77 lines
1.8 KiB
TeX
77 lines
1.8 KiB
TeX
\section{Compound Strategies}
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\definition{}
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A \textit{covered call} is a trading strategy where one simultaneously
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buys a share of stock and sells a call option. When the contract
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expires, the stock is sold to the call buyer (if they choose
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to exercise their contract) or to the market (if they don't).
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\problem{}
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Say we set up a covered call by buying a share of $\mathbb{X}$ for $x_0$
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and selling a call option for $\mathbb{X}$ at $k$ for $p$. \par
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When our contract expires, $\mathbb{X}$
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is worth $x_1$.
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\vspace{2mm}
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What is the gross profit of a covered call?\par
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What is its net profit?\par
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\hint{Gross profit does not take setup cost into account. Net profit does.}
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\vfill
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\definition{}
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We say that trading strategy $A$ \textit{simulates} trading strategy
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$B$ if their net profits are equal.
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\problem{}
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Find a trading strategy that buys stock and call options
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to simulate a single put option with strike price $k$.
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\vfill
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\problem{}
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A \textit{straddle} is a trading strategy where one buys a call and a put
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with the same strike price and expiration. Plot the profit curve. \par
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What do you bet on when you buy a straddle?
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\begin{center}
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\begin{tikzpicture}
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\draw (0,0) -- (10, 0);
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\draw (0,-3) -- (0, 3);
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\node[
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anchor = south,
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rotate = 90
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] at (0,0) {\color{gray}Profit};
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\node[
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anchor = south west,
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] at (0, 0) {\color{gray}Price of $\mathbb{X}$ at $t$};
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\node[anchor = north] at (5, 0) {$k$};
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\filldraw (5, 0) circle (0.5mm);
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\end{tikzpicture}
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\end{center}
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\vfill
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\pagebreak
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\definition{}
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A \textit{butterfly spread} is a trading strategy where one buys two
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calls with strike prices $k_1$ and $k_2$ and sells two calls with strike
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prices $\frac{k_1+k_2}{2}$.
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\problem{}
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When should you set up a butterfly spread? \par
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Find the payoff function.
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\vfill
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\vfill
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\pagebreak
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