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Greeks

Hi,

I have been struggling to understand the concepts around Greeks. Can some one please help me on the below with some examples if possible or further links which could help me understand the concepts better?

- Gamma - when is gamma +ve and when is it -ve?
- Relation between Gamma, Delta and Theta (read it somewhere)
** For a delta neutral portfolio, when theta is large and negative, gamma will tend to be large and positive. The converse of this holds too. Thus, if delta is zero and theta is large and positive, gamma is likely to be large in magnitude and negative in sign.

Thanks in advance
 
Responding respectively

- Always positive for long calls and long puts, always negative for short calls and short puts
- Directly from the Black-Scholes PDE (if V is the value of the option and S is the stock price, V_t is theta, V_S is delta, V_SS is gamma)
- Again, from the Black-Scholes PDE, the V_S term drops out in a delta neutral portfolio, leaving you with the theta and gamma terms on the same side of the equation.
 
Hi,

I have been struggling to understand the concepts around Greeks. Can some one please help me on the below with some examples if possible or further links which could help me understand the concepts better?

- Gamma - when is gamma +ve and when is it -ve?
- Relation between Gamma, Delta and Theta (read it somewhere)
** For a delta neutral portfolio, when theta is large and negative, gamma will tend to be large and positive. The converse of this holds too. Thus, if delta is zero and theta is large and positive, gamma is likely to be large in magnitude and negative in sign.

Thanks in advance

delta shouldn't have to be zero for the gamma/theta relationships to hold. in fact when the delta of an option is zero, both theta and gamma will also be zero.
 
delta shouldn't have to be zero for the gamma/theta relationships to hold. in fact when the delta of an option is zero, both theta and gamma will also be zero.
Yes, for an individual option, when the delta is zero, everything will be zero -- including the option price. It will be deep out-of-the-money. This is a trivial case.

The OP comment refers to a "delta-neutral portfolio."

You have multiple positions, which individually have non-zero deltas, gammas, thetas, etc.

If the positions are constructed in such a way that the total portfolio has zero delta, if it is net long premium, it will be long gamma (it will make money if the market moves up or down) and short theta (it will lose in time-decay of the premium if the market does not move.) Think, for example, of a long straddle position.

And the converse is that if the portfolio is short premium (the trader is a net writer of options) then he would be short gamma (market moves in either direction will cause losses) and long theta (he will earn time-decay on his short premium if the market stagnates.) Think of a short straddle position, for example.
 
Yes, for an individual option, when the delta is zero, everything will be zero -- including the option price. It will be deep out-of-the-money. This is a trivial case.

The OP comment refers to a "delta-neutral portfolio."

You have multiple positions, which individually have non-zero deltas, gammas, thetas, etc.

If the positions are constructed in such a way that the total portfolio has zero delta, if it is net long premium, it will be long gamma (it will make money if the market moves up or down) and short theta (it will lose in time-decay of the premium if the market does not move.) Think, for example, of a long straddle position.

And the converse is that if the portfolio is short premium (the trader is a net writer of options) then he would be short gamma (market moves in either direction will cause losses) and long theta (he will earn time-decay on his short premium if the market stagnates.) Think of a short straddle position, for example.

yes of course, i was just concerned with the statement "Thus, if delta is zero and theta is large and positive, gamma is likely to be large in magnitude and negative in sign." thats all.. the post seemed to reflect that what the delta of a portfolio is really matters.. really nothing has to do with the delta beyond the fact that people who delta hedge are more concerned with what their gamma and theta are than people who don't delta hedge, but that doesnt mean that portfolios that arent delta hedged dont have exactly the same gamma and theta as ones that are

 
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