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+1 vote
in BUS 2016H - Financial Mathematics by (3.1k points)

The question is below:


Honestly, I don't have much of an idea where to begin. I've been told to calculate the value of the security today and again when the investor buys the security (t=26 months) but I'm not sure how that would help. Is there an easier way to do this question?

1 Answer

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Best answer

You only need to calculate the value of the security today. The value in the future is uncertain, because the yield might not stay at \(6\%\).

Let this value be denoted \(P\), and you can show that \(P = 128034\).

Next, calculate the present value today (with risk-free force of interest) of the coupons that will be paid during the term of the forward contract:

$$I = \frac{9000}{2} ( \exp[- 0.05\times \frac{4}{12}] + \exp [ -0.05 \times \frac{10} {12}] + \exp [{-0.05 \times \frac{16} {12}}]) = 12951.8$$

An arbitrage argument can be used to show that

$$K \exp[-0.05\times \frac{18}{12}] = P - I$$

where \(K\) is the forward price.

PS: arbitrage arguments are not very intuitive unless you work with them every day! If you have time, try look at some simpler examples (i.e. easy numbers) and try understand how the arbitrage principle applies.