# Finding the delta and gamma with historical data

I have a complicated product with knock-out barriers combined with other exotic options. I am curious if there is a fast and loose way to figure out the delta, gamma, rho, theta and possibly vega, with the historical prices of the product.

I mean, I would calculate the greeks by hand since it isnt impossible to write them out in a formula, but it would be a hideous expression, and my basic calculus skills are rusty.

So, is there a relatively simple way to get the sensitivities from historical prices? Can I just simply do $$\frac{\Delta P}{\Delta S}$$ with the historical underlying and historical option price for the delta, for instance? Would this be similar to what I would get by differentiating the price formula?

The observed time series of the historical option price would give you a time series of $\Delta P$, however these changes in price is not purely driven by change in spot. You also have the impact of change of vol and theta: $\Delta P \approx \Delta *\Delta S + 0.5 * \Gamma * \Delta S^2 + vega*\Delta \sigma + \theta$