciation from the stock's current price up to the strike plus the premium received. That is ($60 - $58) plus $2, or $4 per share, which is $400 on 100 shares. The short call caps the stock gain at the strike.

Question 30Options Fundamentals and Contract Specifications

An investor holds a long call with a strike of 50 when the underlying declares a 3-for-1 stock split. Which adjustment keeps the contract's economic terms intact?

  1. Keep both the strike and the deliverable unchanged and pay a cash adjustment.
  2. Keep the strike at 50 and triple the number of contracts held.
  3. Reduce the strike to 16.67 and keep the deliverable at 100 shares.
  4. Reduce the strike to 16.67 and increase the deliverable to 300 shares. Correct answer.

Explanation

A stock split changes the price and share count of the underlying, so outstanding option contracts are adjusted to preserve their value. The strike is divided by the split ratio (50 divided by 3, or 16.67) and the deliverable is multiplied by the same ratio (100 becomes 300 shares).

Question 31Options Pricing, Greeks, and Volatility

A call option has a delta of 0.60 and a gamma of 0.05. If the underlying rises by 2.00, approximately what is the new delta after the move?

  1. 0.70 Correct answer.
  2. 0.50
  3. 0.65
  4. 0.55

Explanation

Gamma measures the change in delta per one-unit change in the underlying. A 2.00 move times a gamma of 0.05 gives a delta change of 0.10, so the new delta is roughly 0.60 + 0.10 = 0.70. This is a first-order approximation that ignores higher-order terms.

Question 32Options Pricing, Greeks, and Volatility

For a long at-the-money option position, which Greek is largest in magnitude per unit of time?

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

Explanation

At-the-money options carry the highest vega because their time value is most sensitive to volatility changes. Vega for an ATM option scales with the square root of time to expiry and typically dwarfs rho. Theta is also large near the money, but vega is the standard answer for the largest volatility-driven exposure.

Question 33Options Pricing, Greeks, and Volatility

According to put-call parity for European options on a non-dividend stock, which relationship holds?

  1. C - P = K·e^(-rT) - S
  2. C + P = S - K·e^(-rT)
  3. C + P = S + K·e^(-rT)
  4. C - P = S - K·e^(-rT) Correct answer.

Explanation

Put-call parity states that a call minus a put equals the stock price minus the present value of the strike. This follows from constructing equivalent payoff portfolios. The relationship holds only for European options on non-dividend-paying stocks.

Question 34Options Pricing, Greeks, and Volatility

An option has a delta of -0.40. Which position does this most likely describe?

  1. Short call
  2. Long put Correct answer.
  3. Long call
  4. Short put

Explanation

A long put has negative delta because its value rises when the underlying falls. A delta of -0.40 is consistent with an out-of-the-money or at-the-money long put. Long calls and short puts have positive delta, and short calls have negative delta but with magnitude typically matching a call premium profile.

Question 35Options Pricing, Greeks, and Volatility

Which statement best describes implied volatility?

  1. The volatility input that makes the model price equal the market price Correct answer.
  2. The volatility that maximizes option premium
  3. The realized standard deviation of past returns
  4. The volatility implied by the risk-free rate

Explanation

Implied volatility is backed out of the market price by inverting the pricing model. It reflects the market's expectation of future volatility embedded in the option premium. Realized volatility, by contrast, is computed from historical returns.

Question 36Options Pricing, Greeks, and Volatility

A trader is long a straddle. Which market outcome produces the largest profit?

  1. A gradual rise in implied volatility
  2. A large move in either direction Correct answer.
  3. A small move in either direction
  4. A gradual decline in implied volatility

Explanation

A long straddle consists of a long call and long put at the same strike, so it profits from large moves regardless of direction. The position loses when the underlying stays near the strike. Rising implied volatility helps the position but is not required for the large payoff.

Question 37Options Pricing, Greeks, and Volatility

Which Greek measures the sensitivity of an option's price to a change in the risk-free interest rate?

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

Explanation

Rho measures the change in option value for a one-unit change in the risk-free rate. It is typically the smallest of the major Greeks for short-dated options. Vega, theta, and gamma measure volatility, time decay, and delta curvature respectively.

Question 38Options Pricing, Greeks, and Volatility

For a European call on a non-dividend stock, which condition must hold for the option to be at-the-money?

  1. The strike equals the forward price
  2. Delta equals 1.0
  3. The option has zero time value
  4. The strike equals the spot price Correct answer.

Explanation

At-the-money is defined by the strike equaling the current spot price. Because the forward differs from spot when rates are nonzero, the ATM-forward strike is a distinct concept. Delta of 1.0 and zero time value describe deep in-the-money options, not ATM.

Question 39Options Pricing, Greeks, and Volatility

An option has a vega of 0.20 per 1% volatility change. If implied volatility rises from 20% to 23%, approximately what is the change in the option price?

  1. +0.20
  2. +0.60 Correct answer.
  3. +0.06
  4. +1.20

Explanation

Vega of 0.20 per 1% volatility change means a 3% rise in volatility adds approximately 3 × 0.20 = 0.60 to the option price. This first-order approximation ignores higher-order volatility effects. The calculation assumes vega is roughly constant over the small range.

Question 40Options Pricing, Greeks, and Volatility

A trader holds a long call with delta 0.55 and sells a call with delta 0.30 on the same underlying. What is the net position delta?

