Consider again the setup of Question 1. Suppose we want to price three European style call options written on one period (spot) Libor rates Li with i = 0, 1, 2, 3, as in the above case. Let these option prices be denoted by Ci. Each option has the payoff:
Ci = N max[Li - K,0],
where N is a notional amount that we set equal lo one without loss of any generality.
(a) How can you price such an option?
(b) Suppose we assume the following;
(i) Each ft, is a current observation on the future unknown value of Li.
(ii) Each ft is normally distributed with mean zero and constant variance σi.
(iii) We can use the Black formula to price the calls.
(c) Would these assumptions be appropriate under the risk-neutral measure obtained using money market normalization? Explain.
(d) How would the use of the forward measure that corresponds to each Li improve the situation?
(e) In fact, can you obtain the forward measures for times t = 1, 2?
(f) Price the call option for time t = 2 using the forward measure.