For each of the following portfolios, draw the expiry payoff diagram and explain what

view of the market holding this position expresses:

$($a$)$ long one call and one put, both with strike price $K($this is known as a straddle$)$;

$($b$)$ short one forward and long two calls, all with strike price $K($this is also a straddle

why?$)$;

$($c$)$ Long one call and two puts, all with strike price $K($this is known as a strip$)$;

$($d$)$ Long one put and two calls, all with strike price $K($this is known as a strap$)$;

$($e$)$ Long one call with strike $K_2$ and one put with strike $K_1.$ Compare the cases

$K_2>K_1($known as a strangle$),K_2=K_1,$ and $K_1{K}_2\frac{K_1+K_2}{2}{K}_2.$

$(f)$ Long one call with strike $K_1,$ long one call with strike $K_2,$ and short two calls

with strike $\frac{K_1+K_2}{2}(thisis$ known $as$ a butterfly spread$).$