Skip to content

FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A stock trades at 40 and pays no dividends. A European put with strike 50 and one year to expiry has a continuously compounded risk-free rate of 5%. What is the lower bound for the European put price, and does the bound show that early exercise of the American put may be optimal?

The European put lower bound is 50e^-0.05 minus 40, about 7.56, which is below the immediate exercise value of 10. Because the European put can be worth less than intrinsic value, the American put is worth at least 10 and early exercise may be optimal.

  1. ALower bound 50e^-0.05 - 40 = 7.56; it is below the intrinsic value of 10, so the American put is worth at least 10 and early exercise can be optimalCorrect
  2. BLower bound 50 - 40e^-0.05 = 11.95; early exercise is never optimal
  3. CLower bound 7.56; it exceeds intrinsic value of 10, so early exercise is never optimal
  4. DLower bound 10; the European put must equal the American put

Explanation

50e^-0.05 = 50 x 0.951229 = 47.56, so the bound is 47.56 - 40 = 7.56. Intrinsic value is 10, which is greater than 7.56, so the European put can trade below its immediate exercise value. The American put must be worth at least 10, so early exercise can be optimal.

Did you get it right without looking?

One question tells you little. A timed set on The Black-Scholes-Merton Model shows your real accuracy, how long you take and where you lose marks.

Practise The Black-Scholes-Merton ModelFree diagnostic mock

More The Black-Scholes-Merton Model questions