The implied volatility surface connection with local volatility, SABR, Heston

Abstract

There are many concepts in contemporary volatility models, but they have the same orientation. So in this paper, I want to connect each other. More particularly, we will place the implied volatility surface in the center and analyze Local volatility, SABR, Heston models. In the part of non-parametric volatility, first we collect the theories that are already in use and propose more consistent model named forward local volatility. Afterwards delta hedge is simulated and the right way of using Local volatility model is verified. In the part of parametric volatility, it begins with examining all inputs(dividend, riskless rate, security index futures) of volatility model. Finally, we propose the new methodologies to make the useful models more useful. One is bootstrapping the synthetic option and the other is making the stochastic volatility model as a Mosaic.