14.45 - 15.30
Volatility & Modelling Techniques Stream
A critical (re-)view on Interest Rate Modelling for Portfolio Simulations, Derivative Valuation, Risk Minimization, (Deep) Hedging and ALM
Portfolio simulations and valuations (e.g., xVAs) require a high dimension risk factor simulation (“market simulation”, “world simulation”).
Another area, where high dimensional risk factor simulations are required, are hedge strategies in general risk minimization problems (where “deep hedging” is an appealing method) and ALM simulations.
For such applications, interest rates are very often modelled with short rate models with low (Markov-)dimension (e.g., affine term structure models with or without stochastic volatility). In the context of xVA short rate models have seen a renaissance.
While this is mainly due to computational efficiency – reducing the amount of memory required to represent the interest rate curve (e.g. to just a few (or one) Markovian state variable) –, it comes as a surprise from a modelling perspective:
It is known that such low dimension models lead to unrealistic interest rate curve modelling and inappropriate risk management of complex derivatives (c.f. Piterbarg, Filipovic, F., etc. (at least 2003, 2007)).
In the first part of this presentation, we will discuss this issue, recalling and reviewing some known, but possibly forgotten aspects, taking risk-management of complex derivatives as an example.
In the second part, we propose an alternative based on a quasi- time-homogenous discrete term-structure model (LMM like model).
- Portfolio Simulations
- Derivative Valuation
- Bermudan Swaption Risk Management
- Interest Rate Modelling – a review
- -HJM, Short Rate Models / Affine Term-Structure Models, Discrete Tenor Models
- Time-Homogenous Interest Rate Tenor Modelling
- A quasi Time-Homogenous Discrete Term Structure Model
- Open Source Reference Implementation
- Numerical Results
Head of Model Development, DZ Bank
Christian Fries: Head of Model Development, DZ Bank
Christian Fries is head of model development at DZ Bank’s risk control and Professor for Applied Mathematical Finance at Department of Mathematics, LMU Munich.
His current research interests are hybrid interest rate models, Monte Carlo methods, and valuation under funding and counterparty risk. His papers and lecture notes may be downloaded from http://www.christian-fries.de/finmath
He is the author of “Mathematical Finance: Theory, Modeling, Implementation”, Wiley, 2007 and runs www.finmath.net.
Peter Kohl-Landgraf, XVA Management, DZ BANK