Digital caplet in arrears
Consider an option that pays α at time T if LT > K, and zero otherwise.
By considering the payout of this option (a 'digital caplet in arrears') at T + α, show that its price
![](https://book.transtutors.com/qimg/83985e09-2702-4402-adcf-1b0678131d7e.png)
![](https://book.transtutors.com/qimg/48758ff3-2229-4bfd-93fe-77c76638b2fa.png)
where DK(t, T) is the price of a regular digital caplet, and CK (t, T) is the price of a K-strike caplet with maturity T.