I have 2 questions:
What is the most commonly used equity option pricing model? I learned jump diffusion at school, read about Hensen and a few other models online.
I am actually only calibrating the surface for easy retrieval of historical data. Right now to answer questions like "what is the implied vol of an option with strike = 105% of forward price and time = 3 month, for each day for the past 10 years", I literally have to interpolate on 3650 different option chains. Since each option chain is a 2000 * 4 grid, the process is slow. I am hoping that after calibrating, I only have to look at the parameters, instead of the entire surface.
But since calibrating loses accuracy, my second question is, is it viable to increase accuracy by cutting the surface into a few segments, and then calibrating each segment separately? I am honestly only looking for a function that fits through the surface, and I have no problem making that function piece-wise since any fitting attempt is better than my current method of using the entire surface.