TY  - BOOK
AU  - Pajarín Domínguez,Jorge
AU  - Labrador Arroyo,Félix
TI  - Las Legumbres Del Rey. Mesa y Alimentación en la Corte (siglos XVI-XIX)
SN  - 9788413773636
AV  - GT2853.S7 L448 2021 
U1  - 394.120946 
PY  - 2021///
CY  - Madrid
PB  - Dykinson, S.L.
KW  - Food habits-Spain-History
KW  - Diet-Spain-History
KW  - Spain-Court and courtiers-Food
KW  - Electronic books
N1  - Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Foreword -- Preface -- SECTION I A primer on option pricing and volatility modelling -- CHAPTER 1 ▪ The option pricing problem -- 1.1 DERIVATIVES -- 1.1.1 Forwards and futures -- 1.1.2 Options -- 1.2 NON-ARBITRAGE PRICES AND THE BLACK-SCHOLES FORMULA -- 1.2.1 The forward contract -- 1.2.2 The price of a European option as a risk-neutral expectation -- 1.2.3 The price of a vanilla option and the Black-Scholes formula -- 1.3 THE BLACK-SCHOLES MODEL -- 1.3.1 From the Black-Scholes formula to the Black-Scholes model -- 1.3.2 Option replication and delta hedging in the Black-Scholes model -- 1.4 THE BLACK-SCHOLES IMPLIED VOLATILITY AND THE NON-CONSTANT VOLATILITY CASE -- 1.4.1 The implied volatility surface -- 1.4.2 The implied and spot volatilities -- 1.5 CHAPTER'S DIGEST -- CHAPTER 2 ▪ The volatility process -- 2.1 THE ESTIMATION OF THE INTEGRATED AND THE SPOT VOLATILITY -- 2.1.1 Methods based on the realised variance -- 2.1.2 Fourier estimation of volatility -- 2.1.3 Properties of the spot volatility -- 2.2 LOCAL VOLATILITIES -- 2.2.1 Mimicking processes -- 2.2.2 Forward equation and Dupire formula -- 2.3 STOCHASTIC VOLATILITIES -- 2.3.1 The Heston model -- 2.3.2 The SABR model -- 2.4 STOCHASTIC-LOCAL VOLATILITIES -- 2.5 MODELS BASED ON THE FRACTIONAL BROWNIAN MOTION AND ROUGH VOLATILITIES -- 2.6 VOLATILITY DERIVATIVES -- 2.6.1 Variance swaps and the VIX -- 2.6.2 Volatility swaps -- 2.6.3 Weighted variance swaps and gamma swaps -- 2.7 CHAPTER'S DIGEST -- SECTION II Mathematical tools -- CHAPTER 3 ▪ A primer on Malliavin Calculus -- 3.1 DEFINITIONS AND BASIC PROPERTIES -- 3.1.1 The Malliavin derivative operator -- 3.1.1.1 Basic properties -- 3.1.2 The divergence operator -- 3.2 COMPUTATION OF MALLIAVIN DERIVATIVES; 3.2.1 The Malliavin derivative of an Itô process -- 3.2.2 The Malliavin derivative of a diffusion process -- 3.2.2.1 The Malliavin derivative of a diffusion process as a solution of a linear SDE -- 3.2.2.2 Representation formulas for the Malliavin derivative of a diffusion process -- 3.3 MALLIAVIN DERIVATIVES FOR GENERAL SV MODELS -- 3.3.1 The SABR volatility -- 3.3.2 The Heston volatility -- 3.3.3 The 3/2 Heston volatility -- 3.4 CHAPTER'S DIGEST -- CHAPTER 4 ▪ Key tools in Malliavin Calculus -- 4.1 THE CLARK-OCONE-HAUSSMAN FORMULA -- 4.1.1 The Clark-Ocone-Haussman formula and the martingale representation theorem -- 4.1.2 Hedging in the Black-Scholes model -- 4.1.3 A martingale representation for spot and integrated volatilities -- 4.1.3.1 The SABR volatility -- 4.1.3.2 The Heston volatility -- 4.1.4 A martingale representation for non-log-normal assets -- 4.2 THE INTEGRATION BY PARTS FORMULA -- 4.2.1 The integration-by-parts formula for the Malliavin derivative and the Skorohod integral operators -- 4.2.2 Delta, Vega, and Gamma in the Black-Scholes model -- 4.2.2.1 The delta -- 4.2.2.2 The vega -- 4.2.2.3 The gamma -- 4.2.3 The Delta of an Asian option in the Black-Scholes model -- 4.2.4 The Stochastic volatility case -- 4.2.4.1 The delta in stochastic volatility models -- 4.2.4.2 The gamma in stochastic volatility models -- 4.3 THE ANTICIPATING ITÔ'S FORMULA -- 4.3.1 The anticipating Itô's formula as an extension of Itô's formula -- 4.3.2 The law of an asset price as a perturbation of a mixed log-normal distribution -- 4.3.3 The moments of log-prices in stochastic volatility models -- 4.3.4 Some applications to volatility derivatives -- 4.3.4.1 Leverage swaps and gamma swaps -- 4.3.4.2 Arithmetic variance swaps -- 4.4 CHAPTER'S DIGEST -- CHAPTER 5 ▪ Fractional Brownian motion and rough volatilities -- 5.1 THE FRACTIONAL BROWNIAN MOTION; 5.1.1 Correlated increments -- 5.1.2 Long and short memory -- 5.1.3 Stationary increments