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LOCAL VARIANCE GAMMA AND EXPLICIT CALIBRATION TO OPTION PRICES
Author(s) -
Carr Peter,
Nadtochiy Sergey
Publication year - 2017
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12086
Subject(s) - martingale (probability theory) , econometrics , homogeneous , piecewise , jump , valuation of options , maturity (psychological) , mathematics , markov process , variance (accounting) , economics , binomial options pricing model , mathematical optimization , mathematical economics , computer science , statistics , psychology , mathematical analysis , developmental psychology , physics , accounting , combinatorics , quantum mechanics
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 analyze a special class of pure jump Markov martingale models and provide an algorithm for calibrating such models to match the market prices of European options with multiple strikes and maturities. This algorithm matches option prices exactly and only requires solving several one‐dimensional root‐search problems and applying 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.