Price-Linked Derivative Security Pricing Example

Price-Linked Derivative Security Pricing Example

Prev Question Next Question

Question

A price-linked derivative security pays $300 if the oil price over the next year increases by more than 5%, an event that can happen with a 60% probability.

Otherwise, it pays $50. If the expected return on the security is 15%, how much does the security cost?

Answers

Explanations

Click on the arrows to vote for the correct answer

A. B. C. D.

A

The expected payoff on the security equals 0.6 * 300 + 0.4 * 50 = 200. Since the expected return is 15%, the security must cost 200/1.15 = $173.9

To determine the cost of the price-linked derivative security, we need to calculate the expected value of the security's cash flows and then discount them back to the present value using the expected return rate.

Let's break down the problem step by step:

  1. Calculate the expected value of the cash flows: The security pays $300 with a 60% probability if the oil price increases by more than 5%, and it pays $50 otherwise. We can calculate the expected value as follows:

Expected Value = (Probability of Event 1 * Cash Flow of Event 1) + (Probability of Event 2 * Cash Flow of Event 2)

Expected Value = (0.60 * $300) + (0.40 * $50) Expected Value = $180 + $20 Expected Value = $200

Therefore, the expected value of the price-linked derivative security is $200.

  1. Calculate the cost of the security: The cost of the security is the present value of the expected cash flows. We can use the formula for present value to calculate it:

Cost of Security = Expected Value / (1 + Expected Return Rate)

Given that the expected return rate is 15% (0.15), we can substitute the values into the formula:

Cost of Security = $200 / (1 + 0.15) Cost of Security = $200 / 1.15 Cost of Security ≈ $173.91

Rounded to the nearest dollar, the cost of the security is $174.

Therefore, the correct answer is A. $174.