Model Risk In Financial Markets: From Financial Engineering To Risk Management

From Financial Engineering to Risk Management

Radu Tunaru

• Publisher: WSPC
• Year: 2015
• ISBN:
  9789814663427
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The financial systems in most developed countries today build up a large amount of model risk on a daily basis. However, this is not particularly visible as the financial risk management agenda is still dominated by the subprime-liquidity crisis, the sovereign crises, and other major political events. Losses caused by model risk are hard to identify and even when they are internally identified, as such, they are most likely to be classified as normal losses due to market evolution.

Model Risk in Financial Markets: From Financial Engineering to Risk Management seeks to change the current perspective on model innovation, implementation and validation. This book presents a wide perspective on model risk related to financial markets, running the gamut from financial engineering to risk management, from financial mathematics to financial statistics. It combines theory and practice, both the classical and modern concepts being introduced for financial modelling. Quantitative finance is a relatively new area of research and much has been written on various directions of research and industry applications. In this book the reader gradually learns to develop a critical view on the fundamental theories and new models being proposed.

Contents:

• Introduction
• Fundamental Relationships
• Model Risk in Interest Rate Modelling
• Arbitrage Theory
• Derivatives Pricing Under Uncertainty
• Portfolio Selection Under Uncertainty
• Probability Pitfalls of Financial Calculus
• Model Risk in Risk Measures Calculations
• Parameter Estimation Risk
• Computational Problems
• Portfolio Selection Using Sharpe Ratio
• Bayesian Calibration for Low Frequency Data
• MCMC Estimation of Credit Risk Measures
• Last But Not Least. Can We Avoid the Next Big Systemic Financial Crisis?
• Notations for the Study of MLE for CIR Process

Readership: Graduate students, researchers, practitioners, senior managers in financial institutions and hedge-funds, regulators and risk managers, who are keen to understand the pitfalls of financial modelling, and also those who are looking for a career in model validation, product control and risk management functions.
Key Features:

• Some innovative results are presented for the first time
• Covers a wide range of models, results and applications in financial markets to demonstrate that model risk is generally spread

Chapter 1

Introduction

Why do I consider this book to be relevant to the community of people involved in one way or another with financial modelling? Because the next big crisis already has the seeds planted and its roots are growing stronger and bigger by the day. There are already manifestations of model risk that led to substantial losses and it may sound cliché to say that this is only the tip of the iceberg. In 1987 Merrill Lynch reported losses of 300 million USD on stripped mortgage-backed securities because of an incorrect pricing model and five years later in 1992 J.P. Morgan lost about 200 million USD in the mortgage-backed securities market because of inadequate modelling of prepayments. Bank of Tokyo/Mitsubishi announced in March 1997 that its New York-subsidiary dealing with derivatives had incurred an $83 million loss because of their internal pricing model overvalued a portfolio of swaps and options on USD interest rates. [Dowd (2002)] pointed out that the loss was caused by wrongly using a one-factor Black-Derman-Toy (BDT) model to trade swaptions. The model was calibrated to market prices of ATM swaptions but used to trade out-of-the-money (OTM) Bermudan swaptions, which was not appropriate. With the benefit of hindsight it is known now that pricing OTM swaptions and Bermudan swaptions requires multi-factor models. Also in 1997, NatWest Capital Markets reported a £50 million loss because of a mispriced portfolio of German and U.K. interest rate derivatives on the book of a single derivatives trader in London who fed his own estimates of volatility into a model pricing OTC interest rate options with long maturities. The estimates were high and led to fictitious profits. It is not clear whether the trader simply inflated the volatility estimate or she/he came up with the estimate that was more “convenient” to her/him. [Elliott (1997)] pointed out that these losses were directly linked to model risk. [Williams (1999)] remarked that model risk was not included in standard risk management software and in 1999 about 5 billion USD losses were caused by model risk.

The recent advances of algorithmic trading add another dimension to model risk. It is difficult to say what exactly is happening and who is to blame in this new type of superfast trading, most of it being opaque and difficult to control. A Deutsche Bank subsidiary in Japan used some “smart” models to trade electronically that went wild in June 2010, going into an infinite loop and taking out a $183 billion stock position. The thing about computers is that any mistakes are executed now thousand of times faster than before. There is no doubt in my mind that the next big financial crisis will be generated by model risk.

