Call Put Option Calculator Excel

Options are financial derivatives that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a certain date. This calculator helps you determine the theoretical value of call and put options using the Black-Scholes model, which is widely used in finance and trading.

What is Option Pricing?

Option pricing is the process of determining the value of an option contract. Options can be either call options (giving the holder the right to buy) or put options (giving the right to sell) an underlying asset at a predetermined price (the strike price) before or at a specific expiration date.

Key Terms in Option Pricing

Strike Price - The price at which the underlying asset can be bought or sold
Expiration Date - The last date the option can be exercised
Premium - The price paid to purchase the option
Intrinsic Value - The difference between the market price of the underlying asset and the strike price
Time Value - The portion of the option's premium that has positive expectation of profit

Important Note

Option pricing is based on theoretical models and market assumptions. Actual option prices may differ due to market conditions, volatility, and other factors not accounted for in the model.

The Black-Scholes Model

The Black-Scholes model is the most widely used mathematical model for option pricing. It was developed by Fischer Black, Myron Scholes, and Robert Merton in 1973. The model assumes that the underlying asset follows a geometric Brownian motion with constant drift and volatility.

Black-Scholes Formula

For a call option:

C = S·N(d₁) - X·e^(-r·T)·N(d₂)

For a put option:

P = X·e^(-r·T)·N(-d₂) - S·N(-d₁)

Where:

C = Call option price
P = Put option price
S = Current price of the underlying asset
X = Strike price
r = Risk-free interest rate
T = Time to expiration (in years)
σ = Volatility of the underlying asset
N = Cumulative standard normal distribution function
d₁ = (ln(S/X) + (r + σ²/2)·T) / (σ·√T)
d₂ = d₁ - σ·√T

The model makes several key assumptions:

No arbitrage exists in the market
The underlying asset follows a log-normal distribution
Markets are efficient and prices are instantly adjusted
There are no transaction costs or taxes
Dividends are not considered

While the Black-Scholes model provides a theoretical framework, real-world option prices may differ due to factors like market frictions, liquidity, and investor behavior.

How to Use Excel for Option Pricing

Excel can be used to implement the Black-Scholes model for option pricing. Here's a step-by-step guide:

Step 1: Input Parameters

Create a table with the following input parameters:

Parameter	Description	Example Value
S	Current price of underlying asset	100
X	Strike price	105
r	Risk-free interest rate (annual)	0.05
T	Time to expiration (years)	0.5
σ	Volatility (annual standard deviation)	0.2

Step 2: Calculate d₁ and d₂

Use these formulas in Excel:

Excel Formulas

d1 = (LN(S/X) + (r + σ²/2)*T) / (σ*SQRT(T))

d2 = d1 - σ*SQRT(T)

Step 3: Calculate Option Price

Use the NORM.S.DIST function to calculate the cumulative standard normal distribution:

Call Option Price

=S*NORM.S.DIST(d1, TRUE) - X*EXP(-r*T)*NORM.S.DIST(d2, TRUE)

Put Option Price

=X*EXP(-r*T)*NORM.S.DIST(-d2, TRUE) - S*NORM.S.DIST(-d1, TRUE)

Step 4: Create a Sensitivity Analysis

You can create data tables to analyze how changes in input parameters affect the option price. For example:

How does the option price change with different strike prices?
What is the effect of changing the volatility?
How does the time to expiration impact the option price?

Excel Tip

Use Excel's Data Table feature to create sensitivity analyses. Select the option price cell, then go to Data > What-If Analysis > Data Table to create a table showing how the price changes with different input values.

Example Calculation

Let's calculate the price of a call and put option using the following parameters:

Parameter	Value
Current price (S)	$100
Strike price (X)	$105
Risk-free rate (r)	5% (0.05)
Time to expiration (T)	6 months (0.5 years)
Volatility (σ)	20% (0.2)

Step-by-Step Calculation

Calculate d₁:
d₁ = (ln(100/105) + (0.05 + 0.2²/2)*0.5) / (0.2*√0.5) ≈ -0.0488 + (0.05 + 0.02)*0.5 / (0.2*0.7071) ≈ -0.0488 + 0.055 / 0.1414 ≈ -0.0488 + 0.3889 ≈ 0.3401
Calculate d₂:
d₂ = d₁ - 0.2*√0.5 ≈ 0.3401 - 0.1414 ≈ 0.2087
Calculate call option price:
C = 100*N(0.3401) - 105*e^(-0.05*0.5)*N(0.2087)

N(0.3401) ≈ 0.6336, N(0.2087) ≈ 0.5816

C ≈ 100*0.6336 - 105*0.9753*0.5816 ≈ 63.36 - 61.39 ≈ $2.97
Calculate put option price:
P = 105*e^(-0.05*0.5)*N(-0.2087) - 100*N(-0.3401)

N(-0.2087) ≈ 0.4184, N(-0.3401) ≈ 0.3664

P ≈ 105*0.9753*0.4184 - 100*0.3664 ≈ 43.96 - 36.64 ≈ $7.32

The calculated call option price is approximately $2.97 and the put option price is approximately $7.32.

Interpretation

This means that the buyer of the call option would pay approximately $2.97 for the right to buy the stock at $105 in 6 months, while the buyer of the put option would pay approximately $7.32 for the right to sell the stock at $105 in 6 months.

Common Mistakes to Avoid

When using option pricing models, especially in Excel, there are several common mistakes to be aware of:

1. Incorrect Input Parameters

Using incorrect or outdated input parameters can lead to inaccurate option prices. Always ensure that:

The current price of the underlying asset is accurate
The strike price is correctly specified
The risk-free interest rate is appropriate for the time horizon
The volatility estimate is reasonable for the asset and time period

2. Misinterpreting Results

Option prices calculated using models like Black-Scholes should be interpreted carefully:

Model prices are theoretical and may differ from market prices
Time value is not the same as intrinsic value
Option prices are sensitive to changes in input parameters

3. Overlooking Model Limitations

The Black-Scholes model has several limitations:

It assumes continuous trading and no transaction costs
It doesn't account for dividends
It may not be appropriate for assets with low liquidity
It doesn't consider market frictions or investor behavior

4. Excel Calculation Errors

Common Excel calculation errors include:

Using incorrect function names (e.g., NORM.DIST instead of NORM.S.DIST)
Miscounting or misplacing parentheses in formulas
Not using absolute references when copying formulas
Rounding errors in intermediate calculations

Best Practice

Always double-check your calculations and verify that your Excel formulas are correctly implemented. Consider using Excel's built-in option pricing functions if available in your version.

Frequently Asked Questions

What is the difference between a call and put option?

A call option gives the holder the right to buy an asset at a specified price, while a put option gives the right to sell the asset at that price. Call options are typically used when expecting the price to rise, while put options are used when expecting a price decline.

How accurate is the Black-Scholes model?

The Black-Scholes model provides a good approximation for European options on liquid assets, but it has limitations. Real-world option prices may differ due to factors like market frictions, liquidity, and investor behavior.

Can I use Excel to price options on stocks with dividends?

The basic Black-Scholes model doesn't account for dividends. For stocks that pay dividends, you would need to use a modified model or adjust the parameters to account for the dividend payments.

What is the difference between intrinsic and time value?

Intrinsic value is the difference between the market price of the underlying asset and the strike price, while time value represents the portion of the option's premium that has positive expectation of profit. Time value decreases as the expiration date approaches.

How do I interpret the volatility parameter in option pricing?

Volatility measures the expected price fluctuations of the underlying asset. Higher volatility generally increases the value of options, as it increases the chance of the asset moving significantly in either direction.