Introduction

Welcome to the module on the Black-Scholes-Merton Model. In this chapter, we will provide an overview of this fundamental model, its significance in the world of finance, and the learning objectives you can expect to achieve by the end of this module.

Overview of the Black-Scholes-Merton Model

The Black-Scholes-Merton Model, often referred to as the Black-Scholes Model, is a mathematical tool used to calculate the theoretical price of European-style options. Developed by economists Fischer Black and Myron Scholes, along with mathematician Robert Merton, this model has revolutionized the field of finance since its introduction in the early 1970s. It serves as a cornerstone in options pricing, helping investors and financial institutions make informed decisions regarding options trading and risk management.

Importance of Option Pricing Models

Options are financial derivatives that provide the holder with the right, but not the obligation, to buy or sell an underlying asset at a predetermined price (the strike price) on or before a specified date (the expiration date). Accurate pricing of these options is essential for investors, as it influences trading strategies, risk assessment, and overall portfolio management. The Black-Scholes-Merton Model provides a standardized and widely accepted framework for valuing options, enabling market participants to determine fair market prices.

Learning Objectives

Now, let’s outline the learning objectives of this module:

1) Lognormal Property of Stock Prices, Distribution of Rates of Return, and the Calculation of Expected Return: Understanding the lognormal distribution of stock prices is crucial for comprehending how options are priced. We will delve into the concept of lognormality, explore the distribution of rates of return, and learn how to calculate expected returns.

2) Realized Return and Historical Volatility of a Stock: Volatility plays a pivotal role in option pricing. You will learn how to compute realized returns and historical volatility, which are fundamental inputs for pricing models.

3) Assumptions Underlying the Black-Scholes-Merton Option Pricing Model: To apply the Black-Scholes-Merton Model effectively, it’s vital to grasp the underlying assumptions. We will discuss these assumptions and their implications for option pricing.

4) Value of a European Option on a Non-Dividend-Paying Stock: One of the primary objectives of this module is to equip you with the skills to calculate option prices using the Black-Scholes-Merton Model. We will start with European options on non-dividend-paying stocks.

5) Implied Volatilities and Computation of Implied Volatilities from Market Prices of Options: Implied volatilities provide insights into market expectations. You will learn how to define implied volatilities and how to calculate them using the model and market option prices.

6) Exercise Early for American Call and Put Options: American options offer unique features. We will explore how dividends impact early exercise decisions for American-style call and put options.

7) Value of a European Option Using the Black-Scholes-Merton Model on a Dividend-Paying Stock, Futures, and Exchange Rates: Building on our knowledge, we will extend option pricing to dividend-paying stocks, futures contracts, and foreign exchange options using the Black-Scholes-Merton Model.

8) Warrants, Value of a Warrant, Dilution Cost of the Warrant: Warrants are hybrid securities with unique characteristics. You will gain insights into warrants, learn to calculate their value, and understand their implications for existing shareholders.