Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation

Georg Ch. Pflug, Philipp Thoma
2016 Quantitative finance (Print)  
Monte Carlo simulation methods have become more and more important in the nancial sector in the past years. In this paper, we introduce a new simulation method for the estimation of the derivatives of prices of nancial contracts with respect to (w.r.t.) certain distributional parameters, called the Greeks . In particular, we assume that the underlying nancial process is a Lévy-type process in discrete time. Our method is based on the Measure Valued Dierentiation (MVD) approach, which allows to
more » ... epresent derivatives as dierences of two processes, called the phantoms. We discuss the applicability of MVD for dierent types of option payos in combination with dierent types of models of the underlying and provide a framework for the applicability of MVD for path-dependent payo functions, as Lookback Options or Asian Options. 1 then the martingale corresponding to its exponential satises S(t) ∼ e −rt e mt S(0) exp(X(t)) with m = r − λ (p(1 − b 1 ) −a 1 + (1 − p)(1 + b 2 ) −a 2 − 1) . 6
doi:10.1080/14697688.2015.1114364 fatcat:z32eedxa25hfjinrtymkrzczbi