Types of Options

Different Types of Options

Last time we looked at the basic idea of what an option is. There are many different types of options, and new ones can be imagined easily with some creativity.

In the academic world, there are two main types of options that have have been studied extensively. These options are called "plain vanilla" options, and they are also traded frequently on the options exchanges in the United States:

1. European Option - an option contract that can only be exercised at maturity.
2. American Option - an option contract that can be exercised at any time up to maturity. 

 In addition to the above types of options, there are a couple more that have received attention in academia. The options below are called "exotic" options, and they are not traded frequently on exchanges. Most of the time, exotics are traded "over-the-counter" in bilateral contracts:

     3.  Asian Option - the payoff at maturity depends on the average price of the underlying asset.
     4.  Barrier Option - if the price of the underlying asset hits some pre-specified "barrier" price, then the option contract is voided.

Note that exotics can also be European or American options. For example, you can make an Asian European option, or an American Barrier option, and vice versa. 

Techniques for Pricing the Basic Options

The plain vanilla European and American options are the most basic, and also the most traded options. The techniques used to price European and American options can be extended in many cases to price exotic options. Thus it is important that we pick up the basic toolkits to price these options before we move forward. There are a number of methods, each having its own advantages/disadvantages, and intricacies that will take some time to fully master. The basic ones that I will cover in future posts are:

1. Monte-Carlo Simulations - simulate price paths for the underlying asset (stock price) using random numbers. 
2. Black-Scholes PDE - a set of three equations that can easily be calculated by hand with a scientific calculator gives us the price for a European option.
3. Black-Scholes PDE via the Finite Element (or Difference) Method - a numerical way of calculating the BS PDE. Requires some computational power and number-crunching.
4. Binomial Model - used very widely in industry, it is one of the most resilient ways of pricing options.  

Methods Used to Price Options

One thing to note is that some of the methods listed above cannot be used to price American options. The reason for this comes from complications that arise due to the American Option being exercisable at any time.

In the following posts, we will start looking at these basic methods used to price options one-by-one. It might be worthwhile to note that in some cases, there are very clear "winners" as to which one is the best method to use. The reason why we still study the other methods is because they "might" become handy in other situations. My personal take is to look at this whole "option pricing" ordeal as a mathematical problem - the solution to which is mathematically interesting, but not always practical.

Option Pricing is not Physics

I will just add a small disclaimer for those of us who have received some training in the classical physics that option pricing "models" are not "true" in the sense that they are not made to reflect reality. Due to the complexity involved with the models use to price options, its easy to quickly lose track of this fundamental truth. Unlike "real engineering," where we in many cases we start of with the universal Newton's Laws etc., some fundamental theorem that has been tested to be true in a controlled environment millions of times before, the fundamental assumptions made in "financial engineering" are shaky estimations at best. Thus, many students - myself included - will find the lack of precision in such financial models to be frustrating when they start studying them. What's the point in building models that nobody can prove are accurate? Indeed, it's a cavernous business from the very beginning and some will say that it's more of an art than it is a science.