A mining company issues a bond whose coupons depend on the market price G(t) of one ounce of gold. This bond expires in exactly 2 years, pays off an annual coupon (there are 2 coupons due) plus a principal of 100 at maturity.

Each coupon C(t) is calculated as follows (for t = 1 and t = 2):

c(t) = 6 if G(t) < 27

c(t)= 6 + (2/5) (G(t) 27) if 27 < G(t) < 34.5

c(t)= 6 + 3 otherwise.

a) Show that the bond can be stripped as a series of zero-coupon bonds and portfolios of European options (to be determined) written on the price of the ounce of gold.

b) Knowing that G(0) = 27, the volatility of the ounce of gold price is 30%, and the yield curve is flat at 6.1%, compute the value of this bond (up to 2 decimals) using BS formula. Comment your result, i.e. explain intuitively why the bond price is above or under par.