Observational Equivalence of Discrete String Models and Market Models

In this paper we show that, contrary to the claim made in Longsta, Santa-Clara, and Schwartz (2001a) and Longsta, Santa-Clara, and Schwartz (2001b), discrete string models are not more parsimonious than market models.In fact, they are found to be observationally equivalent.We derive that, for the estimation of both a K-factor discrete string model and a K-factor Libor market model for N forward rates the number of parameters that needs to be estimated equals NK .K (K .1) /2 and not K (K +1)/2 and NK, respectively.string model;market model

Model risk analysis for risk management and option pricing

Due to the growing complexity of products in financial markets, market participants rely more and more on quantitative models for trading and risk management decisions. This introduces a fairly new type of risk, namely, model risk. In the first part of this thesis we investigate the quantitative influence of model risk on risk management with a main focus on regulation issues. We present frameworks for measuring model risk and backtesting procedures for evaluating model quality. Furthermore, we apply these frameworks to derivatives portfolios. The second part of the thesis concerns interest rate derivatives pricing models. We compare Libor market and discrete string models and find them observationally equivalent. Furthermore, we investigate the factor dependence and estimation risk for a range of exotic derivatives priced with these models.

Model Risk Analysis for Risk Management and Option Pricing.

Due to the growing complexity of products in financial markets, market participants rely more and more on quantitative models for trading and risk management decisions. This introduces a fairly new type of risk, namely, model risk. In the first part of this thesis we investigate the quantitative influence of model risk on risk management with a main focus on regulation issues. We present frameworks for measuring model risk and backtesting procedures for evaluating model quality. Furthermore, we apply these frameworks to derivatives portfolios. The second part of the thesis concerns interest rate derivatives pricing models. We compare Libor market and discrete string models and find them observationally equivalent. Furthermore, we investigate the factor dependence and estimation risk for a range of exotic derivatives priced with these models.

Model Risk and Regulatory Capital

capital requirements;(coherent) risk management;option pricing models;derivative pricing models

Testing Expected Shortfall Models for Derivative Positions

In this paper we test several risk management models for computing expected shortfall for one-period hedge errors of hedged derivatives positions.Contrary to value-at-risk, expected shortfall cannot be tested using the standard binomial test, since we need information of the distribution in the tail.As derivatives positions change characteristics and thereby the size of risk exposures over time one cannot apply the standard tests based on stationarity.To overcome this problem, we present a transformation procedure.For comparison purposes the tests are also performed for value-at-risk.testing;models;distribution;risk management;derivatives

Backtesting for Risk-Based Regulatory Capital

In this paper we present a framework for backtesting all currently popular risk measurement methods (including value-at-risk and expected shortfall) using the functional delta method.Estimation risk can be taken explicitly into account.Based on a simulation study we provide evidence that tests for expected shortfall with acceptable low levels have a better performance than tests for value-at-risk in realistic financial sample sizes.We propose a way to determine multiplication factors, and find that the resulting regulatory capital scheme using expected shortfall compares favorably to the current Basle Accord backtesting scheme

Observational Equivalence of Discrete String Models and Market Models

In this paper we show that, contrary to the claim made in Longsta, Santa-Clara, and Schwartz (2001a) and Longsta, Santa-Clara, and Schwartz (2001b), discrete string models are not more parsimonious than market models.In fact, they are found to be observationally equivalent.We derive that, for the estimation of both a K-factor discrete string model and a K-factor Libor market model for N forward rates the number of parameters that needs to be estimated equals NK .K (K .1) /2 and not K (K +1)/2 and NK, respectively

Observational Equivalence of Discrete String Models and Market Models

In this paper we show that, contrary to the claim made in Longsta, Santa-Clara, and Schwartz (2001a) and Longsta, Santa-Clara, and Schwartz (2001b), discrete string models are not more parsimonious than market models.In fact, they are found to be observationally equivalent.We derive that, for the estimation of both a K-factor discrete string model and a K-factor Libor market model for N forward rates the number of parameters that needs to be estimated equals NK .K (K .1) /2 and not K (K +1)/2 and NK, respectively.

Backtesting for Risk-Based Regulatory Capital

In this paper we present a framework for backtesting all currently popular risk measurement methods (including value-at-risk and expected shortfall) using the functional delta method.Estimation risk can be taken explicitly into account.Based on a simulation study we provide evidence that tests for expected shortfall with acceptable low levels have a better performance than tests for value-at-risk in realistic financial sample sizes.We propose a way to determine multiplication factors, and find that the resulting regulatory capital scheme using expected shortfall compares favorably to the current Basle Accord backtesting scheme.