Real Time Risk Management with Adjoint Algorithmic Differentiation

Event Date: 

Wednesday, September 9, 2015 -
10:00am to 12:00pm
Thursday, September 10, 2015 -
10:00am to 12:00pm

Event Location: 

  • Sobel Seminar Room; South Hall 5607F
  • CFMAR Seminar Series

Abstract: Adjoint Algorithmic Differentiation (AAD) is one of the principal innovations in risk management of derivatives securities of the recent times. In this minicourse I will introduce AAD and show how it can be used to implement the calculation of price sensitivities in complete generality and with minimal analytical effort. The focus will be Monte Carlo methods - generally the most challenging from the computational point of view - but I will cover also Partial Differential Equations (PDE) applications. With several examples I will illustrate the workings of AAD and demonstrate how it can be straightforwardly implemented to reduce the computation time of the risk of any portfolio by order of magnitudes.

Outline:

  1. Monte Carlo and Pathwise Derivative Method
  2. Algebraic Adjoint Approaches
  3. Adjoint Algorithmic Differentiation (AAD)
  4. AAD and the Pathwise Derivative Method
  5. First Applications
  6. Case Study: Adjoint Greeks for the Libor Market Model
  7. Case Study: Correlation Greeks for Basket Default Contracts
  8. Case Study: Real Time Risk Management of Counterparty Risk and XVAs
  9. Application to Partial Differential Equations
  10. Market Prices Sensitivities, Calibration and the Implicit Function Theorem
  11. Case Study: Market Prices Sensitivities of Default Intensity Models