Delta Hedging

Delta Hedge = Option + underlying securities

Should growth at risk free rate if dynamically managed

Used for dealers to hedge short calls (still earn the premiums)

Delta = change of option price/ change of stock price

0<Delta<1 for long call or short put

-1<Delta<0 for short call or long put

(Note that this is about the absolute value change not gain. For gains, we know options usually is larger than the stocks)

Delta is not constant: not just depends on S but also other market conditions

Change of Call price > Delta * change of S when S increases

Change of Call price < Delta * change of S when S decreases

Number of stock to hedge = Delta * # of options

Delta increases with the increases in the stock price

*** If well managed, the portfolio value should increase by exp(r/365) everyday! This is a short cut to many calculations.

Gamma = change of delta / change of S

Important when it is at the money or near expiration!