Skip to content

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

A firm grants employee stock options with a 10-year contractual life on a stock that pays no dividends. Based on past behaviour, employees are expected to exercise after about 6 years on average. If the firm uses the Black-Scholes-Merton model with a 6-year expected life as the time to maturity, instead of the 10-year contractual life, how will the estimated option value compare, all else equal?

The estimated value will be lower. For a call on a non-dividend stock, option value rises with time to maturity, so using a 6-year expected life instead of the 10-year contractual life reduces the Black-Scholes-Merton value. This approximates the effect of early exercise by employees.

  1. ALower, because a shorter time to maturity reduces the value of a call on a non-dividend stockCorrect
  2. BHigher, because shorter maturity reduces the present value of the strike price less
  3. CIdentical, because the BSM model ignores time to maturity for non-dividend stocks
  4. DHigher, because early exercise adds value that the contractual term ignores

Explanation

For a call on a non-dividend-paying stock, value increases with time to maturity because of more time value and a lower present value of the strike. Shortening T from 10 to 6 years therefore lowers the estimated value. Using expected life is a way to reflect early exercise and forfeiture, which reduce the cost to the firm.

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