A Workout in Computational Finance

2 Binomial Trees

Binomial trees are widely used in option pricing, but are, as will be discussed later, not our preferred method.¹ In this chapter, we will present the basic binomial tree algorithm and some of its refinements. As we want to apply binomial trees to the valuation of options, we will discuss options beforehand.

2.1 EQUITIES AND BASIC OPTIONS

An equity (stock, share) is a specified portion of ownership of a company, giving the holder of the share several rights, e.g., to participate in the annual general meeting and in the elections there and to obtain a dividend as a part of the profit of the company. Throughout this book, we assume that the stock is exchange-traded, so that the actual trading price of the share can be obtained (maybe with some time delay) by consulting the exchange’s homepage or a Reuters or Bloomberg screen. With the exception of an initial public offering or an increase in capital, a change in the share price does not change the firm’s capital or liquidity, but is – at least in an ideal world – the investors’ consensus on the value of the share. If the universe of investors thinks that the iPhone will be a cash cow, then the stock price of Apple will increase.

As experience during the last years showed, equity prices cannot only rise, but also can drop significantly. In order to limit the impact of downward moves of an investment at a certain point in time, a European call option may be an appropriate instrument:

European call and put options: ...