Hedging derivatives

• Main Author: Rheinlander, Thorsten.
• Corporate Author: World Scientific (Firm)
• Other Authors: Sexton, Jenny.
• Format: Electronic
• Language: English
• Published: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2011.
• Subjects: Hedging (Finance) > Mathematical models.; Derivative securities > Valuation > Mathematical models.; Electronic books.
• Online Access: View fulltext via EzAccess

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....

Table of Contents:

• 1. Introduction. 1.1. Hedging in complete markets. 1.2. Hedging in incomplete markets. 1.3. Notes and further reading
• 2. Stochastic calculus. 2.1. Filtrations and martingales. 2.2. Semi-martingales and stochastic integrals. 2.3. Kunita-Watanabe decomposition. 2.4 Change of measure. 2.5. Stochastic exponentials. 2.6. Notes and further reading
• 3. Arbitrage and completeness. 3.1. Strategies and arbitrage. 3.2. Complete markets. 3.3. Hidden arbitrage and local times. 3.4. Immediate arbitrage. 3.5. Super-hedging and the optional decomposition theorem. 3.6. Arbitrage via a non-equivalent measure change. 3.7. Notes and further reading
• 4. Asset price models. 4.1. Exponential Levy processes. 4.2. Stochastic volatility models. 4.3. Notes and further reading
• 5. Static hedging. 5.1. Static hedging of European claims. 5.2. Duality principle in option pricing. 5.3. Symmetry and self-dual processes. 5.4. Notes and further reading
• 6. Mean-variance hedging. 6.1. Concept of mean-variance hedging. 6.2. Valuation and hedging by the Laplace method. 6.3. Valuation and hedging via integro-differential equations. 6.4. Mean-variance hedging of defaultable assets. 6.5. Quadratic risk-minimisation for payment streams. 6.6. Notes and further reading
• 7. Entropic valuation and hedging. 7.1. Exponential utility indiffence pricing. 7.2. The minimal entropy martingale measure. 7.3. Duality results. 7.4. Properties of the utility indifference price. 7.5. Entropic hedging. 7.6. Notes and further reading
• 8. Hedging constraints. 8.1. Framework and preliminaries. 8.2. Dynamic utility indifference pricing. 8.3. Martingale optimality principle. 8.4. Utility indifference hedging and pricing using BSDEs. 8.5. Examples in Brownian markets. 8.6. Connection to the minimal entropy measure in the unconstrained case. 8.7. Notes and further reading. 9. Optimal martingale measures. 9.1. Esscher measure. 9.2. Minimal entropy martingale measure. 9.3. Variance-optimal martingale measure. 9.4. q-optimal martingale measure. 9.5. Minimal martingale measure. 9.6. Notes and further reading.