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Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential Lévy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options.
This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field.
Sample Chapter(s)
Chapter 1: Introduction (198 KB)
Contents:
- Introduction
- Stochastic Calculus
- Arbitrage and Completeness
- Asset Price Models
- Static Hedging
- Mean-Variance Hedging
- Entropic Valuation and Hedging
- Hedging Constraints
- Optimal Martingale Measures
Readership: Graduate students in financial mathematics or applied probability and researchers in financial mathematics or stochastic processes.
