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Intro: Duration-Based Asset Pricing Similar to bonds, we can define the duration of stock $i$ as $$ Dur_{i,t} = \sum_{s=1}^\infty s\cdot\frac{\mathbb{E}_t[CF_{i,t+s}]e^{-s r_{i,t}}}{P_{i,t}},$$ where $P_{i,t}$ is today's stock price, $r_{i,t}$ a discount rate and $CF_{i,t}$ are cash flows. The variable $Dur_{i,t}$ tells you the weighted average of when a ...


5

The term structure of returns refers to returns on assets with the same underlying cash flows, where the return is measured over the same holding period, but for different maturities. The price of a stock or equity index $S_t$ is given by the discounted value of its dividends $D_t$: $$P_t = \sum^\infty_{n=1} E_t(M_{t:t+n}D_{t+n}) = \sum^T_{n=1} E_t(M_{t:t+n}...


5

Diviends or not, the put-call parity (with European options) always hold: $ C(S,K) - P(S,K) = F - K*DF $ In the RHS, dividends will impact the forward $F$ (higher dividends imply lower forward). So the LHS should be lower as well: the Call costs less and the Put costs more. The proof is straightforward, you just notice that at maturity $T$ you have: $S_T - K ...


4

You ought to compare the $t$-values of two self-financing strategies, under the assumption that there exists a risk-free money market account and that the dividend is deterministic but proportional to the random stock price. Strategy 1 - Entering a forward contract At inception ($t=0$), you do not pay anything by definition, $\Pi_1(0)=0$ At maturity ($t=T)$,...


3

In your example, I believe it's assumed that the exercise date is after the dividend date. If the dividend date is after the exercise date, nothing happens. The value would decrease, consider the following timeline: $t=0$: You have a call option worth $4.73$ and a stock worth $S_0$ $t=1$: The increase in dividend is announced but dividends are not paid out ...


3

When the dividend is paid, the stock price on your tree should drop by the same amount. Ie if the dividend is 10 and the value of stock is 100 before the dividend at a node, you should change it to 90 and then continue building the tree from there. A cursory google brings quite a few results, eg this around slide 46 seems to explain it well


3

The methodology has to be wrong to generate negative prices. Dividends and splits both generate proportional shifts in nominal prices, that are positive. A proportional shift to any positive number generates a positive number. The problem with the company given is that it seems to pay a >100% dividend to its previous close, which is why the previous adj ...


3

The right formula: $$ S_{t+\Delta t} = S_t+(r-q)S_t \Delta t+\sigma\,S_t \sqrt{\Delta t}\,Z+\frac{1}{2}\sigma^2\Delta t(Z^2-1)*S_t $$ We can extract the formula from the Brownian motion equation (Wiener process): $$ dS_t = (r-q) S_t dt + \sigma S_t dW_t $$ where $ W_t $ is Wienere process. Applying Itô's lemma (r, q and $\sigma$ are constants) with $ f(S_t) ...


2

Rearranging the dividend discount model to express the required return $i$ in terms of the other variables gives $$i = \frac{D}{P} + g$$ That is, the return to holding stocks in this model comes partly from dividends (in the form of the dividend yield $D/P$) and partly from dividend growth $g$, which will increase the stock price over time, representing ...


1

Although the answer to this question has been provided, I would like to give another point of view to this problem. It is worth noting that at $t=0$ you should hold less than 1 units of stock ($(1-D)$ units to be precise) to replicate forward payoff. Below I present replicating strategy. At $t=0$ you buy $1-D$ units of stock worth $(1-D)S(0)$, you finance ...


1

This seems to work for me: library(quantmod) # import data sym <- "SHANTIGEAR.BO" x <- getSymbols(sym, auto.assign = FALSE) div <- getDividends(sym) spl <- getSplits(sym) # calculate adjustment ratios ratios <- adjRatios(close = Cl(x), dividends = div, splits = spl) # apply adjustment ratios to original data adjusted <- ...


1

This has already been answered but I will try to provide more insight. The formula that you should use for forward adjusting: $$P_{adj, j}=P_{unadj, j}*\prod_{i=1}^{j} f_i$$ $$f_i=1+\frac{d_i}{P_{unadj, i}}$$ where $d_i$ is a dividend paid on day $j$ and $P_{unadj, j}$ is unadjusted price for that day. for backward adjusting we have: $$P_{adj, j}=P_{unadj,j}*...


1

As you've said, you can apply a version of the DDM, namely the gordon growth model -- assuming a constant growth of dividends. GGM = D1 / (r-g) So you need the cost of equity, the future dividends, and a growth rate. In your case, the required return on equity is basically the cost of equity -- it's just another word for it. Required return on equity is the ...


1

You may want to read this paper for GBM with discrete dividend.


1

They certainly exist - there are even (sort-of-liquid) dividend futures for these on the Eurostoxx index (the old DEDZ, now FEXD, series), and (less liquid) for the Nikkei. These differ from Treasury strips in two important respects. Strips give you either a riskless future income stream (via coupon) or riskless principal. So long as the underlying Treasury ...


1

A viable securitization market requires the following: Credit support mechanism to achieve credit rating targets and satisfy investment criteria for institutional buy-side managers Contractural cashflow schedules with legal maturity dates to offer tranches that produce average lives matching buy-side preferences Private liquidity providers supplying ...


1

Sounds like you want a Dividend Swap? These things trade OTC... there are quote windows in the BBG terminal.


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