Calculate Price of Stock Given Price of Put and Call

Determining the stock price using put and call options prices is a fundamental concept in options trading. This calculator provides a precise method to estimate the stock price based on the prices of European-style put and call options with the same strike price and expiration date.

How to Use This Calculator

To calculate the stock price using put and call options prices:

Enter the price of the call option in the "Call Option Price" field.
Enter the price of the put option in the "Put Option Price" field.
Enter the strike price of the options in the "Strike Price" field.
Enter the risk-free interest rate in the "Risk-Free Rate" field (as a decimal, e.g., 0.05 for 5%).
Enter the time to expiration in years in the "Time to Expiration" field.
Click the "Calculate" button to compute the estimated stock price.

The calculator will display the estimated stock price based on the inputs provided.

Formula Explained

The stock price can be estimated using the following formula derived from the put-call parity relationship:

Stock Price = Call Option Price - Put Option Price + Strike Price × e^{-(Risk-Free Rate × Time to Expiration)}

Where:

Call Option Price - The price of the call option
Put Option Price - The price of the put option
Strike Price - The strike price of the options
Risk-Free Rate - The risk-free interest rate (as a decimal)
Time to Expiration - The time until the options expire (in years)

This formula accounts for the time value of money and the risk-free rate when estimating the stock price.

Worked Example

Let's calculate the stock price using the following inputs:

Call Option Price: $5.00
Put Option Price: $3.00
Strike Price: $50.00
Risk-Free Rate: 0.05 (5%)
Time to Expiration: 0.5 years

Using the formula:

Stock Price = $5.00 - $3.00 + $50.00 × e^{-(0.05 × 0.5)}

= $2.00 + $50.00 × e^-0.025

= $2.00 + $50.00 × 0.9753

= $2.00 + $48.765

= $50.765

The estimated stock price is $50.77.

Interpreting Results

The calculated stock price provides an estimate based on the put-call parity relationship. Here's what the result means:

The estimated stock price is derived from the prices of the call and put options, adjusted for the time value of money.
This method assumes European-style options and continuous compounding of the risk-free rate.
The result is most accurate when the options are deep in-the-money or at-the-money.

Note: This calculation provides an estimate and may not perfectly match the actual stock price due to market conditions and option pricing models.

Frequently Asked Questions

What is the put-call parity relationship?: The put-call parity relationship is a fundamental principle in options pricing that states the difference between the price of a call option and a put option should equal the difference between the stock price and the strike price, adjusted for the risk-free rate and time to expiration.
When is this calculation most accurate?: This calculation is most accurate when the options are European-style, deep in-the-money or at-the-money, and when the risk-free rate and time to expiration are accurately known.
Can I use this calculator for American options?: This calculator is designed for European options. American options may have different pricing dynamics due to early exercise features.
What if the calculated stock price seems unrealistic?: If the calculated stock price seems unrealistic, it may indicate that the options are not perfectly hedged or that there are market inefficiencies. Consider checking the inputs and market conditions.
How does the risk-free rate affect the calculation?: The risk-free rate is used to discount the strike price to its present value, accounting for the time value of money. A higher risk-free rate will result in a lower present value of the strike price.