Question

a stock price is currently $30. during each two-month period for the next four months it will increase by 8% or reduce by 10%. the risk-free interest rate is 5% per annum, compounded continuously. use a two-step tree to calculate the value of a derivative that pays [max(30 - st ,0)]2, where st is the stock price in four months?

Answer 1

The question deals with calculating the present discounted value of a two-year bond at varying interest rates. Using the provided interest rate, future cash flows are discounted to determine their current value. Different discount rates illustrate the impact of interest rate changes on bond valuation.

Step-by-step explanation:

The subject of our question is Mathematics, specifically focusing on the concept of present discounted value and the valuation of derivatives. A simple two-year bond issued for $3,000 with an 8% interest rate provides a clear example. To calculate the present value of this bond at a discount rate of 8%, we can apply the present value formula:

• Interest payment in year 1: $3,000 × 8% = $240
• Interest + principal payment in year 2: $240 + $3,000 = $3,240

The present value (PV) is calculated as follows when the discount rate is 8%:

PV = $240 / (1 + 0.08) + $3,240 / (1 + 0.08)^2

If interest rates rise and the discount rate becomes 11%, the present value would be recalculated using the new rate:

PV = $240 / (1 + 0.11) + $3,240 / (1 + 0.11)^2

These calculations demonstrate the effect of changing discount rates on the present value of future cash flows.