THE GREEKS Flashcards
BSM Formula Inputs
- S- asset price (delta)
- Volatility- Vega
- Interest Rate- Rho
- Passage of TIme- Theta
- X- exercise price
- Gamma- rate of change in delta as stock price changes
Delta and Calls
Positively Related
Delta > 0
Measures change in call price for $1 change in underlying.
Prices up 1, Delta of 0.5, call price expected to move 50 cents.
Delta and Puts
Negatively Related
Delta < 0
Vega and Calls
Positively Related
Vega > 0
Higher volatility always positively impacts price of options
Vega and Puts
Positively Related
Vega > 0
Rho and Calls
Positively Related
Rho > 0
As rates increase, call values increase
Rho and Puts
Negatively Related
Rho < 0
As rates decrease, put values decline.
Theta and Calls
Value - > $0 as call -> maturity.
Negatively related
Theta < 0
Theta and Puts
Value - > $0 as put -> maturity.
Positively related
Theta < 0
Theta’s input
passage of time
Delta’s input
Asset price
Vega’s input
Volatility
Rho’s input
risk-free rate
Delta Def
Change in price of an option for a 1 unit change in price of underlying stock.
Far out of the money call, delta approaches
0
Far in the money call, delta approaches
e^(-dividend yield*T)
Far out of the money put, delta approaches
0
Far in the money, put delta approaches
-e^ (-dividend yield*T)
Dynamic Hedging/Delta Neutral Hedging
Combining a long stock position with short calls so portfolio value doesn’t change with stock price.
of short calls needed = # shares hedged / Delta of call
Delta < 1 so always need more calls than shares.
Dynamic Hedge Formula
of short calls needed =
shares hedged / Delta of call
Gamma
rate of change in delta as stock price changes
positive for both calls and puts
largest when option is ATM and close to expiration
Small for deep ITM and deep OTM options not close to expiration
Gamma and Calls
Positively related
Gamma and Puts
Positively related
Gamma risk
when stock price jumps abruptly (a violation of BSM assumption)
Implied volatility
of continuous returns on underlying stock is “volatility” from BSM model that makes model value = market price
Volatility “implied” by option price.
