Assuming that we are allowed to differentiate under the expectation sign
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Assuming that we are allowed to differentiate under the expectation sign

Exercise 23.2 

The object of this exercise is to connect the forward rates defined in Chapter 22 to the framework above.

(a) Assuming that we are allowed to differentiate under the expectation sign, show that


(b) Check that indeed r(t) = f(t, t).

Hint
StatisticsForward rate is the interest rate which is applicable to a financial transaction that could take place in the future. Also, these rates are calculated from the spot rate and are also adjusted for the cost of carry to mainly determine the future interest rate which equates the total return of a longer-term investment with a strategy of rolling over a shorter-term investment....

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