What trading position $is$ created from a long strangle and a short straddle when both have the same time $to$ maturity? Assume that the strike price $in$ the straddle $is$ halfway between the two strike prices $of$ the strangle.

What trading position $is$ created from a long strangle and a short straddle when both

have the same time $to$ maturity? Assume that the strike price $in$ the straddle $is$

halfway between the two strike prices $of$ the strangle

Long strangle $=$ buying call option with $K1$ and buying put option with $K2.$

Short Straddle $=$ selling a put option with strike price $K1+K\frac{2}{2},$ and selling a call

option with same price $KI+K\frac{2}{2}.$

Total payoff: max$(ST-K1,0)+$max$(K2-ST,0)-$max$(K1+K\frac{2}{2}-ST,0)-$max

$(ST-K1+K\frac{2}{2},0)$

When $=0+K2-ST-\frac{K1+K2}{2}+ST-0=2K2-K1-K2=K2-K1K1+K\frac{2}{2}Kl$

When $K1+K\frac{2}{2}ST,$ payoff $=0+K2-ST-\frac{K1+K2}{2}+ST-0=2K2-K1-K2=K2-K1$

When $Kl$

When $K1+K\frac{2}{2}$