F3.2 Let 12 = {H, TN and let (Ro, R2, ...,RN-1) be an adapted stochastic process such that for all n e {1,2, ...,N} we have Rn > -1. This process is the interest rate process, and an investment of 1 in the risk-free asset at time n produces a return of 1 + R, at time n +1. You create a security that will pay out R, in period n + 1 for each n {0,1,2,....N - 11 (a total of n payments). Assuming that there is a risk-neutral measure, calculate the risk- neutral price of this security at time 0 in terms of the risk-neutral prices of zero-coupon bonds having maturity value 1. Hint: Start by showing that you can finance the payment occuring at time n +1 using a portfolio with positions in two 0-coupon bonds: a long position in a bond maturing at time! n with value 1, and a short position in a bond maturing at time n +1 with value 1 + R F3.2 Let 12 = {H, TN and let (Ro, R2, ...,RN-1) be an adapted stochastic process such that for all n e {1,2, ...,N} we have Rn > -1. This process is the interest rate process, and an investment of 1 in the risk-free asset at time n produces a return of 1 + R, at time n +1. You create a security that will pay out R, in period n + 1 for each n {0,1,2,....N - 11 (a total of n payments). Assuming that there is a risk-neutral measure, calculate the risk- neutral price of this security at time 0 in terms of the risk-neutral prices of zero-coupon bonds having maturity value 1. Hint: Start by showing that you can finance the payment occuring at time n +1 using a portfolio with positions in two 0-coupon bonds: a long position in a bond maturing at time! n with value 1, and a short position in a bond maturing at time n +1 with value 1 + R