Question

Landmines a pure gold producer needs money. Want to raise money by selling a bond. Their investment banker, Bonkman Sacks, designs the bond to sell. It will pay at maturity a year later $1,000 mil +an additional amount. This additional amount (figures are all in $ mil) is tied to gold’s price S(T) and will be:

0 if S(T)<$950

10[S(T)-950] if S(T) ³ $950

If the risk free rate is 10%, the current price of gold is $920 and the volatility of gold price is 20% per year can you find what is the amount of money that they can raise?

Answer 1

The additional amount pay-off structure is that of a European call option

The extra amount amount they will receive above the bond price will that be of 10 call options (because additional amount pay-off is multiplied by 10)

We will use Black sholes pricing model to value the European call option

So: current stock price = 920

K strike price = 950

r risk free rate = 10% = 0.1

s: standard deviation = 20% = 0.2

t: time to maturity = 1 year

d1 = 0.4396

d2 = 0.2396

N(d1) = normsdist(d1) = 0.6699

N(d2) = normsdist(d2) = 0.5947

C: value of call option

e: natural exponent

c = 56.04 (price of 1 call option)

Price of 10 call options = 56.04*10 = 560.4

Let the face value of bond = 1000

Price of zero coupon bond = 1000*exp^(-r*t) = 1000*exp^(-10%*1) = 904.84

where exp is the natural exponent

Amount raised per $1000 face value = $904.84+$560.4 = $1465.24