A stock is currently trading at $100.In each month,the stock will either increase in price by a factor of $u = 1.10$ or fall by a factor of $d = 0.90$ .The risk-free rate of interest per month is 0.1668% in simple terms,i.e. ,an investment of $1 at the risk-free rate returns $1.001668 after one month.What is the early-exercise premium of a 100-strike,six-month American call option when a dividend of $1 is paid at the end of each month? (Assume that if the option is exercised,it is done just before the dividends are paid. )
A)$0.00
B)$0.25
C)$0.30
D)$0.35

Question

Quizplus · Accepted Answer

The early-exercise premium is the difference between the value of the option if it is exercised immediately and the value of the option if it is held until maturity. In this case, the value of the option if it is exercised immediately is $100 - $1 = $99. The value of the option if it is held until maturity is the present value of the expected payoff at maturity. The expected payoff at maturity is $100 if the stock price increases by a factor of 1.10 in each of the six months, and $90 if the stock price falls by a factor of 0.90 in each of the six months. The probability of each of these outcomes is 1/2. Therefore, the expected payoff at maturity is $95. The present value of this payoff is $95 / (1.001668)^6 = $90.25. Therefore, the early-exercise premium is $99 - $90.25 = $8.75.

A Stock Is Currently Trading at $100 u=1.10u = 1.10u=1.10 Or Fall by a Factor Of

A Stock Is Currently Trading at $100 $u = 1.10$ Or Fall by a Factor Of