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Discussion in 'Options' started by union1411, May 5, 2005.

1. Ok, I'll start simple for my first question. I just want to make sure that I'm applying Delta and Gamma concepts right. (I'm making up these numbers)

Underlying: \$100
Strike: \$105
Delta: .40
Gamma: .2
Theoretical value: 5.0

So, now, if the stock price increases to \$101, then theoretical value will increase to 5.4. Because of .2 Gamma, the Delta increase to .42, which means the NEXT time the underlying goes up \$1, the theoretical value will increase by .42 (e.g., underlying goes from \$101 to \$102 results in theoretical value going from 5.4 to 5.82).

Am I finally getting it?

2. Yes you're right. Except that in reality Delta and Gamma work dynamically so the option will increase by slightly more than 0.4 when the underlying price increases by \$1.

3. The rule of thumb I learned is:

Change in Option Price = (change in stock price)*Delta + .5*gamma*(change in stock price)^2

Of course, delta and gamma change with price too, so you cant use this to estimate gigantic leaps in price.

-Tony

4. Where do I find, or how do I calculate, the "Greeks"?

This all seems very simple yet the option boys apparently use funny words combined with math that incorporates more than basic arithmatic--just like the mafia use baseball bats--to scare wannabes from their "corner".

5. Most option calculators or analysis software will calculate the Greeks for you (e.g. check out CBOE website for some free tools - www.cboe.com/LearnCenter/RCTools.aspx ). Otherwise, the Greeks come from an option pricing model, such as the Black-Scholes, but I doubt you wanna do it by hand all the time.

6. There is some math required in order to do it but you can learn. It helps if you've had a bit of
calculus.

Suppose that V was the value function of some kind of derivative instrument, that is, suppose V is
the result of solving some model for the price of the instrument as a function of various
independent variables in the model. So you put in the values of the underlying variables, and
calculating V then gives you the price.

So if you have such a function V, then the `Greeks' are defined to be certain derivatives (in the
sense of differential calculus) of the function V. So for example, if S is the price of the
underlying, r is the interest rate, and T is the time, then I think these are pretty standard
definitions:

delta = dV/dS

gamma = d^2 V/dS^2

theta = dV/dT

rho = dV/dr

These should all be interpreted as partial derivatives: they represent rates of change of V when all
other variables are held constant.

If V is the value function for an option, such as a call or a put, delta is then the rate of change of
option price with underlying price, gamma is the rate of change of delta with underlying price,
theta is the rate of change of option price with time, rho is the rate of change of option price
with interest rate.

If you have the function V in closed form, you can directly calculate the values of delta, gamma,
theta, and rho. For some models of particular kinds of option prices such as Black-Scholes, you do
actually get simple closed form expressions for the Greeks.

This site
has a pretty decent discussion of the Black-Scholes model. See these links:

Deriving the Black-Scholes Equation

Solving the Black-Scholes Equation

The Greek Letters - Delta

The Greek Letters - Theta

The Greek Letters - Gamma

They don't seem to have calculated rho there, but it should be easy enough to do yourself once you've
gone through delta, gamma and theta 7. Thanks for response.

My 2nd question: when Natenberg says to "sell the underlying" to reduce delta by 100, does he mean a) short the underlying or b) sell a share you already own?

It would be odd if it is b), because Natenberg never states in his examples that the fictional trader owns any shares. For example, if Natenberg gives a hypothetical of 10 long calls and 10 long puts and then says that the trader can reduce delta if he sells the underlying, nowhere in the example does he say that trader owned any shares to begin with.

8. You are going short to minimize your delta exposure.

For example, I have Honeywell options up on my screen right now.

A June HON 37.5 Call has a delta of 46.13, Put -52.41.

If you bought one call, your position delta would be 46.13.

You could then go short 46 shares of honeywell, each share having a delta of 1. Delta position of the short shares is -46.

Your net delta position is .13, or pretty much delta neutral.

Position Delta
Long 1 Call 46.13
Short 46 Shares -46
-------------------------------------------
Net Delta .13

Keep in mind lots of things cause delta to change, so from now until option expiration, you will want to periodially adjust your share position.

-Tony

9. You can get free options calculators and more from the OIC plus Man Financial has a terrific options calculator available for free. Both of these calculators can ber downloaded and installed onto your system, the Man Financial calculator requires Shockwave or maybe Java.

10. yes except your gamma is .02 to get you to .42... besides that minor mistake, you're on your way to understanding option pricing... in reality though, your delta/gamma is constantly changing so you cannot apply a linear relationship like you just did... but it gets you close to home.

#10     May 9, 2005
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