Options Pricing, Greeks, and Volatility
Domain 2 - Options Pricing, Greeks, and Volatility
The exam tests whether you can decompose a premium, apply put-call parity, and predict how an option's price reacts to each input.
Premium decomposition
- Premium = intrinsic value + time value. Intrinsic is max(0, S−K) for calls and max(0, K−S) for puts; time value is everything else and decays to zero at expiration.
- Six inputs drive a theoretical value: underlying price, strike, time to expiration, volatility, risk-free rate, and dividends. Volatility is the only one that must be estimated.
- Put-call parity for European options: C − P = S − PV(K) − PV(dividends). Violations create arbitrage.
Greeks
- Delta: call 0 to +1, put −1 to 0; at-the-money is about ±0.50. Delta × 100 × contracts ≈ share equivalent.
- Gamma is largest at the money and near expiration; it measures how fast delta changes.
- Theta is negative for long options - decay accelerates in the final 30 days.
- Vega is positive for long options; higher implied volatility raises both calls and puts.
- Rho: calls gain, puts lose, when rates rise.
Worked example
A stock trades at $62 and the 60 call costs $4.50. Intrinsic = $2.00, time value = $2.50. If implied volatility collapses after earnings, the option can lose value even with the stock unchanged - that is vega risk, not delta risk. Breakeven at expiration is $64.50.
Traps
- Believing a deep in-the-money option is low risk - it carries maximum dollar exposure.
- Treating delta as the exact probability of expiring in the money; it only approximates that.
- Ignoring early exercise of an in-the-money American call just before an ex-dividend date when the dividend exceeds remaining time value.