Exercise value, time value and moneyness — MCQs

Northbridge Options Fund uses listed European options to modify portfolio payoffs and obtain synthetic exposures. Elena Rossi, the fund's option strategist, is reviewing four potential analyses. Unless otherwise stated, the underlying stocks pay no dividends, options can be exercised only at expiration, and markets are free of taxes, transaction costs, and arbitrage opportunities. For the first analysis, Rossi observes a stock, a call option, and a risk-free bond and is asked to infer the value of a put with the same exercise price and expiration date as the call. She plans to use European put–call parity. A colleague proposes using the exercise price without discounting it, but Rossi notes that the parity relationship requires the present value of the exercise price. For the second analysis, Rossi applies a one-period binomial model. The stock can reach only the specified up-state or down-state price at the end of the period. She intends to calculate the risk-neutral probability using the gross risk-free return and then discount the probability-weighted option payoff. The actual probability of an upward stock movement is not needed for no-arbitrage valuation. A portfolio manager then asks Rossi to protect an existing long stock position. The manager requires a minimum expiration value but wants to retain the benefit if the stock appreciates. Premium cost is acceptable, and the manager does not want to sell the shares. Rossi compares buying a put, selling a call, and selling a put on the same stock. Finally, Rossi reviews a covered-call position established by buying a share and simultaneously selling a call. Both positions will be held to option expiration. She explains that the call premium reduces the net initial investment but that the short call limits the stock price at which further gains accrue. Exhibit 1 presents the complete inputs for the four analyses.

Hawthorne Equity Portfolio holds a diversified portfolio of non-dividend-paying shares and uses European options to modify its payoff distribution. The portfolio manager observes the market data in Exhibit 1 for a matched pair of European call and put options. Both options have the same underlying share, exercise price, and expiration date. The call is actively traded, but the put is not, so the manager estimates the put's no-arbitrage value using put–call parity. There are no transaction costs, taxes, short-sale restrictions, or interim cash flows from the underlying share. For a different share, the manager constructs the one-period binomial model in Exhibit 2. The share will have exactly one of the two stated values at the end of the period. A European call expires at that time and pays the greater of zero or the share price less the exercise price. The manager plans to value the call by forming a portfolio of the underlying share and risk-free borrowing that exactly replicates the call's state-contingent payoffs. The risk-free rate is effective for the single period, and borrowing and lending are available at that rate. A client represented by Hawthorne already owns a concentrated share position and expects the shares to appreciate over the next year. The client cannot tolerate an exit value below a specified floor but is willing to pay an option premium to retain participation in price increases. The client does not want a strategy that requires selling the shares today, creates an uncovered option exposure, or completely fixes the future sale price. The manager also reviews how a change in expected volatility affects otherwise identical European calls and puts. The options' exercise prices, time to expiration, risk-free rate, and underlying share price are held constant. Neither option can be exercised before expiration, and both option holders have limited downside equal to the premiums paid. The analysis concerns option value before expiration rather than the options' expiration payoffs or the profit earned after deducting premiums.

A long futures contract was marked to market yesterday at USD 80.00. Today's settlement price is USD 82.50 and the multiplier is USD 1.00. The calculated value of today's settlement cash flow is closest to:

For a two-year annual-pay interest rate swap, discount factors are 0.9700 and 0.9300 for years 1 and 2. The calculated fixed swap rate is closest to:

A two-year annual-pay interest-rate swap has discount factors of 0.9600 and 0.9100 for years 1 and 2. The calculated value of its par fixed rate is closest to:

Gold is USD 70.00 per ounce, the one-year risk-free rate is 5%, and storage of USD 2.00 per ounce is payable at year-end. With no income or convenience yield, the calculated value of the one-year forward price is closest to:

Meridian Capital manages an equity portfolio containing a concentrated position in a non-dividend-paying company. The derivatives team is evaluating European calls and puts on the shares using a one-period binomial model. The model assumes that by the end of the period the share price will take one of the two values shown in Exhibit 1. The one-period risk-free rate is 5.00%, and borrowing and lending are available at that rate. There are no transaction costs, taxes, dividends, or arbitrage opportunities. A junior analyst proposes valuing the call by assigning equal probabilities to the up and down states. The senior analyst rejects that approach, noting that no real-world state probabilities have been supplied and are not required for no-arbitrage valuation. Instead, the team can determine a risk-neutral probability or construct a portfolio of the underlying share and risk-free borrowing that exactly reproduces the call's state-contingent payoffs. The call is European and has an exercise price of USD 100.00. Therefore, its expiration payoff is USD 20.00 in the up state and zero in the down state. The team also considers a European put with the same underlying, exercise price, and expiration date. The senior analyst instructs the team to value this put through European put–call parity using the calculated call value of USD 10.88. Because the stock pays no dividends, the applicable relationship is between the call, the put, the current stock price, and the present value of the exercise price. The risk-free asset used in the parity relationship pays USD 100.00 at expiration. For risk management, Meridian wants to understand the number of shares represented by the call's replicating portfolio. The senior analyst explains that the option's hedge ratio must be based on the change in option value across the two terminal states divided by the corresponding change in the underlying share price. It is not based on the option's unconditional expected payoff. A portfolio manager separately asks whether changing the put from European to American exercise would affect its value. The stock still pays no dividends, but the exercise price is received when a put is exercised. The senior analyst notes that the American holder may exercise at any time through expiration but is not required to do so. All other contract terms would remain unchanged.

A bond's clean spot price is USD 980, accrued interest is USD 12, and a USD 30 coupon is paid in three months. Using a 4% effective annual risk-free rate, the calculated six-month forward price is closest to: