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Mathematical Modeling and Computation in Finance cover
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BookAuthority Best Numerical Analysis Books of All Time

This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.

When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, "do not fall in love with your favorite model." The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.

The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.

Supplementary Material:
Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact sales@wspc.com.


Figure 2.2: Paths and the corresponding densities. Left: X(t) = log S(t) and Right: S(t) with the following configuration: S₀ = 100, μ = 0.05, σ = 0.4; T = 1.


Figure 3.3: Example of a call option with exercise date T = 1, the option surface Vc(t, S) in the (t, S)-domain is computed. An asset path intersects the surface, so thatat each point (t, S), the corresponding option value Vc(t, S) can be read. The surfaces for the hedge parameters delta and gamma are also presented, with the projected stock price.


Figure 4.1: Surface of vega values for a call with T = 1 in the (t, S) domain. An asset path intersects the surface so that at each (t, S(t)) the vega can be read.


Figure 6.2: Recovery of the lognormal PDF for different numbers of expansion terms.


Table 6.1: Maximum error when recovering fX(y) from φX(u) by Fourier cosine expansion.


Figure 12.6: Left: the (positive) Expected Exposure, EE, and the Expected Negative Exposure, ENE, which is defined as ENE(t) = max(–V (t), 0); Right: The EE and two PFE quantities, with levels, 0.95 and 0.99, respectively.


Figure 14.8: Shifted lognormal distributions used for pricing in a negative interest rate environment.

Sample Chapter(s)
Preface
Using this Book

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Contents:
  • Preface
  • Acknowledgment
  • Using this Book
  • Basics about Stochastic Processes
  • Introduction to Financial Asset Dynamics
  • The Black-Scholes Option Pricing Equation
  • Local Volatility Models
  • Jump Processes
  • The COS Method for European Option Valuation
  • Multidimensionality, Change of Measure, Affine Processes
  • Stochastic Volatility Models
  • Monte Carlo Simulation
  • Forward Start Options; Stochastic Local Volatility Model
  • Short-Rate Models
  • Interest Rate Derivatives and Valuation Adjustments
  • Hybrid Asset Models, Credit Valuation Adjustment
  • Advanced Interest Rate Models and Generalizations
  • Cross-Currency Models
  • References
  • Index

Readership: MSc and PhD students of quantitative finance, academic researchers, and quants in the financial industry.