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Mathematics of Financial Markets -- Contents -- Foreword -- Main Notations -- Introduction -- Part I The Deterministic Environment -- 1 Prior to the yield curve: spot and forward rates -- 1.1 INTEREST RATES, PRESENT AND FUTURE VALUES, INTEREST COMPOUNDING -- 1.1.1 Counting the number of days -- 1.2 DISCOUNT FACTORS -- 1.3 CONTINUOUS COMPOUNDING AND CONTINUOUS RATES -- 1.4 FORWARD RATES -- 1.4.1 Generalization: forwards and discount factors -- 1.5 THE NO ARBITRAGE CONDITION -- FURTHER READING -- 2 The term structure or yield curve -- 2.1 INTRODUCTION TO THE YIELD CURVE -- 2.2 THE YIELD CURVE COMPONENTS -- 2.2.1 The money market side -- 2.2.2 Capital market side: the case of the risk-free yield curve -- 2.2.3 Capital market side: the case of the swap yield curve -- 2.3 BUILDING A YIELD CURVE: METHODOLOGY -- 2.4 AN EXAMPLE OF YIELD CURVE POINTS DETERMINATION -- 2.5 INTERPOLATIONS ON A YIELD CURVE -- FURTHER READING -- 3 Spot instruments -- 3.1 SHORT-TERM RATES -- 3.2 BONDS -- 3.2.1 Bond pricing -- 3.2.2 Duration -- 3.2.3 Convexity -- 3.3 CURRENCIES -- 3.3.1 Introduction to the currencies spot market -- 3.3.2 Spot quotations -- FURTHER READING -- 4 Equities and stock indexes -- 4.1 STOCKS VALUATION -- 4.1.1 Discounted cash flows (DCF) method -- 4.1.2 The Gordon-Shapiro method -- 4.1.3 The case of stocks not distributing dividends -- 4.1.4 The real option method -- 4.1.5 The book value method -- 4.2 STOCK INDEXES -- 4.3 THE PORTFOLIO THEORY -- 4.3.1 Introduction to the Portfolio Theory -- 4.3.2 Risk and return measures -- 4.3.3 The Markowitz model -- 4.3.4 Sharpe's CAPM -- 4.3.5 The APT model (Roll and Ross) -- 4.3.6 CAPM versus APT -- 4.3.7 The four-moments CAPM -- FURTHER READING -- 5 Forward instruments -- 5.1 THE FORWARD FOREIGN EXCHANGE -- 5.1.1 Forward exchange operations -- 5.1.2 Forex (or FX) swaps.

5.1.3 Forward forex swaps or forward-forward transactions -- 5.1.4 The NDF market -- 5.2 FRAs -- 5.2.1 Principle and calculation -- 5.2.2 Example of application -- 5.3 OTHER FORWARD CONTRACTS -- 5.3.1 Forward contracts on equities -- 5.3.2 Forward contracts on bonds -- 5.4 CONTRACTS FOR DIFFERENCE (CFD) -- FURTHER READING -- 6 Swaps -- 6.1 DEFINITIONS AND FIRST EXAMPLES -- 6.1.1 A first example of an IRS, on a debt (data from February 2002) -- 6.1.2 An example of CRS liability swap (data from February 2002) -- 6.1.3 Unwinding a swap -- 6.2 PRIOR TO AN IRS SWAP PRICING METHOD -- 6.3 PRICING OF AN IRS SWAP -- 6.4 (RE)VALUATION OF AN IRS SWAP -- 6.5 THE SWAP (RATES) MARKET -- 6.6 PRICING OF A CRS SWAP -- 6.7 PRICING OF SECOND-GENERATION SWAPS -- 6.7.1 Zero-coupon swap -- 6.7.2 EONIA and other basis swap -- 6.7.3 In-arrear swap -- 6.7.4 Constant maturity swap -- 6.7.5 Quanto or diff swap -- 6.7.6 Swapping other types of cash flows: performance swaps -- FURTHER READING -- 7 Futures -- 7.1 INTRODUCTION TO FUTURES -- 7.1.1 Margining system -- 7.1.2 Settlement of the future contract at maturity -- 7.2 FUTURES PRICING -- 7.2.1 Theoretical price of a future -- 7.2.2 Theoretical versus market future price -- 7.2.3 The implied repo rate (IRR) -- 7.2.4 Future versus forward prices -- 7.3 FUTURES ON EQUITIES AND STOCK INDEXES -- 7.3.1 Contract size versus contract value -- 7.3.2 Theoretical versus market price -- 7.3.3 Hedging calculation with index futures -- 7.4 FUTURES ON SHORT-TERM INTEREST RATES -- 7.4.1 Introduction -- 7.4.2 Theoretical future price -- 7.4.3 Hedging calculation with money market rate futures -- 7.5 FUTURES ON BONDS -- 7.5.1 Introduction -- 7.5.2 The conversion factor -- 7.5.3 The cheapest to deliver -- 7.5.4 Theoretical future price -- 7.5.5 Hedging calculation with bond futures -- 7.6 FUTURES ON CURRENCIES.

