Question

Construct payoff diagram for the purchase of a 950-strike S&R call and sale of a 1000-strike S&R call. 

Answer 1

buy 950-strike call and written 1000-strike call

 \( \begin{align*} \text{Payoff of bought call} &= \max(0, S_T - \text{strike price})\\ &=\max(0, S_T-950) \end{align*} \)

\( \begin{align*} \text{Payoff of written call} &= -\max(0, S_T - \text{strike price})\\ &=-\max(0, S_T-1000) \end{align*} \)

\( \begin{align*} \text{Total Payoff} &= \max(0, S_T - 950) - \max(0,S_T -1000)\\ &= \begin{cases} 0 & S_T <950 \\ S-950 & S_T \geq 950 \end{cases} - \begin{cases} 0 & S_T <1000 \\ S-1000 & S_T \geq 1000 \end{cases} \\ &= \begin{cases} 0 & S_T <950 \\ S_T - 950 & 950 < S_T \leq 1000 \\ 50 & S_T \geq 1000 \end{cases} \end{align*} \)

 \( \text{Total Payoff} = \max(0, S_T-950, 50) \)

The total payoff is given by:

\( \text{Total Payoff} = \max(0, S_T-950, 50) \)

\( = \begin{cases} 0 & S_T <950 \\ S_T - 950 & 950 < S_T \leq 1000 \\ 50 & S_T \geq 1000 \end{cases} \)