Digital caplets Consider two possible candidates (I) and (II) for the risk-neutral distribution of LT conditional on LtT. Both are distributions with respect to the numeraire Z (t, T + α).
(a) Assuming no-arbitrage, what is the value of μ?
(b) Calculate the price at time t of the digital caplet that pays α at time (T + α) if LT > K, and zero otherwise, under the two different models (I) and (II).
(c) Calculate the vega of this digital caplet under the two models (I) and (II) - where vega is defined as 
for (II). For what values of K does the digital caplet have zero vega, for (I) and (II) respectively?
(d) What are the prices of the at-the-money-forward digital caplet for (I) and (II)? Explain your answers in terms of the median of lognormal and normal distributions.