# 数学代写|金融衍生品代写Financial derivatives代考|FINA5220

## 数学代写|金融衍生品代写Financial derivatives代考|Short Term Interest Rate Futures

In our example, the interest rate futures are being used which are quoted in price at the exchange, i.e. Price $=1-r$ where $r$ is $3 \mathrm{M}$ Euribor observed at the expiry date of the contract. We use the term “Termination Date (TD)” for date which is 3 months after the expiry date of the contract.

For the first futures contract, we need to find the ZC bond at the beginning date of the contract, i.e., 17 Dec 14 , which is not yet available. This term has to be interpolated from the nearby $P(\mathrm{~T} / \mathrm{N})$ and $P(1 \mathrm{M})$.

From the second futures contract onward, the calculation will be $P\left(t_2\right)=\frac{P\left(t_1\right)}{1+r \times T}$, where $t_2$ and $t_1$ are the Termination Dates of Current Contract and the Preceding Contract, $r$ being the implied rate for the current contract.

In case that the periods covered by two successive futures overlap or have a hole in between, any smooth treatment may be applied for this joining period. If the impact is negligible, one may choose to simply adjust the period length of one of the contracts by keeping the implied rate unchanged.

The bootstrapping of swap contracts is based on the below no-arbitrage relationship:
$$P \text { (Settlement Date })-P\left(t_n\right)-s \sum_{i=1}^n \delta_i P\left(t_i\right) \text {. }$$
We take the ZC bond for the 3Y pillar as example where we have already obtained the following numbers through bootstrapping of instruments with shorter tenors:
\begin{aligned} P(\text { Settlement Date }) &=0.9999875, P(1 \mathrm{Y})=0.9991986, \delta_1=1, \ P(2 \mathrm{Y}) &=0.9979836, \delta_2=1, \delta_3=1, s=0.2570 \% . \end{aligned}
We can solve for $P(3 Y)$ which makes the following equality hold: $P($ Settlement Date $)-P(3 \mathrm{Y})=s \times\left[\delta_1 \times P(1 \mathrm{Y})+\delta_2 \times P(2 \mathrm{Y})+\delta_3 \times P(3 \mathrm{Y})\right]$. Applying the numerical numbers, we obtain $P(3 \mathrm{Y})=0.9923045$.

## 数学代写|金融衍生品代写Financial derivatives代考|Equities and Equity Indices

Equity is the claim of the ownership of a firm. Equity securities issued by corporations are called stocks or shares. ${ }^1$ The securities traded in the equity market can he publicly traded stocks, which are listed on the stock exchange, or privately traded stocks.
The two main equity securities are
Common stock (ordinary stock): a common shareholder has the voting right and is entitled to the dividend. In case of liquidation of the company, the shareholder of a common share has the lowest priority for the assets.
Preferred stock: the holder of a preferred stock has no voting right but has the priority for the dividend payment and liquidation assets over the common share. Many preferred shares pay dividends in the form of fixed coupons, like a perpetual bond. There are several types of preferred shares: a convertible preferred share gives right to its holder to convert the preferred share to a common share; a cumulative preferred share allows the dividends omitted in the past (e.g. due to profitability issue) to be paid later.

A company’s free float refers to the number of shares that are immediately tradable in the public market. A restricted share, usually held by an insider (such as company’s executive officer and employee), is not fully transferable until certain conditions are met. We have
Free Float $=$ Outstanding Shares $-$ Restricted Shares.
The market capitalization of a company is then defined as the market price multiplied by the number of outstanding shares.

# 金融衍生品代考

## 数学代写|金融衍生品代写金融衍生品代考|短期利率期货

$$P \text { (Settlement Date })-P\left(t_n\right)-s \sum_{i=1}^n \delta_i P\left(t_i\right) \text {. }$$

\begin{aligned} P(\text { Settlement Date }) &=0.9999875, P(1 \mathrm{Y})=0.9991986, \delta_1=1, \ P(2 \mathrm{Y}) &=0.9979836, \delta_2=1, \delta_3=1, s=0.2570 \% . \end{aligned}

## 数学代写|金融衍生品代写金融衍生品代考|股票和股票指数

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