From Implied Volatility Surface to Quantitative Options Relative Value Trading

Abstract

The only thing one can say about financial markets is that parsimonious information on option prices is available in time and space, and that we can only use the No-Dominance law (or stronger version of No-Arbitrage) to account for it. Thus, one requires a consistent model to assess relative value between them. We describe a single parametric model for the entire volatility surface with interpolation and extrapolation technique generating a smooth and robust implied volatility surface without arbitrage in space and time. Prices can now be generated such that the No-Dominance principle is preserved, and one can safely assess relative value between them. In order to perform statistical analysis of the relationships between points on the implied volatility surface (IVS), we are left with finding a way of modeling dynamically the agents rational anticipations. We assume that the volatility surface is dynamically modified according to the stock price realisations. Having related the stock price level to the implied volatility surface, we use their respective historic evolution to characterise the transition probabilities, that is, the conditional densities. A statistical technique is used to regress the observed implied smile against the realised stock level. Therefore, the current stock evolution directly influences its future increment which means that, given the stock price at a future time, the conditional density is known.