By Primicerio M., et al. (eds.)

Business arithmetic is evolving into an incredible department of arithmetic. Mathematicians, in Italy specifically, have gotten more and more conscious of this new pattern and are engaged in bridging the distance among hugely really good mathematical examine and the rising call for for innovation from undefined. during this recognize, the contributions during this quantity supply either R&D staff in with a basic view of latest abilities, and teachers with state of the art purposes of arithmetic to real-world difficulties, that may even be included in complex classes.

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Use your result from (a) to show that a ﬂoating leg of libor payments αLTi [Ti , Ti + α] at times Ti+1 , i = 0, 1, . . , n – 1, has value at time t ≤ T0 equal to a simple linear combination of ZCB prices. (c) Hence ﬁnd the value of a spot-starting inﬁnite stream of libor payments, that is, when t = T0 = 0 and as n → ∞. 5. Fixed rate annuity revisited Suppose annually compounded zero rates for all maturities are a constant r, so Z(0, j) = 1 for j = 1, 2, . .. (1+r)j (a) What is the value today of a ﬁxed annuity that pays 1 each year from T1 = 1 to Tn = n?

How does your answer change if the asset pays dividends at constant rate q? 6. Dollar-yen and the carry trade A major currency pair is dollar-yen, quoted in yen per dollar. 10. 41% respectively (semi-annual, act/365 daycount). (a) Calculate the forward price for dollar-yen ﬁve years forward. 5 accrual factor, rather than 182/365 etc, for yen. (b) Suppose you were unable to trade forward contracts, but were able to trade spot FX and borrow or lend dollar and yen cash. How could you synthetically go long the forward contract in (a)?

This page intentionally left blank 5 Futures contracts A futures contract is a derivative with many similarities to a forward, essentially being a contract to trade an underlying asset at a ﬁxed time in the future. However, there are two key differences. Most importantly, a futures contract involves cashﬂows each day up until the maturity date T and not just at T. Secondly, virtually all futures contracts are traded on exchanges rather than as bilateral over-the-counter contracts between two counterparties.