We provide and analyze analytical approximations of backward SDEs in the limit of small nonlinearity and short time, in the case of nonsmooth drivers. We identify the first and second order approximations within these asymptotics and consider two topical financial applications: the two interest rates pricing problem and the funding value adjustment. In the high dimensional diffusion setting, we show how to compute explicitly the first order formula by taking advantage of recent proxy techniques. Numerical tests up to dimension 20 illustrate the efficiency of the numerical schemes. We additionally investigate higher order expansions, which may hold under additional assumptions; we also provide a counterexample where the third order expansion fails to exist.

Gobet Emmanuel, Pagliarani Stefano (2015). Analytical approximations of BSDEs with non-smooth driver. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 6(2015)(1), 919-958 [10.1137/14100021X].

Analytical approximations of BSDEs with non-smooth driver

Pagliarani Stefano
2015

Abstract

We provide and analyze analytical approximations of backward SDEs in the limit of small nonlinearity and short time, in the case of nonsmooth drivers. We identify the first and second order approximations within these asymptotics and consider two topical financial applications: the two interest rates pricing problem and the funding value adjustment. In the high dimensional diffusion setting, we show how to compute explicitly the first order formula by taking advantage of recent proxy techniques. Numerical tests up to dimension 20 illustrate the efficiency of the numerical schemes. We additionally investigate higher order expansions, which may hold under additional assumptions; we also provide a counterexample where the third order expansion fails to exist.
2015
Gobet Emmanuel, Pagliarani Stefano (2015). Analytical approximations of BSDEs with non-smooth driver. SIAM JOURNAL ON FINANCIAL MATHEMATICS, 6(2015)(1), 919-958 [10.1137/14100021X].
Gobet Emmanuel; Pagliarani Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/708967
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