A one year bond is currently selling for $80, has coupons of 5% pa and face value $80. A two year bond is currently selling for $90, has coupons of 3% pa and face value $100. A three year bond is currently selling for $85, has coupons of 10% pa and face value $80. 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 returns R(n, j) over the next three years (that is, for n = 0, 1, 2 and 0 j n), given that the parameters for the HoLee model are = 0.4 and = 0.92 . Note that you should find six different returns.

(c) Identify any returns in part (b) which have an unexpected value. How might you change the HoLee parameters to avoid this issue?