7.7 FUTURES ON (NON-FINANCIAL) COMMODITIES -- 7.7.1 Introduction -- 7.7.2 Contango versus backwardation -- 7.7.3 Market price of a commodity future -- 7.7.4 Trading calculations with commodities futures -- FURTHER READING -- Part II The Probabilistic Environment -- 8 The basis of stochastic calculus -- 8.1 STOCHASTIC PROCESSES -- 8.2 THE STANDARD WIENER PROCESS, OR BROWNIAN MOTION -- 8.3 THE GENERAL WIENER PROCESS -- 8.4 THE ITÔ PROCESS -- 8.5 APPLICATION OF THE GENERAL WIENER PROCESS -- 8.6 THE ITÔ LEMMA -- 8.7 APPLICATION OF THE ITÔ LEMMA -- 8.8 NOTION OF RISK NEUTRAL PROBABILITY -- 8.9 NOTION OF MARTINGALE -- ANNEX 8.1: PROOFS OF THE PROPERTIES OF dZ(t) -- ANNEX 8.2: PROOF OF THE ITÔ LEMMA -- FURTHER READING -- 9 Other financial models: from ARMA to the GARCH family -- 9.1 THE AUTOREGRESSIVE (AR) PROCESS -- 9.2 THE MOVING AVERAGE (MA) PROCESS -- 9.3 THE AUTOREGRESSION MOVING AVERAGE (ARMA) PROCESS -- 9.4 THE AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) PROCESS -- 9.5 THE ARCH PROCESS -- 9.6 THE GARCH PROCESS -- 9.7 VARIANTS OF (G)ARCH PROCESSES -- 9.8 THE MIDAS PROCESS -- FURTHER READING -- 10 Option pricing in general -- 10.1 INTRODUCTION TO OPTION PRICING -- 10.2 THE BLACK-SCHOLES FORMULA -- 10.2.1 Introduction -- 10.2.2 Variants of the Black-Scholes formula -- 10.2.3 Call-put parity -- 10.2.4 The key role of the forward price - meaning of N(d1) and N(d2) -- 10.2.5 Beyond the Black-Scholes formula -- 10.3 FINITE DIFFERENCE METHODS: THE COX-ROSS-RUBINSTEIN (CRR) OPTION PRICING MODEL -- 10.4 MONTE CARLO SIMULATIONS -- 10.5 OPTION PRICING SENSITIVITIES -- 10.5.1 Most usual sensitivities -- 10.5.2 Numerical example -- 10.5.3 Other sensitivities -- 10.5.4 Sensitivities and other option pricing methods -- FURTHER READING -- 11 Options on specific underlyings and exotic options -- 11.1 CURRENCY OPTIONS -- 11.2 OPTIONS ON BONDS.

