Automatic Implicit Function Theorem

Goloubentsev, Dmitri; Lakshtanov, Evgeny; Piterbarg, Vladimir

doi:10.2139/ssrn.3984964

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2022

2024

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Cited by 2 publications

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“…• Ey i -expectations of the call options (S(T i ) − K i ) + at the expiry dates T i 7 Theoretically they should be equal to 1 but in practice that is never achieved due to intricacies in hardware specifics and software optimization. 8 Since the Monte Carlo paths are random variables following a normal distribution, the exponential functions S(T i ) follow a log-normal distribution.…”

Section: Coded Examplesmentioning

confidence: 99%

Automatic Adjoint Differentiation for special functions involving expectations

Brito¹,

Goloubentsev²,

Goncharov³

2022

Preprint

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We explain how to compute gradients of functions of the form G = 1 2 m i=1 (Ey i − C i ) 2 , which often appear in the calibration of stochastic models, using Automatic Adjoint Differentiation and parallelization. We expand on the work of [7] and give faster and easier to implement approaches. We also provide an implementation of our methods and apply the technique to calibrate European options.

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Section: Coded Examplesmentioning

confidence: 99%