LOS i: Illustrate how put-call parity for options on forwards (or futures) is established.

Q1. At time = 0, for a put option at exercise price (X) on a newly issued forward contact at F_T (the forward price at time = 0), a portfolio with equal value could be constructed from being long in:

A)   the underlying asset, long a put at X, and short in a pure-discount risk-free bond that pays X – F_T at option expiration.

B)   a risk-free pure-discount bond that pays F_T – X at option expiration and long in a put at X.

C)   a call at X and long in a pure-discount risk-free bond that pays X – F_T at option expiration.

Q2. Put-call parity for options on forward contracts at the initiation of the option where the forward price at that time (time=0) is FT, can best be expressed as:

A)   c₀ + (X ? FT) / (1 + R)^T = p₀.

B)   c₀ + X / (1 + R)^T ? FT = p₀.

C)   c₀ ? (X ? FT) / (1 + R)^T = p₀.

Q3. Which of the following would have the same value at t = 0 as an at-the-money call option on a forward contract priced at FT (the forward price at time = 0)?

A)   A put option, long the underlying asset, and short a risk-free bond that pays X-FT at option expiration.

B)   A put option, long the underlying asset, and short a risk-free bond that matures at X at option expiration.

C)   A put option on the forward at exercise price (X).

LOS i: Illustrate how put-call parity for options on forwards (or futures) is established. fficeffice" />

Q1. At time = 0, for a put option at exercise price (X) on a newly issued forward contact at F_T (the forward price at time = 0), a portfolio with equal value could be constructed from being long in:

A)   the underlying asset, long a put at X, and short in a pure-discount risk-free bond that pays X – F_T at option expiration.

B)   a risk-free pure-discount bond that pays F_T – X at option expiration and long in a put at X.

C)   a call at X and long in a pure-discount risk-free bond that pays X – F_T at option expiration.

Correct answer is C)

Utilizing the basic put/call parity equation, we're looking for a portfolio that is equal to the portfolio mentioned in the stem (a put option). The put-call parity equation is c₀ + (X – F_T) / (1+R)^T = p₀. Since (X – F_T) / (1+R) is actually just the present value of the bond at expiration, the relationship can be simplified to long call + long bond = put.

Q2. Put-call parity for options on forward contracts at the initiation of the option where the forward price at that time (time=0) is FT, can best be expressed as:

A)   c₀ + (X ? FT) / (1 + R)^T = p₀.

B)   c₀ + X / (1 + R)^T ? FT = p₀.

C)   c₀ ? (X ? FT) / (1 + R)^T = p₀.

Correct answer is A)

Put call parity for stocks (with discrete time discounting) is c₀ + X / (1 + R)^T ? S₀ = p₀. Noting that for the forward contract on an asset with no underlying cash flows, S₀ = FT / (1 + R)^T, and substituting, we get c₀ + (X ? FT) / (1 + R)^T = p₀.

Q3. Which of the following would have the same value at t = 0 as an at-the-money call option on a forward contract priced at FT (the forward price at time = 0)?

A)   A put option, long the underlying asset, and short a risk-free bond that pays X-FT at option expiration.

B)   A put option, long the underlying asset, and short a risk-free bond that matures at X at option expiration.

C)   A put option on the forward at exercise price (X).

Correct answer is C)

Put-call parity for options on forward contracts is c₀ + (X – FT) / (1+R)^T = p₀. Since X = FT for an at-the-money option, the put and the call have the same value for an at-the-money option.

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