The common stock of Trynor's, Inc. is currently priced at $37.90 a share. One year from now, the stock price is expected to be either $38 or $43 a share. The risk-free rate of return is 3.5 percent. What is the current value of one call option on this stock if the exercise price is $40?
A) $0.64
B) $0.71
C) $0.77
D) $0.82
E) $0.91

Question

Quizplus · Accepted Answer

The value of the call option can be calculated using the binomial option pricing model. First, calculate the up and down factors (u and d), and then the risk-neutral probabilities (p and 1-p). However, given the simplicity of the scenario, we can directly calculate the expected payoff and discount it back at the risk-free rate.1. If the stock goes up to $43, the call option will be worth $3 ($43 - $40 exercise price). If the stock goes down to $38, the option will be worth $0 (since it's out of the money).2. The expected payoff of the option is the probability-weighted average of these outcomes. However, without explicit probabilities, we can simplify by considering the outcomes equally likely or use risk-neutral valuation, which essentially does this in a more complex setting.3. Discount the expected payoff at the risk-free rate to get the present value.Expected payoff = (0.5 * $3 + 0.5 * $0) = $1.5 / 2 = $0.75. Then, discount this back one year at the risk-free rate of 3.5%.$$ \text{Present Value} = \frac{\$0.75}{1 + 0.035} = \frac{\$0.75}{1.035} \approx \$0.7246 $$The closest answer to this calculation is $0.71, which is option B. This is a simplified approach and assumes a basic understanding of option pricing and the risk-neutral valuation principle.

The Common Stock of Trynor's, Inc