An oil company issues a bond whose coupons depend on the market price P(t) of a barrel of crude oil. 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) = 4

= 2 x (2 + (P(t) - 18)/5)

= 6

if P(t) < 18

if 18 < P(t) < 23

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 crude oil.

Knowing that P(0) = 18, the volatility of crude oil price is 20%, and the yield curve is flat at 5%, 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