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I want to do market making on options.

Say I have a portfolio made of options.

Denote by $Vega^{\pi}$ the Vega of the portfolio, $Vega_{i}$ the Vega of the $i^{th}$ option and $\tilde{Vega}$ the maximum Vega for my portfolio.

Denote $z_{ i}$ the mean size of orders for the $i^{th} option $.

I choose to quote the $i^{th}$ option as follows : the formula for my bid ( respectively ask side) is given by

$\delta_{i}^{b}(t) = \mathbb{1}_{Vega + z_{i}Vega_{i} \leq \tilde{V}}( \alpha_{1} Vega_{i} +\alpha_{2} \sigma_{impli}^{2} 1/( T_{mat} - t) + \alpha_{3} \frac{Vega^{\pi}}{Vega_{i}}) + \mathbb{1}_{Vega + z_{i}Vega_{i} \geq \tilde{V}} ( BestBidMarket + \epsilon)$

So basically : if the next order on option $i^{th}$ makes me stay within the bounds for my portfolio Vega, I quote my spread as a linear combination of the Vega, implied volatility and portfolio Vega. Otherwise I want to avoid being hit by widening the bid and taking the current best bid on the market for reference and shifting it enough. I also hope it makes me able to be more agressive on the ask side and to be long Vega.

Do you think this model is relevant ? Did I miss something important in this first draw ?

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