In a one-period binomial model, assume that the current stock price is $100, and that it will rise to $110 or fall to $90 after one month. If an investment of a dollar at the risk-free rate returns $1.001668 after one month, and the 98-strike put option is trading at $2, how much arbitrage profit can you make in present value terms?
A) $1.93
B) $2.92
C) $3.93
D) $8.00

Question

Quizplus · Accepted Answer

To find the arbitrage profit, we first calculate the risk-neutral probabilities and the theoretical price of the put option. The risk-neutral probability of the stock rising (p) is calculated using the formula: p = (1.001668 - 90/100) / (110/100 - 90/100) = 0.5834. The theoretical price of the put option is then calculated using the risk-neutral probabilities: P = (1-p) * max(0, 98-110) + p * max(0, 98-90) / 1.001668 = $0.07. Since the market price of the put is $2, the arbitrage profit is $2 - $0.07 = $1.93.

In a One-Period Binomial Model, Assume That the Current Stock