Skip to content

FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

A risk manager prices a caplet on the same tree: the one-year rate is 5% today and 6% or 4% at year 1 with risk-neutral probabilities of 0.5 each. The caplet has notional 100, a strike of 5%, and a payoff based on the one-year rate set at year 1 and paid in arrears at year 2. What is its value today?

The caplet is worth about 0.449. It pays 1 at year 2 only in the up state, which is worth 0.943 at year 1. Weighting by 0.5 gives 0.472, and discounting one more year at the 5% short rate gives 0.449.

  1. A0.449Correct
  2. B0.472
  3. C0.476
  4. D0.899

Explanation

Payoff at year 2 is 100 x (6% - 5%) = 1 in the up state and 0 in the down state. At year 1 the up-state value is 1/1.06 = 0.9434. The expectation is 0.5 x 0.9434 = 0.4717, and discounting at 5% gives 0.4492. Omitting the year-1 discount gives 0.476, and omitting the probability weight gives 0.899.

Did you get it right without looking?

One question tells you little. A timed set on Arbitrage Pricing with Term Structure Models shows your real accuracy, how long you take and where you lose marks.

Practise Arbitrage Pricing with Term Structure ModelsFree diagnostic mock

More Arbitrage Pricing with Term Structure Models questions