# Efficient Estimators for Derivative Price Sensitivities

Project Description

**Efficient Estimators for Derivative Price Sensitivities and their Application to the Quantification of Model Risk**

### Peter Kloeden, Carlos Sanz Chacón

Price sensitivities are of extraordinary importance for the risk management of derivatives since hedging strategies can be developed with their help. Especially, the model risk of valuation models can be quantified by the validation of hedging strategies for exotic derivatives. The model risk arises from possible errors in the modeling of the considered assets, for example unsuited models for the distribution of asset returns or wrong assumptions on the temporal development of market prices. In theory and practice, a large demand exists for efficient estimation methods for price sensitivities of derivatives with discontinuous payoff whose valuation is not possible analytically.

This project is concerned with two aspects:

- the development of efficient estimation methods of price sensitivities of derivatives with discontinuous payoff and
- the quantification of model risks for in literature and practice established valuation models of complex derivatives.

These two aspects emphasize the interdisciplinary approach of the project, i.e. the combination of numerical mathematics with the finance aspects of financial engineering, asset pricing and risk management. As a result of this project, general sensitivity estimates for unstructured intererest rate derivatives will be derived whose efficiency will be backed up by simulation studies. Furthermore, first studies on model risks of selected structured interest rate derivatives will be carried out.

The working group of Prof. Dr. Kloeden has experience in the derivation of efficient estimation methods for stochastic price sensitivities, optimization theory, the numerical analysis of stochastic differential equations (which are the modeling tool) and the modeling of derivatives. Dr. Sanz Chacón completed his dissertation in the area of the first above aspect.

*References*

- Peter E. Kloeden and Carlos Sanz Chacón.

Efficient Price Sensitivity Estimation of Path-Dependent Derivatives by Weak Derivatives,*SIAM Journal on Financial Mathematics*, 2009, submitted.