Calculate the price at time t of the digital caplet

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Reference no: EM131243645

Digital caplets Consider two possible candidates (I) and (II) for the risk-neutral distribution of L_T conditional on Lt_T. 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 L_T > 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.

Reference no: EM131243645

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