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,