Profit and loss decomposition in continuous time and approximations

Gero Junike, Hauke Stier and Marcus C. Christiansen

Papers from arXiv.org

Abstract: Financial institutions and insurance companies that analyze the evolution and sources of profits and losses often look at risk factors only at discrete reporting dates, ignoring the detailed paths. Continuous-time decompositions avoid this weakness and also make decompositions consistent across different reporting grids. We construct a large class of continuous-time decompositions from a new extended version of It\^o's formula and uniquely identify a preferred decomposition from the axioms of exactness, symmetry and normalization. This unique decomposition turns out to be a stochastic limit of recursive Shapley values, but it suffers from a curse of dimensionality as the number of risk factors increases. We develop an approximation that breaks this curse when the risk factors almost surely have no simultaneous jumps.

Date: 2022-12, Revised 2024-12
New Economics Papers: this item is included in nep-rmg
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