Malliavin Monte Carlo Greeks for jump diffusions

By Mark H. A. Davis, Martin Johansson. 2006

113 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9abe6058bb1123e5ca3fa752f75110d6c2ecc670

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Citations in the corpus

Malliavin Greeks without Malliavin calculus (2007, result): “This line of work originated in Fournié, Lasry, Lebuchoux, and Touzi [7] and includes Benhamou [1], Bermin, Kohatsu-Higa, and Montero [2], Cvitanic, Ma, and Zhang [3], Davis and Johansson [4], Fournié et al.”
Canonical Lévy process and Malliavin calculus (2007, background): “[12], and defined derivatives D t in the direction of the n martingale (see also Davis and Johanson [5]).”
Malliavin Calculus in Lévy spaces and Applications to Finance. (2008, background): “Furthermore E [ sup r≤u≤t |DirXn+1s |2 ] ≤ 4 { E [ sup r≤u≤t |σi(r,Xnr−)| 2 ] + E [ sup r≤u≤t ∣∣∣ ∫ u r Dirb(s,Xs−)ds ∣∣∣2] + E [ sup r≤u≤t ∣∣∣ ∫ u r Dirσα(s,Xs−)dW α s ∣∣∣2] + E [ sup r≤u≤t ∣∣∣ ∫ u r ∫ R0 Dirγ(s, z,Xs−)µ̃(dz, ds) ∣∣∣2]} (19) From Cauchy-Schwartz and Burkholder-Davis-Gundy2 inequali”
Integration by parts formula for locally smooth laws and applications to sensitivity computations (2007, methodology): “In this case, one may use the standard Malliavin calculus with respect to the Brownian motion increments after conditioning in a clear way with respect to the Poisson component. This is done in [ 8 , 11, 20].”
Bismut–Elworthy–Li-Type Formulae for Stochastic Differential Equations with Jumps (2010, methodology): “In particular, Davis and Johansson [6] and Cass and Friz [5] studied the case of jump diffusion processes, but their approach does not take any effects from the jump term.”