Gianluca Fusai

Università degli Studi del Piemonte Orientale “Amedeo Avogadro” (UPO)- Bayes Business School

The paper builds on an idea by Erio Castagnoli and expanded in Fusai [1] to identify a diusion process for the stock price that perfetly aligns with observed option prices at specic maturities. This is achieved by modeling stock returns as a monotonic continuous transformation $g$ of a standard Brownian motion (SBM). With the function g dened, 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.