7.9 Option Replication Using Put-Call Parity

Question 1

Put-call parity

Answer 1

an essential concept every trader should understand about options.

It is derived by comparing the payoffs of two portfolio strategies – fiduciary call and protective put.

the two portfolios provide identical payoffs at time T regardless of the ending underlying asset price:

Question 2

A fiduciary call

Answer 2

composed of a risk-free asset with a face value of X to be paid at time T plus a call option c

Question 3

protective put.

Answer 3

A protective put is composed of a long underlying asset S plus a put option p.

Question 4

A long put position is equivalent to

Answer 4

being long a call, short the underlying, and long a risk-free bond:

Question 5

A long call position is equivalent to

Answer 5

being long the underlying, long a put, and short a risk-free bond

Question 6

Owning the underlying can be replicated by

Answer 6

buying a call, selling a put, and owning a risk-free bond:

Question 7

Owning a risk-free bond can be replicated by

Answer 7

owning the underlying, buying a put, and selling a call

Question 8

a covered call strategy

Answer 8

executed by owning an underlying asset and selling a call.

Investors can use this strategy to enhance their returns if they expect that assets in their portfolios are unlikely to appreciate significantly.

Question 9

The payoffs for the two types of capital providers in case of company bankruptcy can be summarized as follows:

Answer 9

Debtholders receive min (D, VT)

Equity owners receive max (0, VT - D)