Volatility and Early Exercise of American Options

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 25

This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.

This is Section 25 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here. See Section 5 here. See Section 6 here. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10

here. See Section 11 here. See Section 12 here. See Section 13 here. See Section 14 here. See Section 15 here. See Section 16 here. See Section 17 here. See Section 18 here. See Section 19 here. See Section 20 here. See Section 21 here. See Section 22 here. See Section 23 here. See Section 24 here.

On an American call option where the volatility is zero, it is optimal to defer exercise as long as the following condition holds:
rK > ∂S

It is optimal to exercise whenever

S > rK/∂

American "call options are early-exercised in order to capture dividends on the underlying stock."

With put options, the reverse holds. It is optimal to exercise early when

S < rK/∂

and it is optimal to defer exercise when rK < ∂S

Meaning of variables:

r = annual continuously-compounded risk-free interest rate.