a. The major factor that affects the value of an option is the price of the underlying asset.
If S_{0} is the price of the underlying asset at the time 0, and S_{T, }the price at the time T:
i. The value of a call is directly related to S_{T}, and
ii. The value of a put is inversely related to S_{T}
One thing that needs to be noted is that the spot price at any time, serves as an upper boundary for the call price, i.e. the call price can never exceed the spot price at that time.
Therefore,
C_{0} ≤ S_{o} & C_{T} ≤ S_{T} |
b. Another factor that affects the value of an option is its exercise price.
So, as an option moves towards getting more and more in-the-money from being out of money, its value keeps on increasing.
If X is the exercise price of an option:
i. Call option values are inversely related to X, and
ii. Put option values are directly related to X.
Also, the exercise price puts the upper limit on the price of a put option. Thus, the upper limits for the options are:
Option |
Upper Limits |
Call |
S_{T} |
Put |
X/(1+r)^{t} or Xe^{-rt } |
c. Another factor that affects the value of an option is the risk-free rate, r. Thus:
i. Call option prices are directly related to the risk-free rate, and
ii. Put option prices are inversely related to the risk-free rate.
This brings us to the concept of put-call parity. According to this concept, the relationship between a put and a call option has the same exercise price, expiration date, and underlying stock.
d. Time is also another that affects the value of an option.
i. The value of a call option is directly related to the time.
ii. The value of a put option is also generally related to the time but the longer the time, the lesser is the present value of the pay-off.
e. The volatility in the prices of the underlying also increases both call and put prices
NOTE: 1. Exercise price and the spot prices determine the intrinsic value of an option, and 2. Time and volatility impact the time value of an option. |