Options Pricing Framework – Introduction

It has been afew months since I made my account on WordPress.com. The motivation behind starting a blog on wordpress was manifold. The most important was to hone writing skills and share knowledge, experience, thoughts, facts and opinions with friends and colleagues. Moreover, I thought this would prove to be a platform to generating fresh and new ideas through constructive criticim.

Many days passed, but I couldn’t manage to take time out and head on with this long awaited wishlist task. Though I wished to write on number of various general issues, now I think I would start with some serious academic topic as I think this will help me in my understanding and my friends around.

The headline for the discussion I have chosen is Option Pricing Framework. The discussion will be designed in such a fashion that it will first provide a discussion on what options are? How can we price them using risk-neutral valuation and replicating approach. What are the basic numerical procedures of pricing? From Binomial to Black-Scholes World, then we will discuss the draw backs of the Black-Scholes Option Pricing. Final touches will lead to dicuss the alternative models that might address the short-coming of the models. We will try to incorporate within discussion empirical literature, if any.

GET SET GO … !!!

WHAT ARE OPTIONS?

Options are financial securities which derive their value from the underlying assets. Since such securities give the holder the right of excersizing, so the name “Option” is assigned to such securities. Elementary options that one can think of having can be having an exclusive right of either buying or selling some underlying asset. If the holder of the option has the right to buy the underlying asset, it is simply termed as “Call” option, and if the holder of the option has the right to sell the underlying asset, it is called “Put” option. As the names suggest, call sounds like you are asking for something i.e., you are buying some underlying asset whereas, put sounds like you are throwing something to the person on the opposite side which gives you a feeling of selling some underlying asset.

The commentary given above does not suffice the true definition of the option. The missing links of the proper definition arise by the questions like ”what price should option holder be buying the underlying asset when she exercises so called call option?” “who determines these exercise prices and when are they determined?”, and “when can the option holder really exercise the option?” 

By now you yourself would have gotten a feeling of what exercise price is? The exercise price is the price at which the option holder will buy the underlying asset, which is also called strike price at times. This exercise price is determined at the initiation of the contract. Moreover, if the option is traded on exchange, you will find the options written on certain stocks are available with different maturities and strikes.

Since options are the financial contracts, they have certain maturity. There can be two basic possibilities of options either to exercise on maturity or anytime during the life of the contract. If the contract gives you the right of exercising on maturity for a certain strike price, such options are flavored as European Options, whereas if the contract gives you the right of exercing anytime during th elife of the contract, such options are termed as American Options.

The readers must have come up by now with a very simple question, if the option holder has the right to exercise the option, what would the option seller would do? If I put this question to you back, I keep you in the shoes of the option seller (one who has granted such a right of buying/selling underlying asset to option holder), I will definitely expect that you will say such an option seller should honor the exercising right of the option holder. In case of call option, if he exercises the option of buying the underlying asset, the option seller is obliged (or has the obligation) of selling the asset to option holder at the agreed strike price at the initiation of contract and vice versa for put option.

Now we can present a very specific definition of the call and put options.

Call option is the financial derivatives contract in which the call option holder has the right, not the obligation, to buy the underlying asset at the agreed strike price on maturity of the contract whereas the call option seller has the obligation to honor such an exercise. Two parties, an option buyer and option writer are known as option holder and option writer respectively. The one who buys the call option is said to be Long Call and other who sell the call option is said to be Short Call.

The Put option will only differ in a sense that now option buyer (holder) will have the right to sell, in contrast to buying in call option, and option seller (writer) will have the obligation of buying the underlying asset from option buyer, with all other conditions same as mentioned in call option definition.

I will continue this discussion tomorrow Happy reading … !!!

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