From f84ff69bdf34e83f9eb34694ffaf2a2bb3ff7a65 Mon Sep 17 00:00:00 2001 From: Mark Date: Sat, 9 Dec 2023 18:18:21 -0800 Subject: [PATCH] Removed Options handout --- Advanced/Options in Finance/main.tex | 45 ----- Advanced/Options in Finance/parts/0 intro.tex | 19 -- Advanced/Options in Finance/parts/1 call.tex | 175 ------------------ Advanced/Options in Finance/parts/2 put.tex | 55 ------ .../Options in Finance/parts/3 compound.tex | 76 -------- 5 files changed, 370 deletions(-) delete mode 100755 Advanced/Options in Finance/main.tex delete mode 100644 Advanced/Options in Finance/parts/0 intro.tex delete mode 100644 Advanced/Options in Finance/parts/1 call.tex delete mode 100644 Advanced/Options in Finance/parts/2 put.tex delete mode 100644 Advanced/Options in Finance/parts/3 compound.tex diff --git a/Advanced/Options in Finance/main.tex b/Advanced/Options in Finance/main.tex deleted file mode 100755 index e77d186..0000000 --- a/Advanced/Options in Finance/main.tex +++ /dev/null @@ -1,45 +0,0 @@ -% use [nosolutions] flag to hide solutions. -% use [solutions] flag to show solutions. -\documentclass[ - solutions, - unfinished -]{../../resources/ormc_handout} -\usepackage{../../resources/macros} - -\usepackage{mdframed} - -\newmdenv[ - topline=false, - bottomline=false, - rightline=true, - leftline=true, - linewidth=0.3mm, - frametitle={Contract:}, - frametitlefont={\textsc}, - % - skipabove=1mm, - skipbelow=1mm, - % - innerleftmargin=2mm, - innerrightmargin=4mm, - leftmargin=2mm, - rightmargin=2mm, -]{contract} - -\uptitlel{Advanced 2} -\uptitler{Fall 2023} -\title{Options in Finance} -\subtitle{ - Prepared by \githref{Mark} on \today{} -} - -\begin{document} - - \maketitle - - \input{parts/0 intro} - \input{parts/1 call} - \input{parts/2 put} - \input{parts/3 compound} - -\end{document} \ No newline at end of file diff --git a/Advanced/Options in Finance/parts/0 intro.tex b/Advanced/Options in Finance/parts/0 intro.tex deleted file mode 100644 index 248e08d..0000000 --- a/Advanced/Options in Finance/parts/0 intro.tex +++ /dev/null @@ -1,19 +0,0 @@ -\section{Introduction} - -\definition{} -An \textit{asset} is any resource that has economic value.\par -Examples: gold, oil, grain, cash, real estate, treasury bonds, etc - -\definition{} -A \textit{stock} is a particular type of asset. -A share of stock represents \say{partial ownership} of a corporation. -Like many assets, stocks are \textit{intangible}---they only exist on paper. - -\problem{} -Let $\mathbb{X}$ be a stock, currently priced at $19\Rub$. \par -Bogdan buys 10 shares of $\mathbb{X}$, and sells them after a month for $23\Rub$ per share. \par -What was his net profit? - - -\vfill -\pagebreak \ No newline at end of file diff --git a/Advanced/Options in Finance/parts/1 call.tex b/Advanced/Options in Finance/parts/1 call.tex deleted file mode 100644 index b33af94..0000000 --- a/Advanced/Options in Finance/parts/1 call.tex +++ /dev/null @@ -1,175 +0,0 @@ -\section{Call Options} - -\definition{} -A \textit{call option} is an agreement between a buyer (B) and a seller (S): \par - -\begin{contract}[frametitle={Contract: Call Option}] - B pays S a premium $p$. \par - In return, S agrees to sell B a certain stock $\mathbb{X}$ for a fixed \say{strike price} $k$ at a future time $t$. -\end{contract} - - - - -\problem{} -B has ten call options for $\mathbb{X}$ at $23\Rub$. The current price of $\mathbb{X}$ is $20\Rub$. \par -How much profit can B make if these contracts expire when $\mathbb{X}$ is worth $30\Rub$? \par -\hint{When the contract expires, B can buy 10 shares of $\mathbb{X}$ at the price the contract set.