A European option is a contract which gives the holder the right to buy or sell the underlying asset for an agreed price on expiry.
European options can only be exercised on date of expiry.
European Call Option
A European call option is a contract which gives the holder the right to buy the underlying asset for an agreed price on expiry.
European Put Option
A European put option is a contract which gives the holder the right to sell the underlying asset for an agreed price on expiry.
Option Valuation (Call and Put Formulas)
The most famous method of valuing European option is Black-Scholes-Merton option pricing formula. The formula for valuing European call option is
Using put-call parity for European option
We can obtain the formula for European put option
Where
Here
So = Price at time o (or spot price)
K = Strike price (or strike)
r = Risk-free interest rate
T = Time (time to maturity)
σ = Volatility (standard deviation)
The functions N(x) or N(d1) or N(d2) are cumulative probability distribution function for a standardized normal distribution. In Excel it can be calculated by using the function =NORMSDIST()
Example
The stock price one year from the expiration of an option is $50, the strike price is $52, the risk-free interest rate is 10% per annum, and the volatility is 40% per annum. Find the value of the option if it can only be exercised at expiry.
Solution
It can only be exercised at expiry, so it is European style option. Here, So = 50, K = 52, r = 0.1, σ = 0.4 and T = 1.
By using the above formulas, we have
And,
Now, using Excel =NORMSDIST(0.3519) = 0.63756, =NORMSDIST(–0.048) = 0.4808, and =NORMSDIST(–0.3519) = 0.362, =NORMSDIST(0.048) = 0.519
Now, by putting all these values in call and put option value formulas, we have
Similarly, the put option value is
Excel Sheet
Download the Excel sheet to calculate option values for different parameters. Download Option Calculator.