For the April 1999 Advanced Certificate in Derivatives exam, in the answer of question 3(ii) part (a), how is the value 0.2429 for t = 1 obtained? I was expecting 3.752 - 3.5 = 0.252. Thanks, Barbados.
ACiD April 1999 Q3(ii)(a) Barbados, The payoff from a caplet is paid at the end of the period, so its value at the option date (ie the start of the period) is: max[r(t)-3.5]/(1+r(t)) So, in the case you mention, we want: (3.752-3.5)/1.03752 = 0.2429 as required. (See Chapter 12, p17 for a summary of caplet valuation.)
Thanks for you reply. But where is the 1.03752 coming from? I was expecting to use 100 / 97.023 = 1.0306.
Your figure comes from using the 1-year ZCB price. This is the same interest rate as the far left entry in the tree given in the question for the annual short rate. It would be used for discounting back from t=1 to t=0. But the caplet value you asked about was the t=1 value, which is the payment due at t=2, discounted back to t=1. This requires the top value in the short rate tree at t=1, which is 3.752.
