Peter Carr Seminar: Gianluca Fusai (Università del Piemonte Orientale)

Abstract

The paper builds on an idea by Erio Castagnoli and expanded in Fusai (2024) to identify a diffusion process for the stock price that perfectly aligns withobserved option prices at specific maturities. This is achieved by modeling stock returns as a monotonic continuous transformation g of a standard Brownian motion (SBM). With the function g defined, deriving the dynamics of log-returns becomes straightforward using Ito's lemma, an improvement over the approach by Dupire [2]. This paper further develops this framework by demonstrating its full implementation in pricing popular energy products, such as calendar spread options traded at Chicago Mercantile Exchange.