Assignment 2-Arbitrage free pricing 2.1 away-moving Price of Gold in Two Currencies (Simple Rates) (A) The 6-month beforehand $ gold monetary think of X (0) = dishonor equipment casualty = $740.0, r$(0, 0.5) = 4.10% (since it is already adjusted for daycount, it produce be apply directly) Therefore, 6-month forrad $ gold price is X (0, 0.5) = X (0) × (1 + r$ × t) = $740.0 × (1 + 0.5 × 4.10%) = $755.17 (B) The point $/₤ FX tell FX (0) is 1.5800 r ($)=Annualized money-market dictate (4.10% on the $) r (₤)=Annualized money-market charge per unit (6.30% on the ₤) So the 6-month onward $/₤exchange rate FX (0, 0.5) is: FX (0, 0.5) × [1 + r (₤) × t] = FX (0) × [1 + r ($) × t] FX (0, 0.5) =FX (0) × = 1.5800 × = × 1.5800 = 1.5632 The dollar trades at a forward amplitude because r$ < r₤ (C) The 6-month forward ₤ gold price lav be calculated development the cash-and-carry equation on the spot price in ₤: X₤ (0) = X$ ÷ FX (0) = $740.0 ÷ 1.5800 ≈ ₤ 468.3544 X₤ (0, 0.5) = X₤ (0) × (1+ r£×t) = ₤468.3544 × (1+0.5 × 6.30%) = ₤483.1076 2.2 prior Price and profess of a € Zero Coupon Bond (A) Generally, we carry the see value of zip fastener voucher follow is €100. The defend value of this 10-year zero coupon bond should be discounted by 6% during the 10 age.
And because 6% is a classic rise turn over, it should be deepen like (1+ r) t So the Spot Price of Zero: PV= = = €55.8395 (B) We already got the stage value of the bond which is €55.8395. The 3-month forward arbitrage-free price potty be calculated by using the 3-months compounded admit based on the present value. X (0, ¼) = X (0) × (1 + r) t = €55.8395 × (1 + 4.00%) ¼ = € 56.3897 The calculation can be explained by the following gift: (In order to get the face value of €100 at maturity, another 9 years will compound on the X (0, 1/4) by the 3-month forward yield r) 0 3-months...If you want to get a full essay, order it on our website:
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