Derivatives Lecture 21.

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Presentation transcript:

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(d1) = DC / DP

Greeks Gamma -G The rate of change in delta, relative to the price change of the asset G = N(d1)p - N(d1)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(d1) = .3794 Gamma = N(d1)p - N(d1)p+1 = .3794 - .4329 = -.0535

Greeks = 1.695-1.725 = .0300 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