2013/08/10 by Peter Carr, Carr, Peter, Sergey Nadtochiy +1 · 1 citation
Economics, Econometrics and Finance · #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1308.2326
openalex publication_date 2013/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for calibrating a pure jump Markov martingale model to match the market prices of European options of multiple strikes and maturities. This algorithm only requires solutions of several one-dimensional root-search problems, as well as application of elementary functions. We show how to construct a time-homogeneous process which meets a single smile, and a piecewise time-homogeneous process which can meet multiple smiles.