I'm starting to sell ATM options in order to buy the tails, and I would like to know how to use gamma/theta or theta/gamma ratio or their sum to manage and exit the short position before the gamma risk reaches maximum point. Does anybody have any idea how to use and interpret those ratios or sums?
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$\begingroup$ Are you looking for theory or a real world solution? Your question is too vague $\endgroup$– user50421Commented Oct 16, 2020 at 22:24
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$\begingroup$ Certainly real world, user 50421, for example, Taleb propose in its Dynamic Hedging book, something like this: Risk Management Rule: An alpha that is lower than the fair value alpha for a short gamma position or higher than a fair value alpha for a long gamma position will result in long-term losses (by the law of large numbers). alpha = decay/gamma or even better alpha = modified decay/gamma. $\endgroup$– luiz otavio RoxoCommented Oct 20, 2020 at 15:26
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$\begingroup$ Taleb would probably warn you on selling options if you don’t know exactly what you’re doing. I do the same. $\endgroup$– Bob Jansen ♦Commented Nov 30, 2020 at 19:42
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$\begingroup$ Bob Jansen, I appreciate your warning and advices. $\endgroup$– luiz otavio RoxoCommented Nov 30, 2020 at 20:10
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2 Answers
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Personally I don't see a huge benefit in these ratios. But you can draw some interesting metrics regardless. Recall that the generic formula for implied volatility is: $$\sigma_i =\sqrt{\frac{2\theta}{\Gamma S^2}} $$ Which is itself just a ratio of theta to gamma (specifically the cash theta to the cash gamma). On a portfolio level with position comprising of N options, your "net" implied volatility is: $$\sigma_i = \sqrt{\frac{2\sum^N_i \theta_i}{\sum^N_i \Gamma_i S^2}}$$
Where one has made the necessary sign adjustments so as not to create an error under the square root. You will see that, in the presence of a volatility skew, you are able to create local pockets of arbitrage, where one can be long gamma, and not pay theta (or even be paid theta), and vice versa. However thanks to 3rd order dS and 2nd order dT greeks, these local pockets of arbitrage are rarely long lasting.
From your post it sounds like you are selling local volatility risk, and buying OTM risk, a fine trade, but consider that your gamma risk is mostly from the ATM, and since you are selling a single strike (or a range of similar strikes), your local gamma risk is directly offset by a higher theta. Any change in gamma (from changes in spot and time) will be mirrored in your theta. Any increase in gamma risk from a falling implied volatility will be compensated for by earning PnL from vega, and vice versa. The net ratio of your cash theta to cash gamma is then analogous to the implied variance, and what matters in that scenario is the implied volatility of the option, and the spread to realised volatility.
I think a problem like this can be solved by looking at a spot/time PnL surface, where the x axis is the underlying, the z axis is time, and the y axis is your PnL. From memory Interactive Brokers offer a graph PnL through spot, and allow you to overlay PnL at different times (holding IV constant), but you may benefit from creating these surfaces yourself, and simulating PnL as your strikes roll through the surface -- keeping a sticky strike model is good enough, though you can experiment with sticky moneyness or other spot/IV models.
Understand where your 'max pain' points are, ask yourself if you can a) financially and b) psychologically handle the losses at those points, then go from there.
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I can tell you about TGR (Theta gamma ratio) and VGR (Vega gamma Ratio) It is said that when both these ratio's are uptreanding then never sell. I hope this clears your doubt. Happy trading
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1$\begingroup$ It would be great if you would elaborate a little bit. This answer is not very useful at the moment. $\endgroup$– amdoptCommented Jun 26, 2023 at 8:55