Pricing Derivatives

A fresh, fundamentals-based approach for accurate derivative pricing

Pricing Derivatives presents a specialized approach to accurately pricing derivatives by stressing the conceptual foundations underlying the mathematics. Noted mathematics professor and investing consultant Ambar Sengupta provides a sound understanding of the essential topics of derivative pricing and outlines methodologies for arriving at exact pricing formulas based on the fundamental relationship between price and probability.

Short, to-the-point chapters present original ideas and approaches for pricing derivative products, supplying professional money managers and institutional investors with the foundation they need to:

• Integrate both the theoretical and mathematical foundations of pricing derivatives
• Establish optimal prices in terms of the no-arbitrage principle
• Derive model-independent pricing formulas for options, futures, forwards, and other key derivatives

Experience has shown that derivative traders must focus on conceptual, as opposed to trading, issues if they are to improve trading accuracy and profitability. Pricing Derivatives presents conceptually sound approaches for pricing derivatives and shows how to use them to compute specific pricing formulas.

Pricing Derivatives unveils a fundamentally clear-cut approach to accurate derivative pricing. Based upon author Ambar Sengupta's years of consulting experience working with derivatives traders to hone their trading performance, it steers around the mechanics of popular financial models to focus on the conceptual foundations and underlying mathematics of pricing derivatives as well as other financial instruments.

Exploring the relationship between price and probability, Pricing Derivatives demonstrates methods for determining model-independent pricing formulas and applying them to specific market models for more distinct and applicable pricing formulas. Proceeding from general information to specific knowledge, this detailed book covers:

• Part I -- Fundamentals--Price and probability, the market equilibrium measure, price as expectation, changing numeraires, no-arbitrage, the min-max argument, conditional price as conditional expectation, the generalized martingale principle
• Part II -- Prices of Basic Instruments -- Measures for understanding and pricing complex instruments, including assets with default risk, futures prices in the discrete and continuous case, option price inequalities, natural time lag and the convexity adjustment, volatility, hedging, and "The Greeks"
• Part III -- Model Prices -- Study of the general framework of stochastic finance models, including derivation of the Option Price formula, Black-Scholes formula, and Green's Functions, Green's Functions for Markov Models and Feynman-Kac, and specific Gaussian and chi-squared models
• Part IV -- Mathematical Tools -- Summary reference for the mathematical concepts, definitions, and results used in Parts I - III, including elements of measure and integration, probability theory, and stochastic processes

More than just a compendium of useful trading techniques, Pricing Derivatives presents and explains the conceptual foundations professionals must use to make the all-important pricing and valuation decisions that drive real-life trading. It explores the types of risk embedded in popular derivative instruments along with pricing techniques that more accurately reflect that risk, and provides a thorough, rigorous practitioner's account of the theory and mathematics that form the basis for modern derivatives pricing.