and self-similarity -- 5.1.4 Hölder continuity -- 5.1.5 The p-variation and the semimartingale property -- 5.1.6 Representations of the fBm -- 5.2 THE RIEMANN-LIOUVILLE FRACTIONAL BROWNIAN MOTION -- 5.3 STOCHASTIC INTEGRATION WITH RESPECT TO THE FBM -- 5.4 SIMULATION METHODS FOR THE FBM AND THE RLFBM -- 5.5 THE FRACTIONAL BROWNIAN MOTION IN FINANCE -- 5.6 THE MALLIAVIN DERIVATIVE OF FRACTIONAL VOLATILITIES -- 5.6.1 Fractional Ornstein-Uhlenbeck volatilities -- 5.6.2 The rough Bergomi model -- 5.6.3 A fractional Heston model -- 5.7 CHAPTER'S DIGEST -- SECTION III Applications of Malliavin Calculus to the study of the implied volatility surface -- CHAPTER 6 ▪ The ATM short-time level of the implied volatility -- 6.1 BASIC DEFINITIONS AND NOTATION -- 6.2 THE CLASSICAL HULL AND WHITE FORMULA -- 6.2.1 Two proofs of the Hull and White formula -- 6.2.1.1 Conditional expectations -- 6.2.1.2 The Hull and White formula from classical Itô's formula -- 6.3 AN EXTENSION OF THE HULL AND WHITE FORMULA FROM THE ANTICIPATING ITÔ'S FORMULA -- 6.4 DECOMPOSITION FORMULAS FOR IMPLIED VOLATILITIES -- 6.5 THE ATM SHORT-TIME LEVEL OF THE IMPLIED VOLATILITY -- 6.5.1 The uncorrelated case -- 6.5.2 The correlated case -- 6.5.3 Approximation formulas for the ATMI -- 6.5.4 Examples -- 6.5.4.1 Diffusion models -- 6.5.4.2 Local volatility models -- 6.5.4.3 Fractional volatilities -- 6.5.5 Numerical experiments -- 6.6 CHAPTER'S DIGEST -- CHAPTER 7 ▪ The ATM short-time skew -- 7.1 THE TERM STRUCTURE OF THE EMPIRICAL IMPLIED VOLATILITY SURFACE -- 7.2 THE MAIN PROBLEM AND NOTATIONS -- 7.3 THE UNCORRELATED CASE -- 7.4 THE CORRELATED CASE -- 7.5 THE SHORT-TIME LIMIT OF IMPLIED VOLATILITY SKEW -- 7.6 APPLICATIONS -- 7.6.1 Diffusion stochastic volatilities: finite limit of the ATM skew slope; 7.6.1.1 Models based on the Ornstein-Uhlenbeck process -- 7.6.1.2 The SABR model -- 7.6.1.3 The Heston model -- 7.6.1.4 The two-factor Bergomi model -- 7.6.2 Local volatility models: the one-half rule and dynamic inconsistency -- 7.6.3 Stochastic-local volatility models -- 7.6.4 Fractional stochastic volatility models -- 7.6.4.1 Fractional Ornstein-Uhlenbeck volatilities -- 7.6.4.2 The rough Bergomi model -- 7.6.4.3 The approximation of fractional volatilities by Markov processes -- 7.6.5 Time-varying coefficients -- 7.7 IS THE VOLATILITY LONG-MEMORY, SHORT-MEMORY, OR BOTH? -- 7.8 A COMPARISON WITH JUMP-DIFFUSION MODELS: THE BATES MODEL -- 7.9 CHAPTER'S DIGEST -- CHAPTER 8 ▪ The ATM short-time curvature -- 8.1 SOME EMPIRICAL FACTS -- 8.2 THE UNCORRELATED CASE -- 8.2.1 A representation for the ATM curvature -- 8.2.2 Limit results -- 8.2.3 Examples -- 8.2.3.1 Diffusion stochastic volatilities -- 8.2.3.2 Fractional volatility models -- 8.3 THE CORRELATED CASE -- 8.3.1 A representation for the ATM curvature -- 8.3.2 Limit results -- 8.3.3 The convexity of the short-time implied volatility -- 8.4 EXAMPLES -- 8.4.1 Local volatility models -- 8.4.2 Diffusion volatility models -- 8.4.3 Fractional volatilities -- 8.4.3.1 Models based on fractional Ornstein-Uhlenbeck processes -- 8.5 CHAPTER'S DIGEST -- SECTION IV The implied volatility of non-vanilla options -- CHAPTER 9 ▪ Options with random strikes and the forward smile -- 9.1 A DECOMPOSITION FORMULA FOR RANDOM STRIKE OPTIONS -- 9.2 FORWARD-START OPTIONS AS RANDOM STRIKE OPTIONS -- 9.3 FORWARD-START OPTIONS AND THE DECOMPOSITION FORMULA -- 9.4 THE ATM SHORT-TIME LIMIT OF THE IMPLIED VOLATILITY -- 9.5 AT-THE-MONEY SKEW -- 9.5.1 Local volatility models -- 9.5.2 Stochastic volatility models -- 9.5.3 Fractional volatility models -- 9.5.4 Time-depending coefficients -- 9.6 AT-THE-MONEY CURVATURE; 9.6.1 The uncorrelated case -- 9.6.2 The correlated case -- 9.7 CHAPTER'S DIGEST -- CHAPTER 10 ▪ Options on the VIX -- 10.1 THE ATM SHORT-TIME LEVEL AND SKEW OF THE IMPLIED VOLATILITY -- 10.1.1 The ATMI short-time limit -- 10.1.2 The short-time skew of the ATMI volatility -- 10.2 VIX OPTIONS -- 10.2.1 The short-end level of the ATMI of VIX options -- 10.2.2 The ATM skew of VIX options -- 10.3 CHAPTER'S DIGEST -- Bibliography -- Index
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