The Binomial Model 1

CFA Level II Derivatives
#1

Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic European call option?

A) Buy the stock; buy a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond.

B) Sell the stock; buy a European put option on the same stock with the same exercise price and the same maturity; invest an amount equal to the present value of the exercise price in a pure-discount riskless bond.

C) Buy the stock; sell a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond.

Correct answer A.

Explanation: According to put-call parity we can write a European call as: C0 = P0 + S0 – X/(1+Rf)T We can then read off the right-hand side of the equation to create a synthetic position in the call. We would need to buy the European put, buy the stock, and short or issue a riskless pure-discount bond equal in value to the present value of the exercise price.

Can anybody please explain this concept. Thanks in advance.

#2

Put-call parity for European options starts with this equation:

C0 + X/(1+Rf)^T = P0 + S0

Subtracting X/(1+Rf)^T from both sides gets you to the formula for C0.

Using the basic equation, you can rearrange the equation to your heart’s content for any synthetic position. To go long(short), the sign of the items is +(-). For example, to short the underlying synthetically, -S0 = P0 - C0 - X/(1+Rf)^T, meaning go long put, short call, short bond.

1 Like