Math 456: Introduction to Financial Mathematics

Abstract

1. Suppose that a risky asset S has spot price S(0) = 100 and that the riskless return to T = 1 year is R = 1.0537. Assuming there are no arbitrages, compute the following: (a) the current zero-coupon bond discount Z(0, T ), (b) the Forward price for one share of S at expiry T , (c) the riskless annual interest rate (assuming continuous compounding), Solution: (a) From the formula on p.3, Z(0, T ) = 1 R = 0.9490. (b) By Eq.1.15, the fair price is K = RS(0) = 105.37. (c) By Eq.1.6, r = (log R)/T = 0.0523, or 5.23%. 2