Options pricing - underlying factors

Note that below discussion is in context of stock options for the simplicity of explanation
Introduction:
Option pricing techniques have become one of the basic necessities for any option trader, in order to  determine the fair price that can be paid for that option contract. Furthermore, options pricing is essential to derive a theoretical value for an option contract in future. This can help  traders to  take speculative positions on the price movements of an option contract. In general, any option pricing technique is based upon a set of underlying factors. These underlying  factors can be forked into two broad categories - Non-quantifiable and Quantifiable.

Non-quantifiable factors:
These are the factors  which cannot be quantified or forecast. Theoretically, these factors do not stand an existence because, an options price should be  completely deterministic from its fundamentals. However, since stock markets never work completely on fundamentals, so does option pricing. In a marketplace, the price of an option contract is determined largely by the forces of supply and demand. Buyers and Sellers place competitive bids on the price, and finally one price which is agreed upon by both is finalised. Further, an unpleasant piece of news about the options underlier can drive public sentiments against that option contract. An unstable political state of affair may also invite counter reactions from the street. All such factors, and many other, together may cause the option price to digress from its theoretical counterpart.

Quantifiable factors:
Theoretical value of an option contract comprises of two main components -
1. Intrinsic value - This component indicates the fundamental value of the option contract based on the value of its underlier and the strike price of the option.In plain terms, it can be considered to be equal to the difference between price of the underlier and the strike price.
2. Time value - Any amount of premium paid over the intrinsic value is the time value of that option contract. It indicates the amount of extra money above intrinsic value that the buyer is willing to pay with the hope that the market will turn in his favour. This value generally decreases (decays) as the time to expiry approaches. on the day of expiry, this value should be zero. This is because, longer the time to expiry, more time the buyer has for the market to turn in his favour. As expiry approaches, the time probability of this happening reduces and hence the time value of the option decreases. This decay is generally faster towards the end of option expiry as compared to that in the initial period. This is shown in the following graph -

courtesy tradingmarkets.com

Based on the above discussion, following are the set of quantifiable factors often used by option pricing models -

1. Stock price of the underlier - This forms a part of the intrinsic value of the option. As this value increases, call options price increase and put option price decrease. As this value decreases, call options price decrease and put option price increase.
2. Strike price - This forms a part of the intrinsic value of the option. As this value increases, call options price decrease and put option price increase. As this value decreases, call options price increase and put option price decrease.
3. Time until expiration - This forms a part of the time value of the option. As this value increases, both call and put option prices increase. As this value decreases, both call and put option prices decrease. This is as explained above.
   
4. Volatility of the underliers stock price -  This forms a part of the time value of the option. Volatility means the variation in the underlying stocks price value. It does not necessarily indicate a bullish  or bearish trend in the stock movement. Just indicates the fluctuations. As this value increases, both call and put option prices increase. As this value decreases, both call and put option prices decrease. This is because, high volatile stock has a greater chance of being more favourable for the long side and similarly the short side).
   
5. Dividends - This is more of a passive factor. However its important because, for a person who is long a call contract, he will get the delivery of stock on  exercising the option. And after that, if the company decides  to give dividends for its shares, then the long party will profit from it. Since, the ex-dividend dates are generally  know in advance, this factor is taken into consideration while determining  the  option price. As this value increases, call options price decrease and put option price increase. As this value decreases, call options price increase and put option price decrease. This is because, the effective stock  price is equal to actual stock price less the dividends paid. This effective stock price  is what is used in intrinsic value calculation. Thus, as dividends increase, effective stock price decreases and vica versa. Thus the above relations.
   
6. Interest rates (time value of money) - This  is an inevitable factor in evaluation of any financial instrument since it indicates the time value of money. As this value increases, call options price increase and put option price decrease. As this value decreases, call options price decrease and put option price increase. This can be explained by a simple example. Consider a trader who wants to buy 100 IBM stocks. Instead of buying them right  now, he can buy one call option. Thus, he now makes a small initial investment of the option premium as opposed  to earlier. This money temporarily saved can be put in an interest bearing account which will fetch him some extra bucks. Thus, he would be willing to pay some more premium in order to make some extra bucks given that interest rates are rising. Thus the above relations. 

To summarize,

Options - Basics

To be, or not to be, that is the question
(Hamlet, Act III, Scene I)
 

What is an option:
An option is an contract between a buyer and a seller, which gives the buyer a right, but not an obligation, to trade (buy/sell) some asset at some point in future at a predecided price. In plain english terms, an option contract would say something like - "Ted (option buyer) can sell 100 IBM stocks (asset) at a price of $10/share on or before 15th July, to Fed". Let us assume that our hypothetical option comes for a price of $2.

