Beginner question about Greeks (reading Natneberg for 2nd time)

Quote from union1411:

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.
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It doesn't matter...he will go short the underlyer to remain delta neutral.
 
Ok makes sense. I guess when Natenberg says "sell the underlying" to reduce delta by 100, he means going short.

Thanks. I have another question or two, but am going to try to answer them on my own. If I can't, I will be back :)

You guys are a great resource.
 
Ok, now for my 3rd question. I am bit confused about gains/losses before expiration.


Suppose the following (call) -

Underlying: 100
Strike: 105
Expiration: June
Premium: 5

Let's say I buy the call on May 10. Now suppose on May 20 the underlying rises to $120. Suppose also that the theoretical value rises to 10 because of the underlying's rise on May 10.

Is my gain $5 because of increase in theoretical value (i.e., $10 theoretical value - $5 initial premium)? Or is it $10 because of value of excerising the option (i.e., $120 underlying - 105 strike - $5 premium)?
 
Quote from union1411:

Ok, now for my 3rd question. I am bit confused about gains/losses before expiration.


Suppose the following (call) -

Underlying: 100
Strike: 105
Expiration: June
Premium: 5

Let's say I buy the call on May 10. Now suppose on May 20 the underlying rises to $120. Suppose also that the theoretical value rises to 10 because of the underlying's rise on May 10.

Is my gain $5 because of increase in theoretical value (i.e., $10 theoretical value - $5 initial premium)? Or is it $10 because of value of excerising the option (i.e., $120 underlying - 105 strike - $5 premium)?
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Your example is a bad one, since the call would be worth at least 15 (as it has $15 of intrinsic value) + whatever time value it has, and not 10 as you suggest.

In your example, it is obviously better to exercise the call, but in reality this will not be the case, as it is usually better to sell the option to capture the remaining time value.
 
I see. Makes sense.

So, my daily "gains/losses" are the increase/decrease in price of the call, right? From $5 to $15, whatever. Because that will be basically the same, if not more (time value), as the early excercise of the option, right?
 
Quote from union1411:

I see. Makes sense.

So, my daily "gains/losses" are the increase/decrease in price of the call, right? From $5 to $15, whatever. Because that will be basically the same, if not more (time value), as the early excercise of the option, right?
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Yes, that's right. An American-style call will generally not be exercised early since it is not optimal to do so because of the remaining time value, which is lost on exercise.

However, it may be exercised early if it is ITM and the stock goes ex-dividend.
 
Quote from dpt:

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 :)
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Just catching up. Finally! I've spent a couple of minutes of my life reading your posts. All I can say is, uh, thank you.
 
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