Goldminers Inc.mines and refines ore and sells pure gold in the global market.To raise funds,it sells a derivative security whose payoff is as follows: •Part of the security is a zero-coupon bond (which is sold at a discount and makes no interest payments)that pays a principal of $1,000 at maturity T.
•Goldminers also pays an additional amount that is indexed to gold's price (per ounce)at maturity S(T):
0
If S(T)$\le$ $1,550
20[S(T)- 1,550]
If $1,550

Question

Goldminers Inc.mines and refines ore and sells pure gold in the global market.To raise funds,it sells a derivative security whose payoff is as follows: •Part of the security is a zero-coupon bond (which is sold at a discount and makes no interest payments)that pays a principal of $1,000 at maturity T.
•Goldminers also pays an additional amount that is indexed to gold's price (per ounce)at maturity S(T):
0
If S(T)$\le$ $1,550
20[S(T)- 1,550]
If $1,550<S(T)$\le$ $1,600
1,000
If $1,600<S(T).
This derivative can be written as a combination of:

Quizplus · Accepted Answer

The derivative's payoff structure mimics a long position in a zero-coupon bond worth $1,000 at maturity, combined with a payoff that increases linearly with the gold price above $1,550 and caps at $1,600. This is equivalent to being long on 20 European call options with a strike price of $1,550 (benefiting from price increases beyond this point) and short on 20 European call options with a strike price of $1,600 (capping the benefit at this price), ensuring the payoff does not increase beyond the gold price of $1,600.

Goldminers Inc ≤\le≤ $1,550 20[S(T)- 1,550] If $1,550<S(T) ≤\le≤ $1,600 1,000 If $1,600<S(T)

Goldminers Inc $\le$ $1,550
20[S(T)- 1,550]
If $1,550<S(T) $\le$ $1,600
1,000
If $1,600<S(T)