Book

Notes on Quantitative Financial Analysis aggregates a set of notions which introduce the fundamentals of quantitative financial analysis in a clear and concise way, providing a very practical approach, as demonstrated by the discussion of numerous case studies. All material can be freely used, quoting the source. Slides can be downloaded and the codes, if not protected by copyright, are available upon request. A specific background is not strictly required for the reader, although basic notions of economics and statistics would be recommended. The book is divided into eight sections and each of them has a chapter structure. Below is a brief summary of the covered topics:

Part I: Fixed Income Instruments

The first chapter is a summary of the main concepts of financial mathematics underlying quantitative analysis, up to the modeling of the interest rates term structure.

The second chapter shows the different types of bonds present in the financial markets, together with the assessment of the risks that an analyst must manage.

The third part explores the heart of quantitative analysis, introducing the best practices for estimating the fair value of a bond, together with its risk measures (duration, modified duration and convexity).

Part II: Futures and Forwards

After the description of the basic concepts for understanding this category of derivatives, the second chapter introduces the specific quantitative analysis of these instruments, with a particular focus on pricing and hedging.

Part III: Options

Given the inherent variety of topics connected to options, this section has been thoroughly covered. In addition to the description of the standard pay-off, the first chapter deals with the foundations of this derivative and introduces the mathematical properties, including the put-call parity.

The second chapter concerns the pricing of plain-vanilla options. The well-known Black-Scholes-Merton pricing framework has been introduced, showing how it can be applied to options written on different underlyings (equity, index, rates, futures and currencies). In addition to the fair value, the sensitivities (Greeks) are also estimated.

The third chapter deals with option strategies: combinations of plain-vanilla options with underlying and with other options, in order to create specific hedging and trading strategies. Among the strategies, covered call, protective put, bull/bear spread, butterfly spread, straddle, strip, strap and strangle are covered.

The fourth chapter reviews the main non-standard (i.e. exotic) options, characterized by special pay-offs. The lognormal pricing framework is extended to these types of options; among them: forward start, cliquet, digital, chooser, compound and path-dependent (barrier, Asian and lookback) options.

Not all options can be adequately priced using a closed formula. For those characterized by particularly non-linear pay-offs or by early exercise features, a numerical methodology has to be implemented.

Chapter 5 is therefore dedicated to binomial stochastic trees, particularly useful for dealing with derivatives characterized by the possibility of being exercised in advance, while chapter 6 is dedicated to the Monte Carlo technique, which is considered suitable for representing any type of pay-off, thanks to its flexibility. The working principle, the internal consistency, the pricing estimation, and the computation of the most important risk measures are illustrated for both algorithms. Once the reader has become confident on the correct approach for the quantitative analysis of the derivative, it is time to focus on the inputs of the model.

Finally, Chapter 7 centers on determining the inputs for the previously exposed techniques. A particular focus has been given to the estimation of volatility (both historical and implied) and to the correlation.

Part IV: Swaps

Similarly to the previous scheme, the section dedicated to swaps is divided into two parts: the first chapter describes the fundamentals of the different types of swaps, while the second deals with the quantitative analysis of the instrument. Particular attention is paid to Interest Rate Swaps (IRS) and Currency Swaps. Two distinct valuation approaches are provided, i.e. considering the derivative as a portfolio of forward contracts, or as two positions (one long and one short) in two bonds. The second chapter concludes with the derivation of long-term spot rates from Interest Rate Swaps, a process known as swap curve stripping.

Part V: Credit Derivatives

This section consists of only one chapter in which Credit Default Swaps (CDS) are presented. It describes how premiums can be used to compute risk-adjusted discount factors in a fixed income instrument pricing context. The chapter ends with an introduction of the most popular models among analysts for the pricing of these derivatives.

Part VI: Inflation

This section covers the main inflation-linked derivatives: Zero-Coupon Inflation-Indexed Swap (ZCIIS) and Year-on-Year Inflation-Indexed Swap (YYIIS). The standard market approach is presented to simulate the prospective values ​​of the CPI preparatory to the pricing of these instruments with particular focus on the modeling of seasonality. The chapter concludes with the case study of "BTP Italia", an exotic security linked to Italian inflation characterized by a non-standard pay-off.

Part VII: Aggregate Risk Measures

The risk measures discussed so far have addressed the single instrument and can hardly be extended to a portfolio, characterized by instruments of a different financial nature. Considering this need, the most common approaches to estimating Value-at-Risk have been introduced: parametric, full-evaluation, Monte Carlo backward and forward looking. The Expected Shortfall and the importance of conducting stress tests and back tests are briefly presented as well.

Part VIII: Credit Risk

The first chapter analyzes the determinants of the Demand and Supply of credit and provides a summary for the core elements that constitute a mortgage/loan: interest rate, repayment plans, mode of extinction, amount and Loan-to-Value, guarantees, duration and the Global effective annual rate.

The second chapter focuses on the definition and on the mathematical models for estimating counterparty risk, which can be interpreted by its nature as a hybrid between financial risk and credit risk.

In particular, it has been shown that the probability of default can be inferred from Credit Default Swap (CDS) premiums, listed bond spreads or stock prices using the KMV (Kealhofer, Merton and Vasicek) model.

The last part of the chapter highlights the structural limits of counterparty risk, validating the need to provide a more complete definition of credit risk. Credit risk is based on three pillars: the probability of default (PD), the Loss Given Default (LGD) and the Exposure at Default (EAD). An effectual discussion is dedicated to each of these three important components.

The third chapter presents the statistical approaches that allow the estimation of PD starting from historical data (not necessarily market data), among which, the Altman's Z-Score, the Logit-Probit and the CreditGrades models are covered.

The fourth chapter introduces the regression models suitable for estimating and forecasting the Loss Given Default.

The fifth chapter deals with the estimation and the predictive models for EAD. In this context, a Monte Carlo model is introduced for the determination of the Credit Valuation Adjustment (CVA) with particular attention to the modeling of the Expected Exposure to the various future time buckets. Once the reader has acquired the required knowledge for a correct credit measurement, we move on to the concept of rating systems.

The sixth chapter introduces Rating Agencies and provides the basic notions for creating transition matrices. The Cohort approach and the Hazard approach are adequately discussed with the relative methods of calculating confidence intervals.

The seventh chapter deals with credit risk managed not on a single position, but at portfolio level. In this phase asset correlation has to be presented and, to this end, the Moment matching and the Maximum Likelihood approaches are explained. An example of estimating a Monte Carlo VaR and a C-VaR is also provided in the credit context.

The part dealing with credit concludes with the main methods for validating credit models. Among those, the Cumulative Accuracy Profile (CAP), the Receiver Operating Characteristics (ROC), the binomial test and the Brier Score are covered.

At the end of each chapter, further food for thought is provided through a bibliography of reference papers or books, which allow useful insights into each topic covered.

Acknowledgements

I would like to express my heartfelt thanks to the AIFIRM Editorial Board for the opportunity to work on this project.

My gratitude also goes to my colleagues and friends in BPER Banca (Financial Administration) and in UNIGE (Department of Economics) for providing many interesting insights.

My heartfelt thanks and affection goes to my parents: I could not aspire to have better guides on the complex journey of life.

Last but certainly not least, I dedicate this book to the memory of my beloved grandparents: Piero, Celeste, Mario and Giuseppina.

Editions

First Edition: ISBN: 979-12-80245-19-9, DOI: 10.47473/2016eda0001, Printed on 15th March 2023