Assumptions:
- Volatility smile = 0.15 - 0.1\times (K-K_{ATM}) + 0.1 \times (K-K_{ATM})^2
- Sticky strike
- Flat volatility term structure
Since \Theta and Vega are similar to \Gamma, we skip presenting those. We are showing:
- Price
- Delta
- Gamma
- Vanna
- Volga
- Charm
- \frac {\partial}{\partial t} Vega
Note:
Vanna = \frac{\partial}{\partial S} \frac{\partial P}{\partial \sigma}
Volga = \frac{\partial^2 P}{\partial \sigma^2}
Charm = \frac{\partial}{\partial S} \frac{\partial P}{\partial T}
Strangle
Short Bear Spread
Back Spread
Calendar Spread
Diagonal Spread
Butterfly
Broken Wing Butterfly
Iron Condor
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