} - -\begin{solution} - B has the right to buy 10 shares of $\mathbb{X}$ at $23\Rub$. \par - If B immediately sells them, his profit is $-230 + 300 = 70\Rub$ -\end{solution} - - -\vfill - - - -\problem{} -If B paid $10\Rub$ for the call options in \ref{firstcall}, how much money did he really make? - -\begin{solution} - $-10 + (-230 + 300) = 60\Rub$ -\end{solution} - - -\vfill - - - - -\problem{} -Now, suppose that B bought and sold $\mathbb{X}$ directly instead of using a call option. \par -How much profit would B have made? - -\begin{solution} - Buy for $200\Rub$, sell for $300\Rub$.\par - $-200 + 300 = 100\Rub$ -\end{solution} - - - -\vfill -\pagebreak - - -\problem{} -Suppose $\mathbb{X}$ is worth $x_0$ right now. \par -Call options to buy $\mathbb{X}$ at strike price $k$ are sold for $p$. - -\begin{itemize} - \item What is the set of B's possible profit if.. - \begin{itemize} - \item B buys a call option? - \item B buys $\mathbb{X}$ directly? - \end{itemize} - \hint{That is, what amounts of money can B make (or lose)?} - - \item Are call options priced above or below the price of their stock? Why? - \item On the previous page, we saw that the profit - made on a call option was much lower than the profit - made by buying a stock directly. - Why would anybody buy a call option? - -\end{itemize} - - -\begin{solution} - \textbf{Call Option:} $[p, \infty)$ \par - If the price of $\mathbb{X}$ rises, there is no limit to how much money B can make. \par - If the price falls, $B$ can choose to let his contract expire, losing only $p$. - - \vspace{2mm} - - \textbf{Direct:} $[x_0, \infty)$\par - If the price of $\mathbb{X}$ rises, there is again no limit to how much money B can make. \par - If the price falls, $B$ will lose everything he paid for his shares of $\mathbb{X}$. - - \vspace{2mm} - - Of course, call options are priced below their stock. There wouldn't be a reason to buy then - if they were priced above! -\end{solution} - - -\vfill - -\problem{} -Suppose $\mathbb{X}$ is worth $x_0$ right now. \par -Call options to buy $\mathbb{X}$ for $k$ are sold for $p$. \par - -\vspace{2mm} -Assume that S owns no stock---if B executes his contracts, she will buy stock and resell it to him. \par -What are S's possible profits if she sells B a call option? - -\begin{solution} - $(-\infty, ~p]$\par - If the price of $\mathbb{X}$ rises, S will have to resell shares to B at a loss. - If the price falls, B could choose to buy shares from S at a loss, but he won't. - In this case, S only keeps the premium B paid for the contract. -\end{solution} - -\vfill -\pagebreak - -\problem{} -How does the price of $\mathbb{X}$ at $t$ relate to the amount of -profit B and S make? Complete the plots below. - -\null\hfill -\begin{minipage}{0.48\textwidth} - \begin{center} - \begin{tikzpicture} - \draw (0,0) -- (5, 0); - \draw (0,-2) -- (0, 2); - - \node at (2.5, 2) {Profit plot for $B$}; - - - \node[ - anchor = south, - rotate = 90 - ] at (0,0) {\color{gray}Profit}; - - \node[ - anchor = south west, - ] at (0, 0) {\color{gray}Price of $\mathbb{X}$ at $t$}; - - \node[anchor = north] at (3, 0) {$k$}; - \filldraw (3, 0) circle (0.5mm); - \end{tikzpicture} - \end{center} -\end{minipage} -\hfill -\begin{minipage}{0.48\textwidth} - \begin{center} - \begin{tikzpicture} - \draw (0,0) -- (5, 0); - \draw (0,-2) -- (0, 2); - - \node at (2.5, 2) {Profit plot for $S$}; - - \node[ - anchor = south, - rotate = 90 - ] at (0,0) {\color{gray}Profit}; - - \node[ - anchor = south west, - ] at (0, 0) {\color{gray}Price of $\mathbb{X}$ at $t$}; - - \node[anchor = north] at (3, 0) {$k$}; - \filldraw (3, 0) circle (0.5mm); - \end{tikzpicture} - \end{center} -\end{minipage} -\hfill\null - -When does B make a positive profit? When does S? \par -Write an equation that calculates S and B's earnings given -$p$, $k$, and the price of $\mathbb{X}$ at the time the contract expires. - - -\vfill -\pagebreak \ No newline at end of file diff --git