“Explicit option pricing with additive processes”
Venerdì 6 Ottobre 2023, ore 11:00 - Aula 2AB40 - Lorenzo Torricelli (Università di Bologna)
Abstract
We propose a simple but realistic option pricing model based on additive processes whose distributions follows generalized Beta laws. The model determines elementary and fully analytic closed formulae for pricing vanilla options, is easy to calibrate and simulate, and fits well the market implied volatility. 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 implied volatility surface. The methodological implication of our study is that, in contrast to widespread belief, realistic continuous time models allowing fully explicit option pricing do exist.
