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

*S*_{o} = 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(d_{1}) or N(d_{2}) 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, S_{o} = 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.