# How accurate are Black-Scholes estimates of Vega, Volga, Vanna

Wikipedia provides analytical formulas for calculating Greeks. I can get Delta, Gamma, Theta all from Bloomberg. I need Vega, Volga, Vanna for my research. Should I use these analytical formulas for now? How accurate are they?

Say the actual Volga of the option is like 1, will they provide an unbiased estimate of Volga like 0.99 or not?

• Hi @Irtza Ahmed. These are analytic formulas. So as long as you implement them right and use the right parameters (forward price and volatility), you'll get the exact Greeks for European vanillas. Commented Oct 10, 2018 at 12:39
• I am not comparing these analytical formulas with monte carlo, or finite difference method. I am comparing the Greeks with the realized ones we experience in the market. Like these greeks depend on the black scholes model assumpetion. BSM does not give correct prices but does it give greeks correct? Commented Oct 10, 2018 at 13:36
• Greeks are associated to a model not to the market. You cannot "experience" "realised" Greeks... This makes no sense. Now maybe your pricing system returns Greeks which you want to compare to these Black-Scholes Greeks? If so clearly even the Deltas will most likely differ, so the second order Greeks will differ even more. Commented Oct 10, 2018 at 13:44
• One can experience greeks. Say the underlying stock moves by 1 cent how much will the call option move. This is approximately delta. Now to estimate this real delta should I use BSM or LV or SV. What do they use when delta hedging Commented Oct 10, 2018 at 13:52
• As you say this is "approximately" delta. It's a market move (hence risk scenario/impact if you like) not a Greek (in the mathematical sense). The difference is that when the stock moves, the impact is not only Delta but also Gamma, Vanna etc. (Taylor expansion) Commented Oct 10, 2018 at 13:55