11.2.1 Callable bonds -- 11.2.2 Putable bonds -- 11.2.3 Convertible bonds -- 11.3 OPTIONS ON INTEREST RATES -- 11.3.1 Single rate processes -- 11.3.2 Modeling the yield curve -- 11.3.3 Modeling the yield curve through forward rates -- 11.3.4 Caps, floors, collars -- 11.3.5 Options on swaps, or swaptions -- 11.4 EXCHANGE OPTIONS -- 11.5 BASKET OPTIONS -- 11.6 BERMUDAN OPTIONS -- 11.7 OPTIONS ON NON-FINANCIAL UNDERLYINGS -- 11.8 SECOND-GENERATION OPTIONS, OR EXOTICS -- FURTHER READING -- 12 Volatility and volatility derivatives -- 12.1 PRACTICAL ISSUES ABOUT THE VOLATILITY -- 12.1.1 Annualized volatility -- 12.1.2 Volatility curve -- 12.1.3 The volatility smile -- 12.1.4 Implied volatility surface -- 12.1.5 Intraday volatility -- 12.2 MODELING THE VOLATILITY -- 12.3 REALIZED VOLATILITY MODELS -- 12.4 MODELING THE CORRELATION -- 12.5 VOLATILITY AND VARIANCE SWAPS -- FURTHER READING -- 13 Credit derivatives -- 13.1 INTRODUCTION TO CREDIT DERIVATIVES -- 13.1.1 How to quantify a credit risk? -- 13.1.2 The two components of a default risk -- 13.1.3 Behind the underlying credit risk -- 13.1.4 Main features of a credit derivative -- 13.1.5 Example of a credit derivative -- 13.2 VALUATION OF CREDIT DERIVATIVES2 -- 13.2.1 Useful measures and relationships -- 13.2.2 Valuation of credit derivatives -- 13.3 CONCLUSION -- FURTHER READING -- 14 Market performance and risk measures -- 14.1 RETURN AND RISK MEASURES -- 14.1.1 Return measures -- 14.1.2 Risk measures -- 14.1.3 Risk versus return ratios, or performance measures -- 14.1.4 Performance contribution and attribution -- 14.1.5 Performance measures in case of non-normal returns -- 14.2 VaR OR VALUE-AT-RISK -- FURTHER READING -- 15 Beyond the Gaussian hypothesis: potential troubles with derivatives valuation -- 15.1 ALTERNATIVES TO THE GAUSSIAN HYPOTHESIS -- 15.1.1 Jump processes -- 15.1.2 Gamma processes.

15.1.3 Other alternative processes -- 15.1.4 Fractional Brownian motion and non-linear models -- 15.1.5 Regime-switching models -- 15.1.6 Neural networks -- 15.2 POTENTIAL TROUBLES WITH DERIVATIVES VALUATION -- 15.2.1 General -- 15.2.2 Continuous time versus discrete time -- 15.2.3 Consequences for option pricing -- 15.2.4 Risk management issues -- FURTHER READING -- Bibliography -- Index.

The book aims to prioritise what needs mastering and presents the content in the most understandable, concise and pedagogical way illustrated by real market examples. Given the variety and the complexity of the materials the book covers, the author sorts through a vast array of topics in a subjective way, relying upon more than twenty years of experience as a market practitioner. The book only requires the reader to be knowledgeable in the basics of algebra and statistics. The Mathematical formulae are only fully proven when the proof brings some useful insight. These formulae are translated from algebra into plain English to aid understanding as the vast majority of practitioners involved in the financial markets are not required to compute or calculate prices or sensitivities themselves as they have access to data providers. Thus, the intention of this book is for the practitioner to gain a deeper understanding of these calculations, both for a safety reason - it is better to understand what is behind the data we manipulate - and secondly being able to appreciate the magnitude of the prices we are confronted with and being able to draft a rough calculation, aside of the market data. The author has avoided excessive formalism where possible. Formalism is securing the outputs of research, but may, in other circumstances, burden the understanding by non-mathematicians; an example of this case is in the chapter dedicated to the basis of stochastic calculus. The book is divided into two parts: First, the deterministic world, starting from the yield curve building and related calculations (spot rates, forward rates, discrete versus continuous compounding, etc.), and continuing with spot instruments valuation (short term rates, bonds, currencies and stocks) and forward instruments valuation (forward forex, FRAs and variants, swaps & futures);

Second, the probabilistic world, starting with the basis of stochastic calculus and the alternative approach of ARMA to GARCH, and continuing with derivative pricing: options, second generation options, volatility, credit derivatives; This second part is completed by a chapter dedicated to market performance & risk measures, and a chapter widening the scope of quantitative models beyond the Gaussian hypothesis and evidencing the potential troubles linked to derivative pricing models.

Library	Material Type	Item Barcode	Shelf Number	Status
IYTE Library	E-Book	1256861-1001	HD2346 .E85 -- R88 2013 EB	Ebrary E-Books