ADVANCES IN MATHEMATICAL FINANCE

By V. NARAT

CONTENTS PART I VARIANCE-GAMMA AND RELATED STOCHASTIC PROCESSES THE EARLY YEARS OF THE VARIANCE-GAMMA PROCESS VARIANCE-GAMMA AND MONTE CARLO SOME REMARKABLE PROPERTIES OF GAMMA PROCESSES A NOTE ABOUT SELBERG’S INTEGRALS IN RELATION WITH THE BETA-GAMMA ALGEBRA ITˆO FORMULAS FOR FRACTIONAL BROWNIAN MOTION PART II ASSET AND OPTION PRICING A TUTORIAL ON ZERO VOLATILITY AND OPTION ADJUSTED SPREADS XXVIII CONTENTS ASSET PRICE BUBBLES IN COMPLETE MARKETS TAXATION AND TRANSACTION COSTS IN A GENERAL EQUILIBRIUM ASSET ECONOMY CALIBRATION OF L´EVY TERM STRUCTURE MODELS PRICING OF SWAPTIONS IN A?NE TERM STRUCTURES WITH STOCHASTIC VOLATILITY FORWARD EVOLUTION EQUATIONS FOR KNOCK-OUT OPTIONS MEAN REVERSION VERSUS RANDOM WALK IN OIL AND NATURAL GAS PRICES PART III CREDIT RISK AND INVESTMENTS BEYOND HAZARD RATES: A NEW FRAMEWORK FOR CREDIT-RISK MODELLING A GENERIC ONE-FACTOR L´EVY MODEL FOR PRICING SYNTHETIC CDOS UTILITY VALUATION OF CREDIT DERIVATIVES: SINGLE AND TWO-NAME CASES INVESTMENT AND VALUATION UNDER BACKWARD AND FORWARD DYNAMIC EXPONENTIAL UTILITIES IN A STOCHASTIC FACTOR MODEL