Vega decomposition for the LV model: an adjoint differentiation approach

Introducing an algorithm for computing vega sensitivities at all strikes and expiries


Joachim Adrien et al present an efficient algorithm for computing the Vega KT in the local volatility model based on the calculation of the local Vega through Monte Carlo simulation and algorithmic differentiation. Unlike the partial differential equation algorithm presented by Guennoun, their algorithm is applicable for general multi-dimensional exotic options

In the Black-Scholes model with a time-dependent volatility, we can easily compute the sensitivity to

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