Question

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?

Answer 1

The net value of Pat's wager is approximately -$4.9998435.

Step-by-step explanation:

To find the net value of Pat's wager, we need to calculate the expected value of the wager. The expected value is calculated by multiplying each outcome by its probability and summing the results.

In this case, there are two possible outcomes: either the price of ABC Corp. is above $85.00 (the favorable outcome) or it is below $85.00 (the unfavorable outcome).

The probability of the favorable outcome is:

(Probability of price above $85.00) = 1 - P(price below $85.00)

(Probability of price above $85.00) = 1 - P(Z < (85 - 75) / 0.25)

(Probability of price above $85.00) = 1 - P(Z < 4)

(Probability of price above $85.00) = 1 - 0.9999683

(Probability of price above $85.00) ≈ 0.0000317

The probability of the unfavorable outcome is 1 - 0.0000317 = 0.9999683.

The net value of the wager is then calculated as:

Net Value = (Outcome value * Probability of outcome) - (Outcome value * Probability of outcome)

Net Value = (5 * 0.0000317) - (5 * 0.9999683)

Net Value ≈ -4.9998435