# 微积分网课代修|导数代写Derivatives theory代考|NE00CC07 SWAPS

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## 微积分网课代修导数代写Derivatives theory代考|SWAPS

Swaps are another type of derivative contract which first appeared in the early 1980s. They are primarily used for hedging interest rate or exchange rate risk over many future periods.
A swap is a negotiated $(\mathrm{OTC})$ agreement between two parties to exchange cash flows over a series of pre-specified future dates (‘reset dates’).
A plain vanilla interest rate swap involves a periodic exchange of interest payments. One set of future interest payments are at a fixed swap rate, $s p_{0}=3 \%$ p.a. (say), which is determined when the swap is initiated. The other set of interest payments are determined by the prevailing level of some ‘floating’ interest rate (usually LIBOR). The swap will be based on a notional principal amount of $\$ 100 \mathrm{~m}$, say. For example, in July 2018 a US firm ‘BigBurger’ might have a swap-deal with JPMorgan where BigBurger has agreed to receive annual interest payments from the swap dealer based on (USD) LIBOR rates on 15 July 2019 and on 15 July 2020 (the reset dates). BigBurger also agrees to pay the swap dealer (JPMorgan) a fixed swap rate of$s p_{0}=3 \%$p.a., on these dates (on a notional principal amount of$\$100 \mathrm{~m}$ ). BigBurger is a ‘floating-rate receiver’ and a ‘fixed-rate payer’ in the swap. The payments are based on a $\$ 100 \mathrm{~m}$(notional) principal amount, but only the interest payments are exchanged (and not the$\$100 \mathrm{~m}$ principal itself). The maturity of the swap, the reset dates, notional principal, the fixed swap rate and the type of floating rate (usually LIBOR) to be used in the swap deal are set at the outset of the contract.

The agreed swap rate is $s p_{0}=3 \%$ p.a. Suppose LIBOR rates turn out to be $\operatorname{LIBOR}{1}=5 \%$ on 15 July 2019 and $\operatorname{LIBOR}{2}=2 \%$ on 15 July 2020 . Then on 15 July 2019 the swap dealer
JPMorgan owes BigBurger, $\$ 5 \mathrm{~m}$in interest based on$\mathrm{LIBOR}{1}=5 \%$and BigBurger owes JPMorgan (the swap dealer)$\$3 \mathrm{~m}$ based on the fixed swap rate of $s p{0}=3 \%$, hence:
$$\text { Swap dealer’s payoff to BigBurger }=\ 100 \mathrm{~m}\left(L I B O R_{1}-s p_{0}\right)=\ 2 \mathrm{~m}$$

## 微积分网课代修导数代写Derivatives theory代考|Hedgers

Examples of hedging using the forward market in foreign exchange are perhaps most common to the lay person. If a US exporter expects to receive $£ 3,000$ in 3 months, then the US exporter can buy dollars today in the forward market at the 3-month forward FX-rate, $F=1.5(\$ / £)$. The key feature is that today, the US company fixes the amount of USD it will receive at$\$4,500$, in exchange for the $£ 3,000$ it provides, in 3 months’ time.

Futures contracts if held to maturity, are like forward contracts – they fix the price that the hedger will pay or receive at maturity of the futures contract. However, it can be shown that even if the futures contract is closed out before maturity much of the risk can be hedged, but a small amount does remain (this is known as basis risk).

Options contracts provide ‘insurance’. Investors in options can protect themselves against adverse price movements in the future but they still retain the possibility of benefiting from any favourable price movements. To obtain this insurance, the option’s purchaser (‘the long’) of either a call or a put has to pay the option premium, today.