Course: Financial Derivatives

Course Objective

This course focuses on the operational mechanisms of the derivative markets which constitute today an active sector of the international financial markets. Its main goal is to present the use of derivatives products, such as Futures Contracts and Options, as well as their pricing techniques in alternative mathematical models. In addition, arbitrage strategies, hedging strategies and various measures of investment risk, related with the necessity of the financial derivatives, will be presented.

Suggested Textbooks

• John C. Hall, Options, Futures, And Other Derivatives, 10^th Edition, Pearson, 2018.

Course Description

The following sections will be presented:

• Futures and Forward Contracts: Terminology – Payoffs – Standardization – Operation of Margins – Interest Rates – Pricing – Arbitrage – Convenience Yield – Hedging – Basis Risk – Minimum Variance Hedge Ratio.
• Swaps: Interest Rate Swaps – Terminology – Profit/Losses – Typical Uses – Financial Intermediary – Comparative Advantage Argument – Pricing – Swap Rate – Currency Swaps – Credit Risk.
• Options Markets: Call and Put Option – Basic Positions – Payoffs and P/L Diagrams – Specification – Trading – Commissions – Margins – Warrants – Executive Stock Options – Convertible Bonds.
• Properties of Stock Options: Basic Assumptions – Factors Affecting Option Prices – Arbitrage Bounds – Put-Call Parity – Early Exercise of American Options – The Effect of Dividends.
• Trading Strategies Involving Options: Strategies Involving an Option and a Stock – Interpretation of Put-Call Parity – Bull Spread – Bear Spread – Butterfly Spread – Straddle – Strangle.
• Binomial Model: One-Step Binomial Trees – Two-Step Binomial Trees – Pricing by Risk Free Portfolios – Risk Neutral Valuation – Pricing European Options – Pricing American Options – Delta Hedging.
• Stochastic Processes and Itô’s Lemma: Types of Stochastic Processes – Markov Property – Weak-Form Market Efficiency – Continuous Time Stochastic Processes – Wiener Processes – Generalized Wiener Processes – Itô Processes – The Process for Stock Prices and Interpretation of Parameters – Itô’s Lemma and Applications.
• Black & Scholes Model: Lognormal Property of Stock Prices – Distribution of Rate of Return – Historical Volatility – Black, Scholes & Merton PDE – Risk Neutral Valuation – Black & Scholes Pricing Formulas – Implied Volatility – The Effect of Dividends.
• The Greek Letters: Covered and Naked Positions – A Stop-Loss Strategy – Delta – Delta Hedging – Theta – Gamma – Relationship Among Delta, Theta and Gamma – Vega – Delta, Gamma and Vega Neutral Portfolios –
• Value at Risk: VaR Measure – C-VaR Measure – Historical Simulation – Model Building Model – The Linear Model – Testing Methods.

Lecture notes will be distributed during the course by the instructor.