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About this book

This book helps students, researchers and quantitative finance practitioners to understand both basic and advanced topics in the valuation and modeling of financial and commodity derivatives, their institutional framework and risk management. It provides an overview of the new regulatory requirements such as Basel III, the Fundamental Review of the Trading Book (FRTB), Interest Rate Risk of the Banking Book (IRRBB), or the Internal Capital Assessment Process (ICAAP). The reader will also find a detailed treatment of counterparty credit risk, stochastic volatility estimation methods such as MCMC and Particle Filters, and the concepts of model-free volatility, VIX index definition and the related volatility trading. The book can also be used as a teaching material for university derivatives and financial engineering courses.

Table of Contents

Frontmatter

1. Introduction

Abstract
Derivatives are financial instruments that are built on (derived from) more basic underlying assets. They are designed to transfer risk easily between different counterparties. Instruments such as forwards, futures, swaps, or options are nowadays normally used by banks, asset managers, or corporate treasurers for hedging or speculation. Trading with derivatives has become increasingly important in the last 30 years throughout the world. It has been made easier due to electronic communication and settlement systems, and has grown exponentially in recent years. On the other hand, derivatives are closely related to many bank failures and even many financial crises, including the global financial crisis of 2007–2008. This chapter will introduce the basic derivative product types and provide a detailed overview of the derivative markets’ institutional framework and their recent developments.
Jiří Witzany

2. Forwards and Futures

Abstract
Forwards are, in general, OTC contracts to buy or sell a specified asset at a specified price, at a future time, and settled later than for normal spot operations. Futures are similar contracts traded on organized exchanges. The arbitrage idea applied in the previous chapter to FX forwards can be generalized to obtain a precise relationship between the spot and the forward (Futures) prices of a general investment asset that must hold on an arbitrage-free and perfectly liquid market. This relationship turns out to be weaker for consumption storable assets, and in particular for non-storable assets such as electricity or some agricultural commodities. In this chapter, we will also discuss how to use forwards and futures to hedge risk in various positions and portfolios.
Jiří Witzany

3. Interest Rate Derivatives

Abstract
Interest rate derivatives belong to the most actively traded derivative instruments both on the OTC and on the organized exchange markets. In this chapter, we are going to explain how to build zero coupon curves given various interest rate quotations and how to use the curves to value the basic interest rate derivative contracts. We focus on the trading mechanics, hedging, and valuation of the plain vanilla derivatives such as forward rate agreements (FRA), short-term, and (STIR) long-term interest rate (LTIR) futures, interest rate swaps (IRS), and cross-currency swaps (CCS).
Jiří Witzany

4. Option Markets, Valuation, and Hedging

Abstract
Options can be compared to forward contracts where one of the counterparties pays a premium for the option to settle or not to settle. Options have become popular both on the OTC and on the organized exchange markets, but their valuation is more complex than in the case of forwards. It requires the underlying asset price volatility as a new input into the valuation models that have, at the same time, become a new market variable. We will explain how value options in the relatively elementary framework of binomial trees and in the theoretically more advanced context of stochastic asset price modeling. The last section will look at the issue of option portfolio hedging using the concept of so-called Greek letters.
Jiří Witzany

5. Market Risk Measurement and Management

Abstract
Qualified market risk management of asset and liability portfolios or trading activities is of key importance for banks and financial institutions. It is not only about quantitative measurement of the risks, but also about organizational and regulatory principles. Besides relatively simple market risk measures, we will define and explain various approaches to Value at Risk (VaR) and Conditional VaR estimation and backtesting. The two risk measures are used for day-to-day management as well as key regulatory capital concepts, or as tools of strategic risk management based on economic capital allocation. Market risk management, in particular in case of OTC derivatives, is also closely related to the counterparty credit risk management and measurement in terms of CVA (Credit Valuation Adjustment) that will be in detail discussed in the last section of this chapter.
Jiří Witzany

6. Stochastic Interest Rates and the Standard Market Model

Abstract
In Chap. 4, we have presented the Black-Scholes option valuation model that has become a market standard. However, the model has several limiting assumptions including the one saying that the instantaneous interest rates are constant. But the interest rates are not constant at all in real financial markets. First, there is a term structure of interest rates, 1-year interest rates are usually greater than over-night interest rates, and 5-year interest rates are usually greater than 1-year interest rates. Evaluating a 1-year European stock option, which interest rate should be used? Recall that a European derivative value was obtained as the present value of the expected payoff. Hence, in the Black-Scholes formula, one could propose to use the 1-year interest rate instead of the presumably constant short rate. It turns out that this simple modification, leading to the so-called Standard Market Model, is correct, but in order to prove it we need to generalize significantly the risk-neutral valuation framework.
Jiří Witzany

7. Interest Rate Models

Abstract
The Standard Market Model developed and applied in the previous chapter assumes that interest rates or bond prices are lognormally distributed. The model does not describe the stochastic dynamics of interest rates over time, and so it cannot be applied to value American-style options, callable bonds, or other more complex interest rate derivatives. In this chapter, we are going to introduce the most important interest rate models, which can be classified into two categories: short-rate and term-structure models. The short-rate models focus on the instantaneous interest rate stochastic dynamics. The rest of the term-structure is derived from the short rate at a point in time, and from the model parameters. Term-structure models, on the other hand, specify equations for (forward) interest rates in all maturities, and these equations are tied by certain consistency (non-arbitrage) conditions. In both cases, the models are developed and applied under a risk-neutral measure, but can be calibrated from the real-world data.
Jiří Witzany

8. Exotic Options, Volatility Smile, and Alternative Stochastic Models

Abstract
This chapter starts with an overview of the zoology of exotic options, i.e., with options that are more complex than plain vanilla ones. Some exotic options can be valued by a modification of the Black-Scholes formula, while for some there are more complicated formulas, developed in the context of the geometric Brownian motion, and the others can be valued only numerically using Monte Carlo simulations, binomial tree techniques, or partial differential equations. For most of the exotic derivatives, it turns out that the geometric Brownian motion model calibrated to value correctly the plain vanilla options might give quite imprecise results. The empirical phenomenon called the volatility smile (or surface) demonstrates that the market does not, in fact, believe in lognormal returns and the volatility constant over time. This fact has led to the development of various alternative stochastic models that try to capture better the behavior of market prices, especially the jumps and stochastic volatilities of the underlying asset returns. We will discuss some of the best-known models in the last section.
Jiří Witzany

Backmatter

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