Quantitative Financial Analysis Study Guide of Final
Quantitative Financial Analysis Study Guide of Final BU.230.710.52.SP16
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Date Created: 05/03/16
FINAL 1. CHAPTER 12 Credit Risk and the Valuation of Corporate Securities Credit risk results in losses incurred by lenders following a counterparty’s default. It is a component of risk from debt and represents one of the major risks that must face most financial institutions. There are also many other sources of risk related to the activities and operations of a firm or a bank. Add to this the advent of Basle II which is scheduled to be effective in 2007, and the quantification and management of credit risk becomes of paramount importance. Credit derivatives’ markets have constantly grown at rapid paces in the past few years. In- vestors increasingly resort to these financial products, more complex and but also more flexible, for the risk management of their activities. Indeed, any investor who wants to eliminate or re- duce a risk that he doesn’t want to assume or is unable to control can use derivative products in order to transfer this risk to other counterparties which are able to manage or willing to absorb it. There are two modern fundamental approaches for the measurement and management of credit risk: the structural approach and the reduced-form approach. Merton’s (1973, 1974) structural model will allow us to value risky debts issued by a risky firm. This approach lays down the foundation of corporate securities valuation and in particular of the capital structure in corporate finance studied by Modigliani and Miller (1958). We must also note that this approach is the basis of many recent commercial models built for the quantification and management of credit risk, such as the popular Moody’s KMV credit risk management model. In this chapter, we begin by presenting Merton’s model for risky debt valuation and the intuitive properties of the term structure of credit risk. Then we explain how a risky debt can be associated with a risk-free debt (issued by a risk-free institution such as a government) minus a put option. This put option constitutes the total loss or the risk premium. This analysis of credit risk using a put option will be used in the following chapter to illustrate the simulation techniques’ application from previous chapters to evaluate the total losses and the financial guarantee in the context of a portfolio exposed to default risk from many counterparties. We end the chapter with an introduction to the reduced-form approach for the valuation of a risky debt. This approach is simple to implement since it only needs an estimation of default rates which are being calibrated from market data. However, its weakness emerges from the difficulty of studying the interaction properties between counterparties involved in the debt contracts. 2. CHAPTER 14 Risk Management and Value at Risk (VaR) Risk management is very important for both individuals and corporate entities (e.g., institu- tional investors, pension funds, insurance companies, asset managers and, particularly, banks). Under its widest scope, risk management includes market risk, liquidity risk, credit risk, in- surance risk, operational risk, legal risk, and so on. Nowadays, we observe that financial and non financial institutions own complex portfolios composed of many financial contracts (for example, futures, options, swaps and other complex derivatives) and non financial products (for example, insurance contracts, contractual clauses, and structured finance). Moreover, the different financial disasters (Barings, Bear Stearns, Enron, Long Term Capital Management, Orange County, WorldCom, etc.) that occurred during recent decades have brought to the fore the crucial necessity and importance for all parties to implement efficient methods for measuring and controlling risk in order to sustain the firm’s competitive advantage, and to assure the survival of institutions and the stability of the financial systems. All stakeholders have an interest in monitoring risks in the economy since the financial health of the economy depends on it. Given that managers like simple concepts and measures that provide a global idea of all the risks their institutions face, the “snapshot” Value at Risk (VaR) fits the bill. Indeed, in order to quantify and manage risks, many institutions use the Value at Risk. The Value at Risk is defined as an aggregate risk measure which gives the expected extreme loss of owning a portfolio or an asset for a given period of time given a specific confidence level. The VaR gives a unique value reflecting the risk level of a portfolio when considering the financial leverage, the diversification and the multidimensional nature and interdependence of risks. Computation approaches for the VaR can be classified into two groups: parametric ap- proaches and non parametric approaches. However, the VaR presents many limitations which can be circumvented by conditional VaR models. In this chapter, we limit ourselves to a pre- sentation of the basic elements related to the computation of the market risk VaR (MarketVaR and no other risk such as credit risk VaR or CreditVaR and operational risk VaR or OpVaR) using Monte Carlo simulations. The remainder of this chapter is structured as follows. We begin by describing each type of risk. Then we give a formal definition of the VaR computation. After this, we discuss the Basle regulatory environment and the concepts of stress testing and back testing. Then we describe the different VaR computation approaches. Finally, since our objective is to provide ingredients for the VaR computation using Monte Carlo simulations, we give two examples of such calculations. In Chapter 8, we characterized the dynamics of asset prices. In Chapter 4, we showed how to generate correlated random variables. We apply those concepts studied in Chapters 4 and 8 in the context of VaR computations. The next chapter gives examples where we apply the Quasi Monte Carlo simulation tech- niques and the Principal Components Analysis technique to evaluate a bond portfolio’s VaR.
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