Calculate a long straddle’s two profit boundaries

Keep one strike and expiry

The original straddle holds one call and one put on the same underlying, both strike 100 and same expiry. Total premium paid is 10. No probability, volatility forecast or current fair price is supplied.

Add the two holder payouts

For S≥100 the call supplies S−100 and the put zero. For S≤100 the put supplies 100−S and the call zero. Combined payoff is the absolute difference from the strike.

Solve both zero-profit boundaries

State the domain and omitted timing

Simple profit is zero at 90 and 110 and lowest at −10 when S=100. Upside payoff increases as S grows; on the nonnegative lower-price side its endpoint is S=0. The diagram is an expiry outcome map, not a claim that a large move will occur.