Computation and simulation for finance. An introduction with Python (Q6553925)

This textbook offers an up-to-date introductory treatment of numerical techniques applied to problems in computational finance, placing particular emphasis on issues such as numerical stability, convergence, and error analysis in both deterministic and stochastic settings. It is aimed at advanced undergraduate or postgraduate students pursuing studies in mathematical finance with an emphasis on simulation and computational techniques. Python has been fixed as the language of instruction, reflecting its growing use among quantitative analysts. Only core Python libraries have been used where possible.\N\NPart I (Modelling Assets and Markets) is an introduction to the mathematics of finance and the pricing and hedging of derivative securities in the Black-Scholes framework, the Itô Calculus, the Box-Muller Transformation, Box-Muller in Practice: Reshaping and Resizing NumPy Arrays, Properties of the Distribution of the Asset Model, Sampling from the Asset Model at Expiry, Simulating an Ensemble of Trajectories, as well as a tutorial introducing the reader to Python as a programming language. Particular attention is paid to important topics: Risk-Neutral Pricing of Financial Derivatives, The Black-Scholes-Merton PDE, Estimation of the Black-Scholes Implied Volatility, Local and Stochastic Volatility Models.\N\NPart II (Computational Pricing Methods in the Black-Scholes Framework) covers the three main computational methods for pricing options and their associated hedge parameters: binomial trees, Monte Carlo methods, and finite difference methods, and demonstrates their application to the valuation of European, American, and exotic options written on a single underlying asset. Topics: Python Implementation for a European Option, Python Implementation Using Conditional Indexing, Barrier Options -- Python Implementation, A Python Example of the Control Variate Technique for Asian Options, Estimating the Greeks: Bump-and-Revalue, Construction of an Explicit Discretisation Scheme -- Python Implementation of the FTCS Scheme and Numerical Instability, Python Valuation of Options Using an Implicit Scheme, Valuing an American Put Using the Method of Projected Successive Over-Relaxation (PSOR) -- Python Implementation are precisely presented.\N\NPart III (Simulation Methods Beyond the Black-Scholes Framework) treats a set of more advanced topics and techniques, introducing Python methods for data analysis (providing a point of entry for students interested in machine learning), and modelling with stochastic differential equations. The financial context includes the modelling of several correlated assets, stochastic models of interest rates, and asset models with local or stochastic volatility.\N\NEach chapter of the book ends with appropriate self-study tasks. The monograph is exclusively professionally written.\N\NIt is a pleasure for me to have this magnificent book in my library!