# Building a simple option market making model

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 ?