For the option discussed in part (e) but not considered in part (e) (put or a call), give an example of when the Australian company might consider buying this option. Explain your answer.

1. A one year bond is currently selling for $95, has coupons of 3% pa and face value $100. A two year bond is currently selling for $95, has coupons of 4% pa and face value $100. A three year bond is currently selling for $98, has coupons of 6% pa and face value $100. All three bonds pay coupons annually, starting one year after purchase.

(a) Use these three coupon bonds to find the zero-coupon bond values P(0,1), P(0,2) and P(0,3). Show all working.

(b) Use the zero-coupon bond values P(0.1), P(0,2) and P(0, 3) to find the re- turns R(n,j) over the next three years that is, for n = 0,1,2 and 0 ),>

(c) A zero-coupon bond which matures in three time steps must, at time n = 3, have value P} 0) = 1 for all states j = 0,1,2,3. Use P}(0) = 1, constant

risk-neutral probability 7 = 0.4, the binomial pricing formula and your variable returns calculated in part (b) to construct a binomial pricing tree for this zero- coupon bond(c.) Check that the premium of this zero-coupon bond agrees with the zero-coupon bond value P(0,3) calculated in part (a).

(d) Use the Ho-Lee model equation

P(0,n+T) h(T)h(T + 1)... h(T +n 1) ginj)T P (T) (1)

P(0,n) h(0)h(1)...h(n-1)

to calculate Pl(2) and show that it agrees with your calculations in part (c).