The current price of a non-dividend-paying stock is $40.Over the next year it is expected to rise to $42 or fall to $37.An investor buys put options with a strike price of $41.What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding.
A) $3.93
B) $2.93
C) $1.93
D) $0.93

Question

Quizplus · Accepted Answer

The value of the put option is calculated using the risk-neutral valuation method. The expected payoff of the option is discounted at the risk-free rate. The expected payoff is calculated by considering the probability of the stock price falling to $37, which would make the option in-the-money with a payoff of $4 (since $41 - $37 = $4). The probability of the stock price falling is calculated using the risk-neutral probabilities, which are derived from the current stock price, the up and down movements, and the risk-free rate. After calculating the expected payoff and discounting it, the value of the option is found to be approximately $0.93.

The Current Price of a Non-Dividend-Paying Stock Is $40