简单的说，学好微积分（数学分析）是一个毁灭自己的先天直觉然后重新塑造一个后天直觉。
转变思维永远不是简单，但是不转变，贪图一时的捷径只是饮鸩止渴罢了。高中的时候，我一个同学很背单词的时候喜欢用汉字去拼那些单词的发音，还喜欢学各种解题技巧，这个时候我和他的成绩是一样的。
国外的老师较为看重学生homework的完成情况，对于同学们来说，完成一门科目作业并获得不错的成绩是尤为重要的事情。但对于不少同学来说，在自身英语说存在局限的情况下，当数学基础较为薄弱时，微积分作业的难度一下子就提升了，很难独立完成微积分作业。Calculus-do™提供的专业微积分代写能为大家解决所有的学术困扰，我们不仅会帮大家完成作业，还提供相应的数学知识辅导课程，以此来提高同学们学习能力。
我们提供的econ代写服务范围广, 其中包括但不限于:
- 单变量微积分
- 多变量微积分
- 傅里叶级数
- 黎曼积分
- ODE
- 微分学
微积分网课代修导数代写Derivatives theory代考|Speculators and Leverage
We have seen that because the call option premium is small relative to the price of the underlying asset, then speculation with calls can provide a high percentage return on the ‘own capital’ used to purchase the option. In our above examples, buying a call option on stocks gave a return of $167 \%$, whereas buying the stock itself only produced a return of $10 \%$ – options therefore provide leverage.
Leverage also applies to futures contracts because a speculator does not have to provide any of her own funds. Suppose on 25 January you ring up Chicago and buy a ‘June-futures’ contract (on stocks-ABC) at a price of $F_{0}=\$ 90$. Assume the futures matures on 25 June. In January you do not pay any money – here we ignore (so-called) margin requirements which are small and earn a competitive interest rate, and therefore are not a cost. Suppose on $15 \mathrm{March}$, you close out your June-futures contract in Chicago by selling at the market price of $F_{1}=\$ 100$. You make a cash profit of $F_{1}-F_{0}=\$ 10$, on 15 March. Because the futures trade (buying then selling) does not require any ‘own funds’, the percentage return and hence leverage is infinite.
By using futures, speculators can make very large losses as well as very large gains. However, there is a difference between futures and options. In the case of futures the potential loss or gain can be very large. But when call or put options are purchased by speculators, the speculator’s loss is limited to the option premium, yet the upside can be very large.
微积分网课代修导数代写Derivatives theory代考|Arbitrageurs
Arbitrage involves ‘locking in’ a riskless profit by entering into transactions in two or more markets simultaneously. Usually ‘arbitrage’ implies that the investor does not use any of his own capital when making the trades. Arbitrage plays a very important role in the determination of both futures and options prices as we shall see in later chapters. Arbitrage is often loosely referred to as the ‘law of one price’ for financial assets. Simply expressed, this implies that identical assets must sell for the same price. We consider a very simple example of arbitrage in Finance Blog $1.2$.
Finance Blog 1.2 Arbitrage: Dolly the Sheep
By way of an analogy consider ‘Dolly’ the sheep. You will remember that Dolly was cloned by scientists at Edinburgh University and was an exact replica of a ‘real’ Highland sheep. Dolly and real Highland sheep are identical and indistinguishable. Dolly is a form of genetic engineering or ‘synthetic’ or ‘replication’ sheep. Assume we could engineer ‘Dolly’ in Edinburgh at a cost (in terms of wages and equipment) of $£ 200$ per Dolly. So you can purchase a Dolly in Edinburgh for $£ 200$.
Suppose the current market price of real sheep being sold in the local market in the Highlands is $£ 220$. ‘Sheep arbitrageurs’ sitting in London seeing these prices on their internet screens would (ethical issues aside) buy a ‘replication’ Dolly in Edinburgh for $£ 200$ and simultaneously they would sell Dolly in the local market in the Highlands for $£ 220$ making an arbitrage (risk-free) profit of $£ 20$. (We ignore any transportation costs of getting Dolly from Edinburgh to the Highlands.)
