ABSTRACT

This paper reports a practical approach to constructing arbitrage-free volatility surfaces that are consistent with the observed options smiles and Samuelson effect in futures markets.A separate volatility surface is created for each futures contract. The algorithm is fast, robust and able to match the entire market-implied volatility surface within a couple of basis points. The local volatility and marginal distribution surfaces for the futures price are also provided.We use data from NewYork Mercantile Exchange West Texas Intermediate (NYMEX WTI) oil to demonstrate the algorithm.