Nicolas Privault

Introduction to Stochastic Finance with Market Examples (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book presents an introduction to pricing and hedging in discrete and continuous time financial models, emphasizing both analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of stochastic calculus for finance.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 662
• Erscheinungstermin: 13. Dezember 2022
• Englisch
• ISBN-13: 9781000779004
• Artikelnr.: 66483447

Autorenporträt

Nicolas Privault received a PhD degree from the University of Paris VI, France. He was with the University of Evry, France, the University of La Rochelle, France, and the University of Poitiers, France. He is currently a Professor with the School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. His research interests are in the areas of stochastic analysis and its applications.

Inhaltsangabe

Introduction. 1. Assets, Portfolios, and Arbitrage. 1.1. Portfolio
Allocation and Short Selling. 1.2. Arbitrage. 1.3. Risk-Neutral Probability
Measures. 1.4. Hedging of Contingent Claims. 1.5. Market Completeness. 1.6.
Example: Binary Market. Exercises. 2. Discrete-Time Market Model. 2.1.
Discrete-Time Compounding. 2.2. Arbitrage and Self-Financing Portfolios.
2.3. Contingent Claims. 2.4. Martingales and Conditional Expectations. 2.5.
Market Completeness and Risk-Neutral Measures. 2.6. The Cox-Ross-Rubinstein
(CRR) Market Model. Exercises. 3. Pricing and Hedging in Discrete Time.
3.1. Pricing Contingent Claims. 3.2. Pricing Vanilla Options in the CRR
Model. 3.3. Hedging Contingent Claims. 3.4. Hedging Vanilla Options. 3.5.
Hedging Exotic Options. 3.6. Convergence of the CRR Model. Exercises. 4.
Brownian Motion and Stochastic Calculus. 4.1. Brownian Motion. 4.2. Three
Constructions of Brownian Motion. 4.3. Wiener Stochastic Integral. 4.4. Itô
Stochastic Integral. 4.5. Stochastic Calculus. Exercises. 5.
Continuous-Time Market Model. 5.1. Asset Price Modeling. 5.2. Arbitrage and
Risk-Neutral Measures. 5.3. Self-Financing Portfolio Strategies. 5.4.
Two-Asset Portfolio Model. 5.5. Geometric Brownian Motion. Exercises. 6.
Black-Scholes Pricing and Hedging. 6.1. The Black-Scholes PDE. 6.2.
European Call Options. 6.3. European Put Options. 6.4. Market Terms and
Data. 6.5. The Heat Equation. 6.6. Solution of the Black-Scholes PDE.
Exercises. 7. Martingale Approach to Pricing and Hedging. 7.1. Martingale
Property of the Itô Integral. 7.2. Risk-neutral Probability Measures. 7.3.
Change of Measure and the Girsanov Theorem. 7.4. Pricing by the Martingale
Method. 7.5. Hedging by the Martingale Method. Exercises. 8. Stochastic
Volatility. 8.1. Stochastic Volatility Models. 8.2. Realized Variance
Swaps. 8.3. Realized Variance Options. 8.4. European Options - PDE Method.
8.5. Perturbation Analysis. Exercises. 9. Volatility Estimation. 9.1.
Historical Volatility. 9.2. Implied Volatility. 9.3. Local Volatility. 9.4.
The VIX® Index. Exercises. 10. Maximum of Brownian motion. 10.1. Running
Maximum of Brownian Motion. 10.2. The Reflection Principle. 10.3. Density
of the Maximum of Brownian Motion. 10.4. Average of Geometric Brownian
Extrema. Exercises. 11. Barrier Options. 11.1. Options on Extrema. 11.2.
Knock-Out Barrier. 11.3. Knock-In Barrier. 11.4. PDE Method. 11.5. Hedging
Barrier Options. Exercises. 12. Lookback Options. 12.1. The Lookback Put
Option. 12.2. PDE Method. 12.3. The Lookback Call Option. 12.4. Delta
Hedging for Lookback Options. Exercises. 13. Asian Options. 13.1. Bounds on
Asian Option Prices. 13.2. Hartman-Watson Distribution. 13.3. Laplace
Transform Method. 13.4. Moment Matching Approximations. 13.5. PDE Method.
Exercises. 14. Optimal Stopping Theorem. 14.1. Filtrations and Information
Flow. 14.2. Submartingales and Supermartingales. 14.3. Optimal Stopping
Theorem. 14.4. Drifted Brownian Motion. Exercises. 15. American Options.
15.1. Perpetual American Put Options. 15.2. PDE Method for Perpetual Put
Options. 15.3. Perpetual American Call Options. 15.4. Finite Expiration
American Options. 15.5. PDE Method with Finite Expiration. Exercises. 16.
Change of Numéraire and Forward Measures. 16.1. Notion of Numéraire. 16.2.
Change of Numéraire. 16.3. Foreign Exchange. 16.4. Pricing Exchange
Options. 16.5. Hedging by Change of Numéraire. Exercises. 17. Short Rates
and Bond Pricing. 17.1. Vasicek model. 17.2. Affine Short Rate Models.
17.3. Zero-Coupon and Coupon Bonds. 17.4. Bond Pricing PDE. Exercises. 18.
Forward Rates. 18.1. Construction of Forward Rates. 18.2. LIBOR/SOFR Swap
Rates. 18.3. The HJM Model. 18.4. Yield Curve Modeling. 18.5. Two-Factor
Model. 18.6. The BGM Model. Exercises. 19. Pricing of Interest Rate
Derivatives. 19.1. Forward Measures and Tenor Structure. 19.2. Bond
Options. 19.3. Caplet Pricing. 19.4. Forward Swap Measures. 19.5. Swaption
Pricing. Exercises. 20. Stochastic Calculus for Jump Processes. 20.1. The
Poisson Process. 20.2. Compound Poisson Process. 20.3. Stochastic Integrals
and Itô Formula with Jumps. 20.4. Stochastic Differential Equations with
Jumps. 20.5. Girsanov Theorem for Jump Processes. Exercises. 21. Pricing
and Hedging in Jump Models. 21.1. Fitting the Distribution of Market
Returns. 21.2. Risk-Neutral Probability Measures. 21.3. Pricing in Jump
Models. 21.4. Exponential Lévy Models. 21.5. Black-Scholes PDE with Jumps.
21.6. Mean-Variance Hedging with Jumps. Exercises. 22. Basic Numerical
Methods. 22.1. Discretized Heat Equation. 22.2. Discretized Black-Scholes
PDE. 22.3. Euler Discretization. 22.4. Milshtein Discretization. Exercises.
Bibliography. Index