Firefyter51,
Ceterus paribus, an option that is closer to expiration will mimic the change in price of the underlying security more closely than an option that is further from expiration. This is the case because as an option approaches maturity a larger portion of the options value is determined by its intrinsic value (i.e. the difference between the strike price and the stock price), rather than its time value. However, if we relax this assumption then the question becomes a little more complicated because it is influenced by the six option pricing factors: stock price, strike price, volatility, expected dividends, time to expiration, and the risk free rate. Luckily, however, academics have examined this topic in depth and have coined the concept the options delta, which is literally the ratio of the change in option price over the change in stock price. We can retrieve an options delta from the Black-Scholes Pricing formula. The delta for a European call option is as follows:
Delta Call = N(d1)
where:
N = Cumulative normal distribution, (this can be obtained from table or by using the NORMSDIST() function in excel)
d1 = (ln(S/K)+(r+v^2/s)*T)/(v*sqrt(T))
where
ln = natural log
S = current stock price
K = option strike price
r = risk free rate
v = standard deviation or volatility
T = time to expiration
sqrt = square root
For a put option it can be expreseed as
Delta Put = N(d1) - 1
With this information we can actually calculate precisely what you are asking. For example, the Oracle Sep 08 $15 Call currently trades for $7/option. The price of Oracle at the close on Friday was $21.68. The 3-month T-Bill current yields 1.8% and the implied volatility is 58.09%. The option matures in roughly four months or 1/3 of a year (tecnically four months and a week). Plugging this information into the formula above we discover that the options delta is 0.90 Thus, if the price of Oracle stock increases from $21.68 to $22.68, or $1. Then we should expect the option price to increase by $0.90 to $7.0. Let's see what happens if we adjust the maturity to 1 month or 1/12 of a year and leave all other factors constant. If we do this the delta of the option increase to 0.988. This implies that changes in the option price more closel mimic changes in the the stock price as the option approaches maturity, which is consistent with what I said before. Notice, however that over time deltas change and as the underlying variables change the detla also changes. Thus, at any given time the change in option price in relation to the change in stock price will be different.
Hope this helps. If you have any more questions please feel free to ask.
Angell