The website gloriamundi.com accumulated by the summer of 2014 about 7500 papers dedicated to financial risk management, covering hundreds of different models and methods to calculate Value at Risk (VaR), for example. This flurry of papers was very much the result of an effervescence in the 1990s. Nevertheless, this mountain of research could not stop the Enron disaster and the dotcom bubble of 2002. The next chapter in financial evolution was in the 2000s with an explosion of research focused on credit risk, once the credit markets took off on the back of the credit default swap (CDS) concept. As of July 2014, more that 1600 credit risk papers were available to download from www.defaultrisk.com, over 250 of which were papers on credit risk models. Add to that the thousands of papers on derivatives pricing and hedging across various asset classes and you get the picture, very much of a jungle.

This book does not aim to describe prescriptive science for finance problems. The main purpose is to illustrate pitfalls that may be obscured in the specialised literature but not known to a wider audience. Hence, the focus in this book is on Model Risk in Finance, covering theoretical as well as practical issues related to options pricing and financial engineering, risk management and model calibration, computational and heuristical methods applied to finance. Models in general are described through mathematical concepts such as equations, probability distributions, stochastic processes and so on. The model is a simplified version of the complex realities observed in financial markets. Essential to the modelling process is the determination of parameters fixing the coordinates of the evolution of asset prices, hedging ratios, risk measures, performance measures and so on. The uncertainty inherently present in parameter estimation is one major source of what we call model risk. Should the volatility parameter σ be 35% or 25%? Maybe both values are feasible but one is more likely than the other. Model risk is more than parameter estimation uncertainty but at the same time the parameter estimation is a procedure that is done daily by thousands of financial houses and banks around the world so the exposure to this type of risk is arguably the highest among the many facets of model risk.

Parameter estimation may cause direct losses to a financial investor or institution as hinted at by some examples above but model risk is much more than the uncertainty in parameter estimates. It also includes model identification and model selection as well as incompatibilities with known theoretical results or empirical evidence. Model risk has been identified previously in all asset classes, see [Gibson (2000)] and [Morini (2011)] for interest rate products, [Satchell and Christodoulakis (2008)] and [Rösch and Scheule (2010)] for portfolio applications, [Satchell and Christodoulakis (2008)], [Rösch and Scheule (2010)] and [Morini (2011)] for credit products, and [Campolongo et al. (2013)] for asset backed securities. It has also been recognized in relation to measuring market risk, see [Figlewski (2004)], [Escanciano and Olmo (2010)], [Boucher et al. (2014)].

The concepts of risk and uncertainty have been intertwined. Since the backbone of this book is one of quantitative finance I consider risk as being associated with a given, fully specified set of possible outcomes, the question being with what probability a possible outcome may occur. Uncertainty on the other hand is a recognition of the existence of outcomes unspecified that may still occur and with which we do not have any way of associating a probability. Playing cards or roulette falls in the first category, saying whether there is life on a far away planet is an example of the latter and predicting the next type of fish you will encounter when going deep in the ocean is an example where both risk and uncertainty are combined. Likewise, we can make statements about the possible future value of the share price of Apple but we cannot say very much on the source of the next big crash in financial markets. In other words, the share price of Apple is risky while the source of the next big financial collapse is uncertain. The important distinction between risk and uncertainty goes back to [Knight (1921)] who pointed out that risk stems from situations where we do not know the outcome of a scenario, but can accurately measure the probability of occurrence. In contrast, uncertainty is associated with scenarios where it is not possible to know all the information required to determine the scenario probabilities a priori.

With the nascency of modern finance in the 1960s and 1970s, model risk and uncertainty in general have preoccupied researchers in relation to various problems studied. Thus, early mentions of model risk and uncertainty in finance include [Merton (1969)], [Jorion (1996)], [Derman (1996)], [Crouhy et al. (1998)], [Green and Figlewski (1999)]. Further notable contributions can be found in [Cairns (2000)], [Hull and Suo (2002)], [Brooks and Persand (2002)], [Talay and Zheng (2002)], [Charemza (2002)], [Alexander (2003)], [Cont (2006)], [Kerkhof et al. (2010)], [Boucher et al. (2014)].

