It is important to know that interest rates and volatility exert an influence on option prices. When interest rates are highel; call option prices are higher and put option prices are lower. This effect is not obvious and strains the intuition somewhat. When investors buy call options instead of the underlying, they are effectively buying an indirect leveraged position in the underlying. When interest rates are higher, buying the call instead of a direct leveraged position in the underlying is more attractive. Moreover, by using call options, investors save more money by not paying for the underlying until a later date. For put options, however, higher interest rates are disadvantageous. When interest rates are higher, investors lose more interest while waiting to sell the underlying when using puts. Thus, the opportunity cost of waiting is higher when interest rates are higher. Although these points may not seem completely clear, fortunately they are not critical. Except when the underlying is a bond or interest rate, interest rates do not have a very strong effect on option prices. Volatility, however, has an extremely strong effect on option prices. Higher volatility increases call and put option prices because it increases possible upside values and increases possible downside values of the underlying. The upside effect helps calls and does not hurt puts. The downside effect does not hurt calls and helps puts. The reasons calls are not hurt on the downside and puts are not hurt on the upside is that when options are out-of-the-money, it does not matter if they end up more out-of-the-money. But when options are in-the-money, it does matter if they end up more in-the-money.
Volatility is a critical variable in pricing options. It is the only variable that affects option prices that is not directly observable either in the option contract or in the market. It must be estimated.