  1. 0.55
  2. 0.30
  3. 0.25 Correct answer.
  4. 0.85

Explanation

Net delta is the sum of position deltas, with short positions carrying negative sign. Long 0.55 plus short 0.30 gives 0.55 - 0.30 = 0.25. This is a delta-spread position with reduced directional exposure.

Question 41Options Pricing, Greeks, and Volatility

Under the Black-Scholes model, which assumption is required?

  1. Volatility is stochastic
  2. Returns follow a normal distribution Correct answer.
  3. Interest rates are stochastic
  4. Prices follow a jump-diffusion process

Explanation

Black-Scholes assumes log returns are normally distributed, which implies the underlying follows geometric Brownian motion. It also assumes constant volatility and constant interest rates. Stochastic volatility and jumps are extensions beyond the basic model.

Question 42Options Pricing, Greeks, and Volatility

A trader is short a call and wants to be delta-neutral. The short call has delta of 0.40 per option on 100 shares. To hedge one short call, the trader should:

  1. Sell 100 shares of the underlying
  2. Sell 40 shares of the underlying
  3. Buy 100 shares of the underlying
  4. Buy 40 shares of the underlying Correct answer.

Explanation

A short call has delta of -0.40 per share-equivalent, so one contract carries -40 deltas. Buying 40 shares adds +40 deltas, offsetting the position to roughly zero. The hedge is dynamic because delta changes with the underlying.

Question 43Options Pricing, Greeks, and Volatility

An option has theta of -0.05 per day. If the underlying and implied volatility do not change, what is the approximate one-day price change for a long position?

  1. +0.05
  2. 0.00
  3. -0.10
  4. -0.05 Correct answer.

Explanation

Theta of -0.05 per day means the option loses about 0.05 in value per day from time decay. For a long position, this is a loss of approximately 0.05. Theta is typically negative for long options and positive for short options.

Question 44Options Pricing, Greeks, and Volatility

Which market condition would most likely cause a volatility skew where out-of-the-money puts trade at higher implied volatility than out-of-the-money calls on equity indices?

  1. Demand for downside protection and crash risk premium Correct answer.
  2. Consistently low realized volatility
  3. Persistent positive skewness in equity returns
  4. A flat term structure of interest rates

Explanation

Equity index options typically exhibit a negative skew because investors pay up for downside protection. The crash risk premium and hedging demand push OTM put implied volatility above OTM call implied volatility. Equity returns are negatively skewed, not positively skewed.

Question 45Options Pricing, Greeks, and Volatility

A calendar spread involves selling a near-term option and buying a longer-term option at the same strike. Which exposure does this position primarily exploit?

  1. Differences in dividends across stocks
  2. Differences in implied volatility across expiries Correct answer.
  3. Differences in strike prices
  4. Differences in credit spreads

Explanation

A calendar spread trades the term structure of implied volatility by pairing options at different expiries. The position benefits if the near-term option decays faster than the longer-term option. Strike, dividend, and credit differences are not the primary exposures.

Question 46Options Pricing, Greeks, and Volatility

A portfolio has a vega of 500 per 1% volatility change. If implied volatility falls by 2%, approximately what is the P&L impact?

  1. +500
  2. +1,000
  3. -1,000 Correct answer.
  4. -500

Explanation

Vega of 500 per 1% means a 2% drop in volatility produces roughly 2 × 500 = 1,000 loss. The sign is negative because the portfolio is long vega and volatility declined. This first-order estimate ignores convexity in volatility.

Question 47Options Pricing, Greeks, and Volatility

Which statement about gamma is true for a long option position?

  1. Gamma is independent of the underlying price
  2. Gamma is highest for deep in-the-money options
  3. Gamma is always negative for long options
  4. Gamma is highest for at-the-money options near expiry Correct answer.

Explanation

Gamma for a long option peaks when the option is at-the-money and rises sharply as expiry approaches. Deep in-the-money and deep out-of-the-money options have low gamma. Long options always have positive gamma.

Question 48Options Pricing, Greeks, and Volatility

A trader observes that an at-the-money call with 30 days to expiry has higher implied volatility than the same strike call with 180 days to expiry. This pattern is best described as:

  1. A flat volatility surface
  2. A positive volatility skew
  3. A contango term structure
  4. An inverted volatility term structure Correct answer.

Explanation

When near-term implied volatility exceeds longer-term implied volatility, the term structure is inverted. This often occurs around event risk or market stress. Contango describes the opposite upward-sloping pattern.

Question 49Options Pricing, Greeks, and Volatility

Which of the following best explains why an out-of-the-money option has a lower absolute delta than an at-the-money option?

  1. Its probability of finishing in-the-money is lower Correct answer.
  2. Its vega is always zero
  3. Its rho is always negative
  4. Its theta is always positive

Explanation

Delta approximates the risk-neutral probability of finishing in-the-money, so deep OTM options have small absolute delta. As the option moves closer to the money, delta approaches 0.50. Theta, vega, and rho are not the reason delta is small.

Question 50Options Pricing, Greeks, and Volatility

A risk manager wants to estimate the P&L of an option portfolio for a large move in the underlying. Which expansion is most appropriate?

  1. Rho-only approximation
  2. Vega-only approximation
  3. Delta-only linear approximation
  4. Delta-gamma approximation including theta Correct answer.

Explanation

For large moves, a delta-only estimate misses the curvature captured by gamma, and theta accounts for time decay. A delta-gamma-theta expansion gives a more accurate P&L estimate. Vega and rho alone ignore underlying price changes.