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I guess you may want to express it in terms of convexity. What you claim about the slope of the tangent can be expressed with delta. Would it be something like "positive convexity (long gamma) means an increase in profit wrt absolut delta" ?

Hi Dmo, Your daily pnl is about : 0.5*gamma*ds*ds-theta (gamma could BS's one or a modified one and ds=daily move). So what did you mean when you wrote:"a simple mathematical way of describing a long-gamma (smile) curve vs a short-gamma (frown) curve?"

"For american pricing you just need to use Haug's code with skewness and kurtosis if you want with the american option feature, the boundary condition : an america call value is max((S-K); same european node value)) everywhere on the tree ( S=spot K= strike). The same for american put pricing."...

Binomial model with skewness and kurtosis code p 297 p 298. It may be worth you try with a trinomial model. The implementation is straightforward.

I understand. I know what a gram charlier or an edgeworth series expansion is and I didn't mean that you'd better use one model instead of another. But take a look at what Brown and Robinson wrote on how to avoid such a problem ( I will try to post the pdf here). Longstaff wrote on problems...

See Longstaff or Brown and Robinson for modified Corrado Su model to avoid negative probabilities and arbitrage. Or try this: http://eprints.lse.ac.uk/24938/1/dp419.pdf

Huh ? I'm sorry, I didn't experience the same problem with Edgeworth series expansion for option pricing. The only thing I wanted to stress is that with a kurtosis<3, you get an inverse smile. You're certainly right, I don't get your question.

What do you want to know about edgeworth or Gram Charlier series expansion ? What kind of problem you got with other skewness ( <-0.8 or >0.8) and other kurtosis (<3,>5.5) ? Models based on edgeworth series expansion work very well behind those levels :cool: . Take a look at what kind of...

Right, assuming zero interest rate, that's why bigger gamma/bigger theta for short term options remains the same as lower gamma/lower theta for long term options. Gamma and theta walk along the same way. The additional risk for LEAPS is vega something.

"they also have more gamma, thus more profit potential?" They also have more gamma risk :p . NNT just states that writing a short term option has the same expected profit (assume 0 interest rates) as a long term option, except that you earn less premium for the risk you take. Short term...

There is no such a thing as a pure greeks calculation that will tell you how volatility would move. The only way is by forecasting a behavior for short term volatilty wrt long term volatility. Then to weight vegas the same way.

It depends on which type of underlying you trade, and what you do with. If you trade skew volatility on currency options, then there is a robust model to price every options based on vanna and volga. That way, it's useful. Every option trader derives weighted vegas. Sometime vegas are weighted...

My bad. 'Shadow gamma' is explained p138, and vanna is called 'Ddelta/dvol' p200 . DdeltaDvol is an explicit way to describe that vanna is a partial derivative of an option delta wrt volatility. It's easier to remind what it means.

Vanna is called 'shadow gamma' by NNT p 200 Volga is called 'vega convexity' described p184 p 238 and the following ones.

At the money forward, theta is the same for calls and puts.

ha ha ha

Hi, Everybody knows there is a week end. Market makers too. So basically theta is already priced before saturday. Some traders price it friday afternoon, some friday morning...

Very good stuff Dmo.

OP, Remember that a american digital is exercized since it hits the trigger, it's another story with vanilla options. Hence, narrow spread would only help you to see the limit for european digitals. It's an interesting stuff though.

Never mind.