Valuing Caps and Floors
The arbitrage-free binomial model can be used to value a cap and a floor. This is because, as previously explained, a cap and a floor are nothing more than a package or strip of options. More specifically, they are a strip of European options on interest rates. Thus to value a cap the value of each period’s cap, called a caplet, is found and all the caplets are then summed. The same can be done for a floor.
To illustrate how this is done, we will once again use the binomial interest-rate tree to value an interest rate option. Consider first a 5.2%, three-year cap with a notional amount of $10 million. The reference rate is the one-year rates in the binomial tree. The payoff for the cap is annual.
Exhibit 25-12 shows how this cap is valued by valuing the three caplets. The value for the caplet for any year, say year X, is found as follows. First, calculate the payoff in year X at each node as either zero if the one-year rate at the node is less than or equal to 5.2%, or the notional principal amount of $10 million times the difference between the one-year rate at the node and 5.2% if the one-year rate at the node is greater than 5.2%
Then, the backward induction method is used to determine the value of the year X caplet. Read the rest of this entry »
The interest-rate swap was developed in late 1981. By 1987, the market had grown to more than $500 billion (in terms of notional principal amount). What is behind this rapid growth? As our asset/liability application earlier demonstrated, an interest-rate swap is a quick way for institutional investors to change the nature of assets and liabilities or to exploit any perceived capital market imperfection. The same applies to borrowers such as corporations, sovereigns, and supranationals.
In fact, the initial motivation for the interest-rate-swap market was borrower exploitation of what were perceived to be “credit arbitrage” opportunities because of differences between the quality spread between lower- and higher-rated credits in the U.S. and Eurodollar bond fixed-rate market and the same spread in these two floating- rate markets. Basically, the argument for swaps was based on a well-known economic principle of comparative advantage in international economics. Read the rest of this entry »
Sloth is often a function of time. It may be that you don’t have the hours or don’t want to put in the hours necessary to be a good investor. That’s fine. Though there is a minimum amount of work every investor needs to do, you must find the right investing mode given the hours you are willing to expend. Your sloth may result from being in the wrong mode; you’re trying to do it yourself when you really should be relying on a money manager. The three modes, therefore, are:
- Doing it yourself
- Focusing on mutual funds
- Using a money manager
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It’s likely that most investors, at some point in their investing careers, buy and sell much too quickly. Perhaps they get caught up in a market upturn or downswing or they are going through a difficult period in their personal lives and turn to day trading as a form of escape. If overactive trading is an anomaly rather than a pattern, then you probably aren’t guilty of this sin. On the other hand, if you find that you periodically fall into the habit of overactive investing, gluttony may be a problem you need to address. Read the rest of this entry »
