
Explanation:
First, determine the risk-neutral probability of an upward movement: ,
The expected value of the option at maturity is:
The present value of the option is discounted at the risk-free rate:
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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?
A
USD 7.62 million.
B
USD 8.09 million.
C
USD 8.59 million.
D
USD 9.15 million.