This increase in demand for a Dolly in Edinburgh and sale of a Dolly in the Highlands (by many arbitrageurs in London doing the same trades) would mean the price of a Dolly would be bid up in Edinburgh and the price of a Dolly in the Highlands would fall – this is ‘supply and demand’ at work. Arbitrage and ‘supply and demand’ would ensure that the price of a Dolly in Edinburgh and the Highlands would quickly move to equality at say $£ 210$ for each – at which point arbitrage activity would stop – since there are now no risk-free profits to be made. Economists would say that $£ 210$ is the current equilibrium price of a Dolly.
Arbitrage ensures that the price of real Highland sheep must eventually equal the cost of producing an identical ‘Dolly replicant’. Dolly is like a ‘synthetic’ or ‘replication’ portfolio in financial economics. As we shall see, this is how we price many derivatives – we create a ‘synthetic’ or ‘replication’ portfolio, which has identical payoffs to the derivative itself.
微积分网课代修导数代写Derivatives theory代考|Speculators and Leverage
我们已经看到，由于看涨期权的溢价相对于标的资产的价格来说很小，因此看涨期权的投机可以为用于购买期权的“自有资本”提供高百分比的回报。在我们上面的例子中，购买股票的看涨期权的回报是167%，而购买股票本身只会产生10%– 因此，期权提供了杠杆作用。
杠杆也适用于期货合约，因为投机者不必提供任何自己的资金。假设您在 1 月 25 日致电芝加哥并以F0=$90. 假设期货在 6 月 25 日到期。1 月份您无需支付任何费用——在这里我们忽略了（所谓的）保证金要求，这些保证金要求很小并且可以赚取有竞争力的利率，因此不是成本。假设15米一个rCH，您通过以市场价格卖出平仓芝加哥的六月期货合约F1=$100. 您获得现金利润F1−F0=$10，3 月 15 日。因为期货交易（买入然后卖出）不需要任何“自有资金”，所以回报百分比和杠杆是无限的。
通过使用期货，投机者可以赚取非常大的损失和非常大的收益。但是，期货和期权是有区别的。在期货的情况下，潜在的损失或收益可能非常大。但是当投机者购买看涨或看跌期权时，投机者的损失仅限于期权溢价，但上涨空间可能非常大。
微积分网课代修导数代写Derivatives theory代考|Arbitrageurs
套利涉及通过同时在两个或多个市场进行交易来“锁定”无风险利润。通常，“套利”意味着投资者在进行交易时不使用任何自有资金。正如我们将在后面的章节中看到的，套利在确定期货和期权价格方面起着非常重要的作用。套利通常被松散地称为金融资产的“一价定律”。简单地说，这意味着相同的资产必须以相同的价格出售。我们在 Finance Blog 中考虑一个非常简单的套利示例1.2.
金融博客 1.2 套利：羊多莉
通过类比考虑“羊多莉”。你会记得多莉是爱丁堡大学的科学家克隆的，是“真正的”高地绵羊的精确复制品。多莉和真正的高地羊是相同的，无法区分。多莉是基因工程或“合成”或“复制”绵羊的一种形式。假设我们可以在爱丁堡以以下成本（在工资和设备方面）设计“多莉”££200每多莉。所以你可以在爱丁堡购买一辆多莉££200.
假设在高地当地市场上出售的真羊的当前市场价格为££220. 坐在伦敦的“绵羊套利者”在他们的互联网屏幕上看到这些价格（抛开道德问题不谈）会在爱丁堡购买“复制品”多莉££200同时他们会在高地的当地市场上出售多莉££220套利（无风险）利润££20. （我们忽略了将多莉从爱丁堡带到高地的任何运输成本。）
爱丁堡对多莉的需求增加和高地多莉的出售（伦敦的许多套利者做同样的交易）意味着多莉的价格将在爱丁堡和高地的多莉价格上涨会下降——这是“供求关系”在起作用。套利和“供求关系”将确保爱丁堡和高地的多莉车价格迅速趋于平等££210对于每一个——套利活动将停止——因为现在没有无风险的利润可以赚取。经济学家会说££210是多莉的当前均衡价格。
套利确保真正的高地绵羊的价格最终必须等于生产相同的“多莉复制人”的成本。多莉就像金融经济学中的“合成”或“复制”投资组合。正如我们将看到的，这就是我们为许多衍生品定价的方式——我们创建了一个“合成”或“复制”投资组合，其收益与衍生品本身相同。
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