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

A stock dividend is a payment (e.g. yearly or quarterly) made by a corporation to its shareholders as a distribution of profits. The dividend amount is decided by the Board of the company at each time. For a detailed discussion on the dividend policy and practice, we refer to [72].

When a dividend is declared, an ex-dividend date is specified. It is the date on which shares bought no longer come attached with the right to be paid the declared dividend. Other factors remaining equal, the share price will normally drop on the ex-dividend date by the amount equivalent to the after-tax dividend. Before exdividend date, the stock is said to trade cum dividend.

A stock dividend can be either a cash dividend in monetary form, or a stock dividend which involves the company issuing more shares to its existing shareholders. For example, a 5\% stock dividend means that the shareholders receive one new share for every twenty already owned shares. Unlike the cash dividend, the stock dividend does not change the company’s market capitalization. In modelling, stock dividends are also called proportional dividends.

Suppose that a stock pays a dividend value of $D$ with ex-dividend date $t_d$. Let $S_{t_d}$ be the stock price just before the ex-dividend date. The quantity $d=D / S_{t_d}$ is called the dividend yield.

Obviously, $S_{t_d}-$ cannot be equal to $S_{t_d}$. If it was, the strategy of buying the stock immediately before $t_d$, collecting the dividend, and selling straight away, would yield a risk-free profit. In fact, in the absence of other factors such as taxes, the asset price must fall by exactly the amount of the dividend payment. That is, for a stock paying both proportional dividend at rate $d^{\text {prop }}$ and cash dividend amount $D^{\text {cash }}$. we have
$$S_{t_d}=S_{t_d^{-}}\left(1-d^{\text {prop }}\right)-D^{\text {cash }} .$$
In continuous-time modelling, the proportional divided rate is the value $d$ such that $e^{-d}=1-d^{\text {prop }}$. Hence,
$$S_{t_d}=S_{t_d-} e^{-d}-D^{c a s h} .$$

## 数学代写|金融衍生品代写Financial derivatives代考|Stock Split, Reverse Stock Split, Rights Issue

A stock split is a corporate action in which a company divides each existing share into multiple shares which impacts the share price by the same ratio. It increases the number of the company’s outstanding shares while keeping the market capitalization unchanged. If a stock’s price has reached such a high level making it unaffordable to small investors, the stock split helps to increase the stock’s liquidity.

A reverse stock split is the opposite of stock split. A company having its stock price dropped to a very low level such that one tic (i.e. the minimum quotation unit) for its price becomes significant may consider undertaking a reverse stock split for bringing back the price to a normal unit.

A company can raise money through a rights issue which is offered to existing shareholders for purchasing new shares in the company with a subscription price at a discount to the market price. The right can be either renounceable, allowing the shareholder to trade it in the market, or non-renounceable which is not tradable.

# 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|股票分红

.

$$S_{t_d}=S_{t_d^{-}}\left(1-d^{\text {prop }}\right)-D^{\text {cash }} .$$

$$S_{t_d}=S_{t_d-} e^{-d}-D^{c a s h} .$$

## 数学代写|金融衍生品代写金融衍生品代考|股票拆分，反向股票拆分，配股发行

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