Question

1. The spot price of an investment asset is $50 and the risk-free rate for all maturities is 8% with continuous compounding. The asset provides an income of $2 at the end of the first year and at the end of the second year. What is the three-year forward price?

    A) $56.32                          B) $59.03                    C) $53.55                    D) $57.31

Answer 1

The three year forward price is computed as shown below:

= Spot price x e ^{risk free rate x 3} - $ 2 x e ^{risk free rate x 1} - 2 x e ^{risk free rate x 2}

= $ 50 x 2.71828 ^{0.08 x 3} - $ 2 x 2.71828 ^{0.08 x 1} - $ 2 x 2.71828 ^{0.08 x 2}

= $ 50 x 2.71828 ^0.24 - $ 2 x 2.71828 ^0.08 - $ 2 x 2.71828 ^0.16

= $ 50 x 1.271248945 - $ 2 x 1.083287009 - $ 2 x 1.173510745

= $ 59.03 Approximately

So, the correct answer is option B.

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