Option Replication Using Put–Call Parity

Question 1

A fiduciary call is a …

Answer 1

A call and a risk-free bond replicating a protective put

Question 2

A protective put is a …

Answer 2

Buying an underlying asset and purchasing a put on the same asset

Question 3

A protective put and a fiduciary call on the same assets have the same payoff structures, this is …

The formula is …

Answer 3

Put-Call parity

P + S = C + X/(1+r)^T

Question 4

Put–call forward parity;

Answer 4

P + F/(1+r)^T = C + X/(1+r)^T

Question 5

A synthetic protective put is …

Answer 5

A combination of the synthetic underlying position (forward purchase and a risk-free bond) and a purchased put on the underlying

Question 6

A firm has risky debt because the bondholders receive D only in the case of solvency. Therefore, debtholders demand a …

Answer 6

… premium

similar to a put option premium from shareholders in order to assume the risk of insolvency

Question 6

A shareholder’s combination of a purchased put option and a long position in the firm’s assets is equivalent to a … .

The risky debt held by the debtholders is a combination of the …

Answer 6

call option on the firm’s assets

risk-free debt and the put option sold to shareholders

Question 7

From a firms perspective the PC parity can look like;

Answer 7

V + P = C + PV(D)

D = debt
V = value of firm (eq + debt)

Question 8

V + P = C + PV(D)

The shareholder has a position with a payoff similar to that of a … .

The debtholder has a position of PV(D) – P, or …

Answer 8

call option on firm value

risk-free debt of the firm plus a sold put option on firm value

Question 9

V + P = C + PV(D)

The put option may be interpreted as …, or …

This put option … in value to shareholders as the likelihood of insolvency increases.

From a debtholder’s perspective, the more valuable the sold put, the … credit risk is present in the firm’s debt.

Answer 9

the credit spread on the firm’s debt

the premium above the risk-free rate the firm must pay to debtholders to assume insolvency risk

increases

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