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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

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 ...

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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 ...

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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 <- ...

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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}*...

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