Some terminology:
The asset on which the buyer of the option has a right to trade is called as the option underlying or underlier. 
The date till which the option is effective is called as the expiration date of the option.
The price at which the underlier gets traded is called as the option strike price.
Since an option contract gives the buyer a right but not an obligation, to trade the underlier, it has some cost associated with it. The buyer agrees to pay a one time amount called as option premium to the seller to buy the option.
So in our example above,
underlier => IBM stock
expiration date => 15th July
strike price => $10
premium => $2

Exercising an option:
When the buyer decided to use his right to trade the underlying security of the option that he owns, then this is called as exercising the option. In our example above, if on 13th July, Ted decided to sell 100 IBM stock shares to Fed at $10/share, then Ted is said to be exercising his option.

Types of option - put / call
When an option contract gives the buyer a right to buy the underlier at the strike price from the seller, on/before the expiration date, then it is called as a call option.
When an option contract gives the buyer a right to sell the underlier at the strike price to the seller, on/before the expiration date, then it is called as a put option.

Types of option - American / European / Bermudan
If the option can be exercised at any time on and before the expiration date, then it is called as an American option.
If the option can be exercised only at the expiration date, then it is called as an .European option.
If the option can be exercised only on a discrete set of days on and before the expiration date, then it is called as an Bermudan option. 

Buying and Selling puts and calls:
Buying a call option gives the buyer a right to buy the underlier at the strike price on/before the expiration date. 
Buying a put option gives the buyer a right to sell the underlier at the strike price on/before the expiration date.
Selling a call option obliges the seller to sell the underlier at the strike price on/before the expiration date, when (and if) the buyer wishes to exercise his option.
Selling a put option obliges the seller to buy the underlier at the strike price on/before the expiration date, when (and if) the buyer wishes to exercise his option.
Note that selling an option is more popularly known as writing an option.

in-the-money, out-of-money, at-the-money:
At the expiration date, if, for a -
call option, the current market price of the underlier is more than the strike price
OR
put option, the current market price of the underlier is less than the strike price
then, that option is said to be in-the-money. This is because it is offering the buyer of the option a more favourable price than the market price while exercising the option.

At the expiration date, if, for a -
call option, the current market price of the underlier is less than the strike price
OR
put option, the current market price of the underlier is more than the strike price
then, that option is said to be out-of-money. This is because it is offering the buyer of the option a less favourable price than the market price while exercising the option.

At the expiration date, if, for a -
call option, the current market price of the underlier is equal to the strike price
OR
put option, the current market price of the underlier is equal to the strike price
then, that option is said to be at-the-money. This is because it is offering the buyer of the option the same price as the market price while exercising the option.

As is obvious from above definitions, an option will be exercised only if it is in-the-money or at-the-money. When the option is out-of-money, the buyer of the option might as well chose to let the option expire and not exercise it since he is getting a better price in the market.

Some terminology:
Going Long: In the context of options, going long would mean to buy an option contract. So, the person who goes long on an option would have a right but no obligation to exercise the option. Further, his potential loss is limited by the amount of the premium paid.

Going Short: In the context of options, going short would mean to sell (write) an option contract. So, the person who goes short on an option would have an obligation to fullfill the assignment if the option holder decides to exercise the option. Further, his potential loss is theoritically unlimited (practically limited by the fact that stock price cannot go below zero).

Open a position: In the context of options, opening a position means to add to an existing set of positions already undertaken. One can open a new position by -

1. Going long i.e. opening a long position (buying an option contract).
2. Going short i.e. opening a short position (selling an option contract).

Close a position: In the context of options, closing a position means to reduce from an existing set of positions already undertaken. One can close an existing position by -

1. Going long i.e. Buying an option contract to offset an existing option contract that is written.
2. Going short i.e. Selling an option contract to offset an existing option contract that is bought.

With respect to options, a closing transaction is done to avoid actual delivery of the underlier. For e.g. a company may have strategically gone long on a call option to buy 100 cows. Now, they don't intend to actually exercise this option and take care of the cattle. Instead, they will simply close their transaction by going short on  a call option to sell away those 100 cows. Note that an option position can only be closed before the option holder exercises the option.

Exercising an option - Process flow

The diagram above depicts the typical participants involved in the process of exercising an option. When a client wants to exercise his option, he should inform his broker well before the expiration date. This broker will in turn inform the OCC (Options Clearing Corporation) of the intent of its client to exercise his option. The OCC would then pick up one clearing members from a pool of clearing members. Clearing members are nothing but brokers for short clients. The selected clearing member would have many clients who would have written an option contract with the same terms as the one the original client wants to exercise. The clearing member will pick up one such client randomly and then assign him the job of making the actual delivery.

Trivia: A short client may chose to close his position to avoid assignment as mentioned above. In case of stock options, a call option holder may chose to exercise the option well before the expiry since the company may be giving dividends and he  may want his share in the dividends. So, in such cases, the option writers should be alert as to the date of dividends so that they may close their positions well before that date.