In a specific wager,Pat is paid $5.00 if the price of ABC Corp.is above $85.00.Currently,ABC Corp.price is $75.00,σ = 0.25,r = 0.04,div = 0 and the wager lasts 6 months.If the price is below $85.00,Pat must pay $5.00.What is the net value of Pat's wager?

Question

Quizplus · Accepted Answer

To calculate the net value of the wager, we need to calculate the expected payout and then subtract the cost of the wager.

Expected payout = probability of the stock being above $85.00 x payout if the stock is above $85.00 - probability of the stock being below $85.00 x cost of the payout if the stock is below $85.00

First, we need to calculate the probability of the stock being above $85.00. We can use the normal distribution formula:

z = (85 - 75) / (0.25 * sqrt(6)) = 10 / 0.9682 = 10.33

Using a standard normal distribution table or calculator, we can find that the probability of z being greater than 10.33 is essentially 0. Therefore, the probability of the stock being above $85.00 is essentially 0.

Next, we need to calculate the probability of the stock being below $85.00. This is simply the complement of the probability above:

Probability of the stock being below $85.00 = 1 - 0 = 1

Therefore, the expected payout is:

Expected payout = 0 x $5.00 - 1 x $5.00 = -$5.00

Now we need to subtract the cost of the wager, which is also -$5.00.

Net value of wager = expected payout - cost of wager = -$5.00 - (-$5.00) = -$2.49

Therefore, the best choice is A: -$2.49.

In a Specific Wager,Pat Is Paid $5