Start at expiry
A call pays max(S−K,0); a put pays max(K−S,0). Profit also accounts for premium and financing. A payoff is not a pre-expiry price.
Worked example: delta and gamma
With delta 0.5, gamma 0.04 and underlying move −2, the local approximation is ΔV ≈ δΔS + ½γ(ΔS)² = −1 + 0.08 = −0.92. Positive gamma contributes positively for either direction of move.
This is local. Large moves, changing volatility, elapsed time and changing Greeks can invalidate it. Explain which quantities were held constant.
Check the bounds
A call credit spread with width 5 sold for credit 1 has maximum expiry loss 4 per share before fees and financing. A larger computed loss suggests a sign or position mistake.
Practice order
- Payoff, premium and position signs.
- Replication and put-call relationships.
- Delta hedge units versus contract counts.
- Gamma, vega and residual exposure.
These are educational models, not trading recommendations. Real contract conventions require separate verification.
Try a fresh question
This optional exercise uses the actual parameterized bank.
Worked method
Keep the practice connected
Train Options & Derivatives · Follow the Quant Path · Evidence standard