dstefan
03-22-2008, 01:17 PM
Chapter 1, Problem 12:
Draw the payoff diagram at maturity of a bull spread with a long position in a call with strike 30 and short a call with strike 35, and of a bear spread with long a put of strike 20 and short a put of strike 15.
Solution:
Bull Spread: V_1(T) ~=~ \max(S(T)-30,0) ~-~ \max(S(T)-35,0)
\begin{tabular}{|c|c|c|c|}\hline & S(T) < 30 & 30 < S(T) < 35 & 35 < S(T) \\ \hline V_1(T) & 0 & S(T)-30 & 5 \\ \hline \end{tabular}
Bear Spread: V_2(T) ~=~ \max(20-S(T),0) ~-~ \max(15-S(T),0)
\begin{tabular}{|c|c|c|c|}\hline & S(T) < 15 & 15 < S(T) < 20 & 20 < S(T) \\ \hline V_1(T) & 5 & 20-S(T) & 0 \\ \hline \end{tabular}
Draw the payoff diagram at maturity of a bull spread with a long position in a call with strike 30 and short a call with strike 35, and of a bear spread with long a put of strike 20 and short a put of strike 15.
Solution:
Bull Spread: V_1(T) ~=~ \max(S(T)-30,0) ~-~ \max(S(T)-35,0)
\begin{tabular}{|c|c|c|c|}\hline & S(T) < 30 & 30 < S(T) < 35 & 35 < S(T) \\ \hline V_1(T) & 0 & S(T)-30 & 5 \\ \hline \end{tabular}
Bear Spread: V_2(T) ~=~ \max(20-S(T),0) ~-~ \max(15-S(T),0)
\begin{tabular}{|c|c|c|c|}\hline & S(T) < 15 & 15 < S(T) < 20 & 20 < S(T) \\ \hline V_1(T) & 5 & 20-S(T) & 0 \\ \hline \end{tabular}