Learn to manage a position's Greeks — Hinglish notes

5.3.10 · Stock-Market › The Greeks

Greeks ko manage KYUN karein?

YEH master tool KYUN hai: kyunki Greeks derivatives hain aur derivatives linear hote hain. Agar $P = \sum_{i} n_{i} V_{i}$ hai to $\frac{\partial P}{\partial S} = \sum_{i} n_{i} \frac{\partial V _{i}}{\partial S} .$ Woh ek fact — differentiation ki linearity — yahi wajah hai ki aap risks ko bilkul "add up" aur "cancel" kar sakte hain. Neeche sab kuch bas $n_{i}$ choose karna hai taaki koi sum zero ho jaaye.

Har Greek ko neutralise KAISE karein

1. Delta-hedging (pehli cheez jo sab karte hain)

KAISE: Underlying add karo (Delta = 1 per share/future) jab tak sum zero na ho jaaye. $n_{stock} = - Δ_{options}$

2. Lekin Delta-neutral RISK-FREE nahi hota — Gamma aata hai

Gamma ko neutralise KAISE karein: stock ka $Γ = 0$ hota hai (uska Delta constant hai), isliye stock Gamma fix nahi kar sakta. Aapko doosra option chahiye. Ek saath do equations solve karo.

Maano option A (aapka) aur hedging option B, $n_{B}$ contracts aur $n_{S}$ shares ke saath: $Γ : Γ_{A} + n_{B} Γ_{B} = 0 \Rightarrow n_{B} = - \frac{Γ _{A}}{Γ _{B}}$ $Δ : Δ_{A} + n_{B} Δ_{B} + n_{S} = 0 \Rightarrow n_{S} = - (Δ_{A} + n_{B} Δ_{B})$

Figure — Learn to manage a position's Greeks

3. Theta aur Vega — jinhe aap stock se hedge nahi kar sakte

Vega ko neutralise KAISE karein: phir se doosra option use karo — Vega at-the-money, longer-dated options ke liye sabse zyada hota hai, isliye Vega equation solve karne ke liye ek hedging option chunein, bilkul Gamma ki tarah: $n_{B} = - \frac{ν _{A}}{ν _{B}} .$ Jitne zyada Greeks zero karne hain, utne zyada independent instruments chahiye (Delta ke liye stock ke saath ek option per Greek).

Forecast-then-Verify drill

Common Mistakes

Flashcards

Stock ko Gamma ya Vega hedge karne ke liye kyun use nahi kar sakte?

Stock ka Delta constant hai, isliye uska Gamma aur Vega dono 0 hain; yeh sirf Delta shift karta hai.

Portfolio Delta formula kya hai?

Δ_{p or t} = \sum_{i} n_{i} Δ_{i}

(derivatives ki linearity).

Option B se Gamma hedge karne ke liye kitne contracts chahiye?

n_{B} = - Γ_{A} / Γ_{B}

Gamma-neutralise karne ke baad, bacha hua Delta kya fix karta hai?

Underlying ke

n_{S} = - (Δ_{A} + n_{B} Δ_{B})

shares short/long karo.

Gamma ko Delta se pehle hedge KYUN karein?

Stock sirf Delta affect karta hai, isliye Delta step pehle se fix Gamma ko disturb nahi kar sakta (triangular structure).

Long option ke liye opposite signs ke saath kaunse do Greeks trade off karte hain?

Gamma (positive) vs Theta (negative).

Delta-neutral short straddle — bade move par kya hurt karta hai?

Negative Gamma (convex losses) plus agar IV bade to aap short Vega hain.

Sabse bada Vega kis options mein hota hai?

At-the-money, longer-dated options.

N Greeks zero karne ke liye kitne independent instruments chahiye?

Roughly N (Delta ke liye stock ke saath ek option per option-only Greek).

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho tumhari bike alag alag tarike se hil sakti hai: aage-peeche, side-to-side, upar-neeche. Har "hilna" ek Greek hai. Agar tumhe sirf aage jaana hai, to tum chhote chhote support lagate ho (extra options, kuch stock) taaki baaki ki hilnayen cancel ho jaayein. Stock ek aisa support hai jo sirf side-to-side hilna fix karta hai; "upar-neeche" (bade jump) waali hilnayi rokne ke liye tumhe alag support chahiye — doosra option. Pehle mushkil wali hilnayi fix karo, phir aasaan wali, taaki apna hi kaam na undo ho jaaye.

Connections

Delta - directional sensitivity
Gamma - rate of change of Delta
Theta - time decay
Vega - volatility sensitivity
Black-Scholes model
Delta hedging and re-hedging costs
Straddles and Strangles
Implied Volatility