So if an underlying stock goes up 2%, what percentage would a given call go up? Stock goes down how much does a put go down? Do I have to do elaborate calculations to understand the answer to this question? Do I need to understand Black-Scholes? I'm trying to figure this out for hedging purposes. If anyone can point me in the right direction I'd be greatful.
1) Depends; 2) Depends; 3) No, there are a number of models out there; 4) No, you don't need to understand the model, just the outputs; 5) All you need is the Delta from any of the programs or quote providers, that will probably suffice for your needs.
The delta is what you use to establish your hedge, i.e. "hedge ratio"; it is an output of a valuation model ...
Options don't really move in relation to the percent move of the stock. It's more in relation to the actual dollar amount the stock moves. The option usually moves from 25% to 80% of the dollar amount the stock moves, depending how close it is to expiration and how much the stock price is inside or outside the option's strike price. An option on a stock that goes from $10 to $15 (50% stock increase) could move "nearly" the same as an option on a stock that moves from $50 to $55 (10% stock increase). In both cases the option's value could increase 100%-200%.
Since everyone seems to be too busy making fun of your question, I will try to show you the information I would be looking for if I were to ask a question like yours. If you go to http://www.pcquote.com/options/stri...ALS=1&RANGE=999&SHOW=1&FIRSTMONTH=0&MONTHS=24 You will find a long list of options on IBM: Calls on the left, puts on the right. In the column "delta" you will see the delta of the respective option. The delta is the number of cents the option will move (theoretically) if the stock moves 1 cent. For example a delta of -0.82 means if IBM goes up .01, then the put with a delta of -0.82 will go down .0082. Of course, that's just theoretical value, in reality the tick size would be .1, so the option would probably not move at all. I picked the example in cents, not dollars, because as you might know, delta is just an approximation. If IBM goes up $100, then the put will not go down $82, because delta is a local value, and its changes as the underlying price changes. The change of delta per unit of underlying price change also has a name: gamma. A gamma of 0.103 means that if the underlying goes up $.01, the delta of that option will (theoretically) increase by .00103. But just like delta, gamma is only local and therefore only an "approximation". If you have a math background try to think of it this way: If p is the stock price and x is the option price then delta is dx/dp and gamma is d(delta)/dp or (d^2/(dp)^2)x