Final month is the most crucial. During this month, managing yourself, your psychology is more important than preparing for the exam. Anxiety is at it\’s peak and most candidates, despite knowing the entire material,...
In this article, we will concentrate on callable bonds and putable bonds, although we’ll mention prepayable and convertible bonds as well.
The common method of valuing a callable or putable bond is to use a binomial interest rate tree. For the examples that follow, we’ll use the binomial tree we created here; it has 10% interest rate volatility:
In this article, we’ll be concerned with the application of binomial trees to the valuation of call and put options (on, for example, stocks or commodities).
Most companies don’t remain the same size (i.e., have the same amount of earnings, net income) forever; with a soupçon of luck, a company’s earnings will grow, year after year. The value of a company’s opportunities to grow in the future is known, with no great originality, as the present value of growth opportunities (PVGO). Given the right information, calculating PVGO is trivial: it’s the difference between the (present) value of the company as is (i.e., including those growth opportunities) and the (present) value of the company assuming zero growth:
Interest rate caps and floors are, essentially, collections of interest rate options: each option has a positive payoff when it expires in the money and a zero payoff when it expires out of the money. The individual options are called, respectively, caplets and floorlets.
Note that caps and floors are commonly based on LIBOR or similar floating interest rates; as such, they are governed by the usual LIBOR characteristics:
They are based on a 360-day year, with 30-day months
The interest rates are quoted as nominal, annual rates…
To create a binomial interest rate tree, you need to start with:
A yield curve
An interest rate volatility
The yield curve can be a par curve, a spot curve, or a forward curve. (If you’re a bit fuzzy on the differences among these curves, look here.) For the remainder of this article, we’ll assume that we’re given a par curve; as we could generate the other curves given any one of them, it doesn’t really matter which one we get.
In his recent article, What Practitioners Need to Know…About Time Diversification , Mr. Kritzman offers a comprehensive view on time diversification. As an example, Mr. Kritzman outlines the following…
Generally speaking, ‘valuation’ can be defined as the process for finding the ‘value’ of anything. In the world of finance, value of anything (tangible or intangible) would be reflected by the price that potential buyers and sellers agree to conduct the transaction for the transfer of ownership, which may obviously change with time. The demand and supply for are the drivers of the process of ‘price discovery’ of any asset in any market.