There are many previous definitions of model risk. Here are some from various authors, just to show the wide perspective on model risk in the previous literature. [Gibson et al. (1999)] state

“Model risk results from the inappropriate specification of a theoretical model or the use of an appropriate model but in an inadequate framework or for the wrong purpose.”

while for [McNeil et al. (2005)] model risk can be defined as

“the risk that a financial institution incurs losses because its risk-management models are misspecified or because some of the assumptions underlying these models are not met in practice.”

For [Barrieu and Scandolo (2013)]

“The hazard of working with a potentially not well-suited model is referred to as model risk”

and [Boucher et al. (2014)] define model risk as

“the uncertainty in risk forecasting arising from estimation error and the use of an incorrect model”.

Model risk has also been identified to some extent by the Basel Committee on Banking Supervision in the Basel II framework, see [Basel (2006)] and [Basel (2011)]. Financial institutions ought to gauge their model risk. Furthermore, model validation is one component of the Pillar 1 Minimum Capital Requirements and Pillar 2 Supervisory Review Process. Unfortunately, in the Basel III framework (see [Basel (2010)]) it is stated that there are “a number of qualitative criteria that banks would have to meet before they are permitted to use a models-based approach”. Hence, the “Model validation and backtesting” guidelines, which focus mainly on counterparty credit risk management, allow qualitative or subjective decisions. For example, insurance or reinsurance companies can compute their solvency capital requirement using an internal risk model if it is approved by the supervisory authorities. This can be interpreted in many ways and it allows room for discretion, which may compound model risk rather than control it.

In this book I distinguish between model risk and operational risk, even if the latter has multiple facets and it may be bundled together with model risk by some financial operators. One important aspect of operational risk, that should not be considered part of model risk, is data input error. The Vancouver stock exchange started a new index initialized at the level of 1000.000 in 1982. However, less than two years later it was observed that the index was constantly decreasing to about 520 despite the exchange setting records in value and volume as described in the Wall Street Journal in 1983. Upon further investigations it was revealed that the index, which was updated after every transaction, was recalculated by removing the decimals after the third decimal instead of rounding off. Hence, the correct value of 1098.892 became the published value of 520. Although it was a computational error, this is an example of operational risk after all and not of model risk.

Another facet of operational risk is given by fiscal-legal updating. Sudden changes in law may expose a bank to great losses. In the UK a law on lower dividend tax credit was exploited by UBS in the 1990s. The law was changed in 1997 and caused many banks to suffer immediate losses with UBS incurring huge losses. In general, see [Gibson (2000)], models used by banks simply ignore the impact of sudden fiscal change.

While innovation is in general beneficial, the proliferation of models applied in finance may cause havoc in the immediate future because too little time and effort are dedicated to verifying all these models and the pitfalls associated with them. Ignoring model risk may provide the wrong incentive for new financial products innovation. This book aims to help initiate procedures that will make model validation and product control more stringent and the models that are used in the industry more robust. An applied econometrician was saying once that Finance is all about discounted cash-flows. Maybe that was the case in the 1950s but certainly it is not the case nowadays. As I shall point out later, even discounting simple cash-flows may not be as straightforward as one may think. Moreover, modern finance evolves in a dual world, looking back at historical asset prices and series of events to learn stylized facts and looking forward trying to decide how future prices will take shape.

The graph in Fig. 1.1 illustrates the two adjacent finance worlds associated with an asset whose value is described as a stochastic process S = {S_t}_t≥0 defined over a measurable space (Ω,

). Model risk in a nutshell can be conceptualised as different probability measures

defined over this measurable space and under which suitable financial calculus related to S is done. It is als...

Table of contents

• Cover
• Halftitle
• Title Page
• Copyright Page
• Dedication
• Preface
• List of Notations
• Contents
• List of Figures
• List of Tables
• 1. Introduction
• 2. Fundamental Relationships
• 3. Model Risk in Interest Rate Modelling
• 4. Arbitrage Theory
• 5. Derivatives Pricing Under Uncertainty
• 6. Portfolio Selection under Uncertainty
• 7. Probability Pitfalls of Financial Calculus
• 8. Model Risk in Risk Measures Calculations
• 9. Parameter Estimation Risk
• 10. Computational Problems
• 11. Portfolio Selection Using the Sharpe Ratio
• 12. Bayesian Calibration for Low Frequency Data
• 13. MCMC Estimation of Credit Risk Measures
• 14. Last But Not Least. Can We Avoid the Next Big Systemic Financial Crisis?
• 15. Notations for the Study of MLE for CIR process
• Bibliography
• Index