Chapter 10: Pricing and Valuation of Options

In this section

• Determinants of Option Value
  Explore the core factors that shape an option’s worth, including intrinsic value, time value, volatility, interest rates, and dividends, with practical examples and diagrams.
• Put–Call Parity and Put–Call Forward Parity
  Explore the theory, formulas, and applications of Put–Call Parity and Put–Call Forward Parity, foundational no-arbitrage relationships in option pricing.
• Binomial Option Pricing Model (One-Period)
  Learn how to value options using the one-period binomial model by computing up and down outcomes, determining risk-neutral probabilities, and discounting the expected payoff. Explore hedged portfolios, real-world scenarios, and exam-focused insights.
• Risk-Neutral Valuation
  An in-depth exploration of the arbitrage-free, risk-neutral framework for option pricing, its foundational principles, and practical applications in binomial and continuous models.
• Black–Scholes–Merton Model Assumptions
  Explore the critical theoretical underpinnings of the Black–Scholes–Merton model, its key assumptions, and how real-world markets often deviate from this foundational framework for pricing options.
• Dividends in Option Pricing
  Explore how dividends affect option valuation, covering discrete and continuous dividend models, early exercise considerations for American calls, and practical forecasting challenges.
• Introduction to the Black–Scholes–Merton Model
  Learn the fundamentals of the Black–Scholes–Merton Model, its origins, formulas, and practical applications in options pricing and risk management.
• Option Sensitivities (Greeks)
  Explore how Greeks quantify an option’s sensitivity to price changes, volatility, time decay, and interest rates—all core tools for advanced derivatives risk management.
• Volatility Smiles and the Implied Volatility Surface
  Explore how implied volatility varies across strikes and maturities, leading to volatility skews, smiles, and surfaces in practical options pricing. Understand how these patterns arise, why standard assumptions fall short, and how practitioners account for them in real-world markets.
• Variance and Volatility Swaps
  A deep dive into the mechanics, valuation, and practical uses of variance and volatility swaps, highlighting advanced strategies and portfolio applications for CFA candidates.
• Monte Carlo Methods for Complex Option Pricing
  Discover how Monte Carlo simulations can be used to model, price, and manage complex path-dependent options, supported by variance reduction methods, real-world examples, and practical exam tips.
• Multi-Period Binomial Trees for American Options
  A comprehensive guide on using multi-period binomial trees to value American-style options, focusing on early exercise decisions and practical applications.
• Finite Difference Methods in Option Pricing
  Learn how finite difference methods tackle the Black–Scholes PDE by discretizing time and price into a grid. Explore explicit, implicit, and Crank–Nicolson schemes, boundary conditions, implementation tips, advantages, and pitfalls.
• Early Exercise Considerations in American-Style Options
  Insights into the mechanics, valuation, and practical implications of early exercise for American-style calls and puts, focusing on dividend-paying assets, deep-in-the-money puts, and the trade-off between intrinsic value and extrinsic value.
• Static Replication Approaches for Barrier Options
  Learn how to replicate barrier option payoffs using vanilla options in a static framework. This section explores the intricacies of constructing knock-in and knock-out payoffs, managing path dependence, and overcoming replication challenges.
• Machine Learning Approaches in Option Pricing
  Dive into how data-driven models, including neural networks and gradient boosting, refine option pricing by uncovering complex market relationships.
• Options on Implied Volatility
  Discover the fundamentals, pricing challenges, and hedging strategies for options on market-implied volatility, with a focus on instruments like VIX options.
• Jump-Diffusion Models in Option Pricing
  Explore how jump-diffusion models extend standard option pricing frameworks to account for sudden price moves and market discontinuities.
• Stochastic Volatility and Heston Model
  In-depth exploration of the Heston Model for Stochastic Volatility and advanced derivative pricing under uncertain volatility dynamics.