Maan lo S = expiry par stock price, K = center, w = wing width, C = net credit received.
Expiry par har option ki value (sirf intrinsic):
Long call payoff: max(S−Kc,0)
Long put payoff: max(Kp−S,0)
Short = upar wale ka negative.
Charon legs ko sum karo, phir credit C add karo jo aapko mila tha.
P(S)=Cshort call−max(S−K,0)short put−max(K−S,0)long call wing+max(S−(K+w),0)long put wing+max((K−w)−S,0)
Key point S=K par evaluate karo (kyun: sabhi "distance" terms vanish ho jaate hain, toh peak dikhti hai):
P(K)=C−0−0+0+0=C
Toh max profit = net credit C, tab milti hai jab stock center strike ko pin kare. Yeh step kyun?S=K par har option at- ya out-of-the-money hoti hai → sabhi intrinsic values 0 hain → aap poora credit rakh lete ho.
Ek wing par evaluate karo, maan lo S=K+w (kyun: yahan wing kick karti hai aur bleeding rokti hai):
P(K+w)=C−short call loses ww−0+0+0=C−w
K+w se aage, long call ke gains exactly short-call ke further losses ko offset karte hain, toh loss C−w par flat rehta hai. Symmetry se yahi S=K−w par bhi hota hai.
Breakevens K±C par kyun hain?S=K par peak C se shuru karke, jaise S door jaata hai profit slope 1 se girta hai (ek short option ITM ja rahi hai). Yeh 0 tak paunchta hai C distance move karne ke baad. Toh breakeven =K±C.
Recall Forecast-then-Verify (answers cover kar lo!)
Max profit kahan hai? → S=K par, net credit C ke barabar.
Max loss formula? → w−C.
Breakevens? → K−C aur K+C.
Isse kaunse vol environment mein sell karo? → High IV.
Aap kis outcome ke liye root karte ho? → Stock center strike ko pin kare.
Recall Feynman: ek 12-saal ke bachche ko samjhao
Socho tum bet lagaate ho ki ek spinning coin ek table ke bilkul beech mein apni edge par land karegi. Agar yeh dead-center land kare, tum poora prize jeeto (credit). Agar thoda roll kare, kam jeeto. Agar table ke edge ki taraf roll kare, tum haarte ho — lekin tumne edges ke paas fences (wings) lagaaye hain taki tum kabhi sab kuch na haaro. Tum chahte ho ki coin beech mein freeze ho jaye.
