Using TikZ and PGFPlots for a class on Options and Derivatives
Options and Derivatives
To use the code just insert it into any LaTeX code with the appropriate tikz libraries; see here for examples.
List of figures:
Payoff of a Forward Contract
Payoff of a forward contract is linear in the underlying security:
\begin{tikzpicture}
\begin{axis}[
height=10cm,
width=14cm,
axis x line=bottom,
axis y line=left,
xlabel = Spot Price $S_T$,
ylabel = Payoff,
ymin=-32, ymax=32,
xmin=70, xmax=132,
xtick={80, 100, 120, 130},
ytick={-20, 0, 20, 30},
grid = major,
grid style={dashed},
scatter/classes={
a={mark=*, mark size = 3pt,draw=black, fill = black}
}
]
\definecolor{maroon}{RGB}{128, 0, 0}
\addplot[color=black, domain=70:130, line width=1pt]
{x - 100};
\addplot[color=maroon, dashed, domain=70:130, line width=1pt]
{100 - x};
\node[pin={[pin edge={thick}, text width=3cm, pin distance=2cm]-90:{{\centering Forward Price $F_{0,T}$}}}, align=center] at (axis cs:100, -1) {};
\addplot[scatter,only marks,
scatter src=explicit symbolic]
coordinates {
(100,0) [a]
};
\node[text width=3cm,align=right] at (axis cs:120, 20) [anchor=south east] {\textbf{Long Forward}\\$S_T - F_{0,T}$};
\node[text width=3cm,align=left] at (axis cs:80, 20) [anchor=south west] {\textbf{Short Forward}\\$F_{0,T} - S_T$};
\end{axis}
\end{tikzpicture}
Covered Interest Parity
Replicating foreign interest rate using exchange rate and a forward:
% Definition of blocks:
\tikzset{%
block/.style = {draw, thick, rectangle, minimum height = 3em,
minimum width = 3em},
sum/.style = {draw, circle, node distance = 2cm}, % Adder
input/.style = {coordinate}, % Input
output/.style = {coordinate}, % Output
>={Latex[width=2mm,length=2mm]},
% Specifications for style of nodes:
base/.style = {rectangle, rounded corners, draw=black,
minimum width=4cm, minimum height=1cm,
text centered, font=\sffamily},
activityStarts/.style = {base, fill=blue!30},
startstop/.style = {base, fill=red!30},
activityRuns/.style = {base, fill=green!30},
process/.style = {base, minimum width=2.5cm, fill=orange!15,
font=\ttfamily}
}
\begin{tikzpicture}[
node distance=2cm,
every node/.style={fill=white, font=\sffamily},
align=center
]
% Specification of nodes (position, etc.)
\node (start) [activityStarts] {US Investor at $t=0$};
\node (borrowing0) [process, above=2.5cm of start] {US Bank};
\node (exchange0) [process, below=2.5cm of start] {Exchange Counterparty};
\node (lending01) [process, right=3.5cm of start] {Japanese Investor};
\node (end) [activityStarts, right=3.5cm of lending01] {US Investor at $t=1$};
\node (borrowing1) [process, above=2.5cm of end] {US Bank};
\node (exchange1) [process, below=2.5cm of end] {Exchange Counterparty};
% Link the nodes
\draw[->](borrowing0) -- node[]{Borrowing in USD} (start);
\draw[->](start) -- node[]{Buy Yen at rate $x_0$\\ buy for $\$1$ receive $\text{\textyen}\ 1 / x_0$}(exchange0);
\draw[->](start) -- node[text width = 2.4cm]{Lend $1/x_0$ Yens at $t=0$} (lending01);
\draw[->](lending01) -- node[text width = 2.4cm]{Receive Yens: $\frac{1}{x_0} \cdot (1+r^{\text{\textyen}})$} (end);
\draw[->](end) -- node[]{Repay USD loan at $t=1$ for \\$1+r$} (borrowing1);
\draw[->](exchange1) -- node[]{Exchange the \textyen \ investment in USD\\ $\frac{1}{x_0} \cdot (1+r^{\text{\textyen}}) \cdot F_{0,1}$} (end);
\end{tikzpicture}