Explicit Option Pricing With Additive Processes

Abstract

We propose a fully explicit and empirically sound option pricing model based on additive processes. The model yields analytic closed formulae for pricing vanilla options, is easy to calibrate and simulate, and fits very well the market implied volatility at an extremely low computational cost. The explicit expressions for commonly traded products implicate that both large and small time leading orders of the implied volatility level and skew -- as well as large strike asymptotics -- can be determined exactly. A plethora of implied volatility shapes can thus be reproduced by just supplying appropriate term functions, leading to nearly complete control of the implied volatility surface.
The methodological implication of our study is that in contrast to widespread belief realistic continuous time models allowing explicit option pricing do exist. We finally argue that explicit additive models need not to be only of the proposed Beta type, but by taking into account skew generation mechanisms, analiticity of vanilla prices can be potentially determined by other kinds of distributions.

Keywords: additive processes, explicit option pricing, implied volatility surface, implied volatility skew, large strike implied volatilities, infinitely-divisible distributions