Financial Risk Manager Part 1

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Explanation:

The portfolio either moves up by 10% or down by 10%. Thus,

up move factor = $u = e^{\sigma\sqrt{t}} = e^{0.1} = 1.1$ down move factor = $d = \frac{1}{1.1} = 0.9$ Probability of an up move = $\frac{e^{rt} - d}{u - d} = \frac{e^{0.06} - 0.9}{1.1 - 0.9} = 0.809$ Value of the option = $e^{-0.06} [0.809 \times 10 + 0.191 \times 0] = \`$ 7.62`1 $ million

Explanation:

The portfolio either moves up by 10% or down by 10%. Thus,

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Q.56 Rahim Associates manages a portfolio of USD 100 million. After one year, if the value of the portfolio moves up, the value would be 110 million, and if the value of the portfolio moves down, the value would be 90 million. The risk-free rate is 6 percent per annum, compounded continuously. Rahim Associates takes a short options position to make the portfolio riskless. The value of options would be USD 10 million if the value of the portfolio moves up to USD 110 million and zero if the value of the portfolio moves down to USD 90 million. What is the present value of the option?

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RRohit

Last updated: June 22, 2026 at 14:25

USD 7.62 million.

USD 8.09 million.

USD 8.59 million.

USD 9.15 million.