Lab · Derivatives
Options & Greeks Lab
Black-Scholes-Merton, European exercise, no dividends. Units are per one option.
Option value
4.29
Δ Delta
0.549
Γ Gamma
0.0403
ν Vega /1%
0.139
Θ Theta /day
-0.052
ρ Rho /1%
0.062
Value today vs payoff at expiry
The gap between the curves is time value, which theta eats away each day.
Δ Delta across spot
Γ Gamma across spot
ν Vega across spot
Θ Theta across spot
Greek surface: spot × time to expiry
ΔDelta0.549
Change in option value for a 1-unit move in the underlying.
If the underlying moves from 100 to 101, this position changes by about 0.55.
Also a rough probability of finishing in the money, and your hedge ratio.
ΓGamma0.0403
How fast delta itself changes as the underlying moves.
After that 1-unit move, delta would shift by about 0.0403.
Peaks at-the-money near expiry. Long gamma likes big moves.
νVega0.139
Change in value for a 1 percentage-point rise in volatility.
If volatility rises from 28% to 29%, value changes by 0.139.
Long options are long vega. Biggest for long-dated, at-the-money options.
ΘTheta-0.052
Value lost per calendar day as time passes, all else equal.
Tomorrow, with nothing else changing, the position is worth 0.052 less.
The rent you pay for gamma. Accelerates in the final weeks.
ρRho0.062
Change in value for a 1 percentage-point rise in interest rates.
If rates rise from 6.0% to 7.0%, value changes by 0.062.
Matters most for long-dated options. Calls gain, puts lose when rates rise.
Check your understanding
1. An at-the-money call has a delta closest to…
2. Gamma is highest for which option?
3. Volatility jumps from L2 Steady to L5 Extreme. A long put's value…
4. For a long option position, theta is usually…