Comparison of Short Plain Vanilla Forward with Short Target Forward Contract

Question

This question concerns a simplified version of the target forwards contract introduced in class during the Aracruz Cellulose discussion.

You are comparing two alternatives:

• A short plain vanilla forward contract with a delivery price of K₁ = 100; and

• A short target forward with a delivery price of K₂ = 103.

Both instruments have a maturity of one month and are written on the same underlying asset. Both instruments are zero value at inception, i.e., you do not have to pay anything upfront to get into the respective contracts. If S_T denotes the price of the underlying asset at maturity, the payoff from the short forward at maturity is

100 - S_T

for all S_T, while the payoff from the short target forward at maturity is

103 - S_T,          if S_T < 103

2 x (103 - S_T), if S_T ≥ 103

Answer the following questions:

1. For what range of values of S_T will the short target forward with delivery price 103 result in a larger payoff at maturity than the short vanilla forward contract with delivery price 100?

2. Show that the target forward with a delivery price of 103 is identical to a portfolio of two items: (i) a short position in a vanilla forward with a delivery price of 103, and (ii) a short position in a plain vanilla call option with a strike of 103. (In words, being short a target forward is like being short an ordinary forward and, in addition, being short a call option.) That is, fill in the payoffs of each instrument in the following table and show that the total payoff is exactly the same as the target forward's payoff give above.

Summary: This question belongs to finance and discusses about discusses about simplified version of the target forwards contracts.

Answer is in Excel format