Financial derivatives ([Pricing, Applications, and Mathematics])

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Features: This book provides a concise discussion of the fundamental principles of pricing financial derivatives. Chapter 1 introduces the reader to basic stochastic calculus and discusses theorems related to concepts such as uncertainty and time, random walks, and geometric Brownian motion. Chapter 2 covers general pricing methods for assets and derivatives, clarifies the concepts of stochastic discount factors and price kernels, and then applies this concept to price traditional derivatives and exotic derivatives. Chapter 3 applies pricing theory to special cases in the interest rate market, such as bonds and swaps, and discusses factor models and term structure consistent models. Chapter 4 covers various mathematical topics related to derivative pricing and portfolio decision-making, such as mean-reverting processes and jump processes, and discusses stochastic calculus tools like Kolmogorov equations, martingale techniques, stochastic control, and partial differential equations.