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

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|NE00CC07 SWAPS

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.

For example, a US exporter to the UK can ‘insure’ (i.e. set a lower limit for) her future US dollar receipts in 3 months’ time, if today she buys a put option on sterling at a strike price of $K=2(\$ / £$, USD/GBP), which matures in 3 months. Suppose the put option is for ‘delivery’ of $£ 3,000$. The put option implies she will receive a minimum of $K=2$ USD/GBP by exercising her put in Chicago in 3 months’ time – so the minimum she will receive from exercising the put is $\$ 6,000$ (even if the quoted spot-FX rate in 3 months’ time is $S_{T}=1.5 \mathrm{USD} / \mathrm{GBP}$, say). But if in 3 months’ time, the spot exchange rate is $S_{T}=2.1$ USD/GBP, she can ‘walk away’ from the put option contract (i.e. not exercise the put) and exchange her $£ 3,000$ at the higher spot rate (and receive $\$ 6,300$ from the spot FX-dealer). For the privilege of having this ‘option’ to choose the best outcome in the future, she has to pay the put premium, at the outset.

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

微积分网课代修导数代写Derivatives theory代考|SWAPS

掉期是另一种衍生合约,最早出现于 1980 年代初期。它们主要用于对冲未来许多时期的利率或汇率风险。
交换是协商的(○吨C)两方之间在一系列预先指定的未来日期(“重置日期”)交换现金流量的协议。
普通利率掉期涉及定期交换利息。一组未来的利息支付是固定的掉期利率,sp0=3%pa (say),这是在交换开始时确定的。另一组利息支付由一些“浮动”利率(通常是 LIBOR)的现行水平决定。掉期将基于名义本金金额$100 米, 说。

例如,2018 年 7 月,一家美国公司“BigBurger”可能与摩根大通达成掉期交易,其中 BigBurger 已同意从掉期交易商处收到基于 2019 年 7 月 15 日和 2020 年 7 月 15 日(美元)伦敦银行同业拆借利率的年度利息(重置日期)。BigBurger 还同意向掉期交易商 (JPMorgan) 支付固定掉期利率sp0=3%pa,在这些日期(名义本金金额为$100 米)。BigBurger 是互换中的“浮动利率接收者”和“固定利率支付者”。付款是基于一个$100 米(名义)本金金额,但只交换利息支付(而不是$100 米校长本身)。掉期到期、重置日期、名义本金、固定掉期利率和掉期交易中使用的浮动利率类型(通常是 LIBOR)在合同开始时就已确定。

约定的掉期利率为sp0=3%pa 假设 LIBOR 利率为伦敦银行同业拆借利率⁡1=5%2019 年 7 月 15 日和伦敦银行同业拆借利率⁡2=2%2020 年 7 月 15 日。然后在 2019 年 7 月 15 日,掉期交易商
摩根大通欠 BigBurger,$5 米兴趣基于大号我乙○R1=5%BigBurger 欠摩根大通(掉期交易商)$3 米基于固定互换利率sp0=3%, 因此:

 将经销商的收益换成 BigBurger =$100 米(大号我乙○R1−sp0)=$2 米

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

使用外汇远期市场对冲的例子可能是外行最常见的。如果美国出口商期望收到££3,0003 个月后,美国出口商今天可以在远期市场以 3 个月的远期汇率购买美元,£F=1.5($/£). 关键特征是,今天,这家美国公司将收到的美元金额固定为$4,500, 以换取££3,000它提供,在 3 个月的时间内。

期货合约如果持有至到期,则类似于远期合约——它们确定了套期保值者在期货合约到期时将支付或收取的价格。然而,可以证明,即使期货合约在到期前平仓,大部分风险也可以对冲,但仍有少量风险(这称为基差风险)。

期权合约提供“保险”。期权投资者可以保护自己免受未来不利的价格变动的影响,但他们仍然保留从任何有利的价格变动中受益的可能性。为了获得这种保险,看涨或看跌期权的购买者(“多头”)必须在今天支付期权费。

例如,美国对英国的出口商可以为她未来 3 个月后的美元收入“投保”(即设定下限),如果她今天以行使价购买英镑看跌期权£ķ=2($/£, USD/GBP),在 3 个月内到期。假设看跌期权是“交割”££3,000. 看跌期权意味着她将获得至少ķ=2USD/GBP 通过在 3 个月内行使她在芝加哥的看跌期权 – 所以她从行使看跌期权中获得的最低收益是$6,000(即使 3 个月后的即期汇率报价为小号吨=1.5在小号D/G乙磷, 说)。但如果在 3 个月内,即期汇率为小号吨=2.1美元/英镑,她可以“离开”看跌期权合约(即不行使看跌期权)并交换她££3,000以较高的即期汇率(并收到$6,300来自现货外汇交易商)。为了有这个“选择权”来选择未来最好的结果,她必须在一开始就支付看跌期权的溢价。

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