a/Advanced/Options in Finance/parts/2 put.tex b/Advanced/Options in Finance/parts/2 put.tex deleted file mode 100644 index dfe5d91..0000000 --- a/Advanced/Options in Finance/parts/2 put.tex +++ /dev/null @@ -1,55 +0,0 @@ -\section{Put Options} - -\definition{} -A \textit{put option} is an agreement between a buyer (B) and a seller (S): \par - -\begin{contract}[frametitle={Contract: Put Option}] - B pays S a premium $p$. \par - In return, S agrees to buy a certain stock $\mathbb{X}$ from S for a fixed \say{strike price} $k$ at a future time $t$, - if B decides to exercise this contract. -\end{contract} - -As before, the \textbf{buyer} decides whether or not this contract is put into action. \par -Also, note that B does not need to own any shares of stock to buy a put option. \par -He may buy them whenever he wishes. - -\problem{} -How is a put different from a call? \par -What is S betting on? What is B betting on? - -\vfill - -\problem{} -Suppose B paid $100\Rub$ for 300 put contracts on $\mathbb{X}$ at $17\Rub$.\par -At time the contracts expired, the price of $\mathbb{X}$ was $20\Rub$.\par -What is B's profit? - -\vfill - -\problem{} -Plot profit curves for selling a put option, buying a put option, -and buying a stock directly on the axis below. - -\begin{center} - \begin{tikzpicture} - \draw (0,0) -- (10, 0); - \draw (0,-3) -- (0, 3); - - - \node[ - anchor = south, - rotate = 90 - ] at (0,0) {\color{gray}Profit}; - - \node[ - anchor = south west, - ] at (0, 0) {\color{gray}Price of $\mathbb{X}$ at $t$}; - - \node[anchor = north] at (6, 0) {$k$}; - \filldraw (6, 0) circle (0.5mm); - \end{tikzpicture} -\end{center} - -\vfill -\pagebreak - diff --git a/Advanced/Options in Finance/parts/3 compound.tex b/Advanced/Options in Finance/parts/3 compound.tex deleted file mode 100644 index 09a68f2..0000000 --- a/Advanced/Options in Finance/parts/3 compound.tex +++ /dev/null @@ -1,76 +0,0 @@ -\section{Compound Strategies} - -\definition{} -A \textit{covered call} is a trading strategy where one simultaneously -buys a share of stock and sells a call option. When the contract -expires, the stock is sold to the call buyer (if they choose -to exercise their contract) or to the market (if they don't). - -\problem{} -Say we set up a covered call by buying a share of $\mathbb{X}$ for $x_0$ -and selling a call option for $\mathbb{X}$ at $k$ for $p$. \par -When our contract expires, $\mathbb{X}$ -is worth $x_1$. - -\vspace{2mm} - -What is the gross profit of a covered call?\par -What is its net profit?\par -\hint{Gross profit does not take setup cost into account. Net profit does.} - - -\vfill - -\definition{} -We say that trading strategy $A$ \textit{simulates} trading strategy -$B$ if their net profits are equal. - -\problem{} -Find a trading strategy that buys stock and call options -to simulate a single put option with strike price $k$. - -\vfill - - -\problem{} -A \textit{straddle} is a trading strategy where one buys a call and a put -with the same strike price and expiration. Plot the profit curve. \par -What do you bet on when you buy a straddle? - -\begin{center} - \begin{tikzpicture} - \draw (0,0) -- (10, 0); - \draw (0,-3) -- (0, 3); - - \node[ - anchor = south, - rotate = 90 - ] at (0,0) {\color{gray}Profit}; - - \node[ - anchor = south west, - ] at (0, 0) {\color{gray}Price of $\mathbb{X}$ at $t$}; - - \node[anchor = north] at (5, 0) {$k$}; - \filldraw (5, 0) circle (0.5mm); - \end{tikzpicture} -\end{center} - -\vfill -\pagebreak - -\definition{} -A \textit{butterfly spread} is a trading strategy where one buys two -calls with strike prices $k_1$ and $k_2$ and sells two calls with strike -prices $\frac{k_1+k_2}{2}$. - -\problem{} -When should you set up a butterfly spread? \par -Find the payoff function. - -\vfill - - -\vfill -\pagebreak -