Calculate the price of a one-month European put option given the following information: the exercise price is $19,the current share price is $15 and the risk-free interest rate is 12% p.a.Furthermore,the share price is expected to be either $20 or $13 at the end of the month.Assume a risk-neutral world.

Question

Quizplus · Accepted Answer

Using the risk-neutral valuation formula, we can calculate the price of the one-month European put option as:

P = e^(-rT)[(X - S*P(D)) / (P(U) - P(D))]

where P(D) and P(U) are the probabilities of the share price going down or up, respectively, and T is the time to expiration, which is one month in this case.

First, we need to calculate the risk-neutral probabilities. Since the share price can either go up to $20 or down to $13, we can use the binomial distribution to determine these probabilities. Let p be the probability of the share price going up, then 1-p is the probability of it going down. We can set up the following equations:

$20 = $15 * u ==> u = 1.33
$13 = $15 * d ==> d = 0.87
1 = p + (1-p) ==> p = 0.5

Using the risk-free interest rate of 12% p.a., we can calculate the discount factor:

e^(-rT) = e^(-0.12/12 * 1) = 0.9901

So, the price of the put option is:

P = 0.9901 * [(19 - 15*0.87) / (1.33 - 0.87)] = $4.12

Therefore, the answer is B.

Calculate the Price of a One-Month European Put Option Given