Derivatives Lecture 21 Greeks Delta Gamma Theta Vega

Derivatives Lecture 21

Greeks Delta Gamma Theta Vega Rho • The Greeks measure the various risks of an option. • Every option has risk related to the variables contained in the price of the option. • Knowing these risks allows us to create strategies and select the best option to include in the strategy.

Greeks Delta - D the rate of price change for an option, relative to the price change in the underlying asset Also called the Hedge Ratio D = N(d 1) = DC / DP

Greeks Gamma -G The rate of change in delta, relative to the price change of the asset G = N(d 1)p - N(d 1)p+1

Greeks Theta - Q The rate of change in the option price relative to a one day change in expiration Also called Time Decay Q = Ct - Ct-1

Greeks Vega - L The rate of change in the option price relative to a 1% change in the volatility L = Cv - Cv+. 01

Greeks Rho The rate of change in the option price relative to a 1% increase in the discount rate Rho = Cr - Cr+. 01

Greeks Example - original data Call = 1. 70 r = 10% Stock = 36 time = 90/365 days Strike = 40 volatility =. 40 Delta = N(d 1) =. 3794 Gamma = N(d 1)p - N(d 1)p+1 =. 3794 -. 4329 = -. 0535

Greeks example - continued Theta = Ct - Ct-1 = = 1. 700 - 1. 675 =. 0248 (daily) =. 0248 x 260 = 6. 448 (annual) Vega = Cv - Cv+. 01 = 1. 70 - 1. 7683 = -. 0683 Rho = = Cr - Cr+. 01 (using NUMA Web Option Calculator) = 1. 695 -1. 725 =. 0300