Put-Call Parity Calculator
An essential tool for options traders to determine the theoretical fair value of a call option based on its corresponding put option. This relationship is a cornerstone of arbitrage-free pricing.
The market price of the corresponding European put option.
The current market price of the underlying asset.
The exercise price for both the put and call options.
Parity Balance Visualizer
What is a calculate call option using put call parity calculator?
A calculate call option using put call parity calculator is a financial tool that applies the put-call parity principle to determine the theoretical fair value of a European call option. Put-call parity is a fundamental concept in options pricing that establishes a no-arbitrage relationship between the prices of a European put option, a European call option, the underlying asset’s price, and the strike price, assuming they all share the same expiration date.
This calculator is used by options traders, financial analysts, and students to quickly check for potential mispricings in the market. If the actual market price of a call option deviates significantly from the value calculated by the put-call parity formula, an arbitrage opportunity may exist.
The Put-Call Parity Formula and Explanation
The core of this calculator relies on the put-call parity equation. For European options (which can only be exercised at expiration), the relationship is defined as follows:
C + PV(K) = P + S
To make the calculator more direct for finding the call price, and by assuming the calculation is for the moment of expiration (where the present value of the strike price, PV(K), is simply the strike price K), we can rearrange the formula to solve for the Call Price (C):
C = P + S – K
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| C | Call Option Price | Currency ($) | Positive value |
| P | Put Option Price | Currency ($) | Positive value |
| S | Current Stock Price | Currency ($) | Positive value |
| K | Strike Price | Currency ($) | Positive value |
| PV(K) | Present Value of Strike Price | Currency ($) | Slightly less than K |
Note: The full formula includes the risk-free interest rate and time to expiration to discount the strike price (K). For a deeper analysis, consider using a Black-Scholes vs Put-Call model.
Practical Examples
Example 1: At-the-Money Option
Suppose a stock is trading exactly at its strike price.
- Inputs:
- Put Option Price (P): $4.50
- Current Stock Price (S): $150.00
- Strike Price (K): $150.00
- Calculation: C = $4.50 + $150.00 – $150.00
- Result: The theoretical Call Option Price (C) is $4.50.
Example 2: In-the-Money Put
Consider a scenario where the put option has intrinsic value. An understanding of options pricing model is crucial here.
- Inputs:
- Put Option Price (P): $12.00
- Current Stock Price (S): $88.00
- Strike Price (K): $95.00
- Calculation: C = $12.00 + $88.00 – $95.00
- Result: The theoretical Call Option Price (C) is $5.00.
How to Use This Put-Call Parity Calculator
- Enter the Put Option Price: Input the current market price of the European put option in the first field.
- Enter the Stock Price: Input the current market price of the underlying stock.
- Enter the Strike Price: Input the strike price that is common to both the put and call option. Learn more about understanding strike price to make better decisions.
- Review the Result: The calculator automatically computes and displays the theoretical call option price in the green box. This represents the fair value of the call option if no arbitrage opportunity exists.
- Analyze the Chart: The bar chart provides a quick visual check. If the two bars are not equal, it suggests a potential deviation from parity. This could be a starting point for exploring arbitrage opportunities.
Key Factors That Affect Option Prices
While our calculator uses three direct inputs, the true market price of an option is influenced by several factors that are implicitly captured in the prices you enter. Understanding these is vital for any option trading strategies.
- Underlying Asset Price (S): The most direct influence. As the stock price rises, call prices increase and put prices decrease.
- Strike Price (K): The price at which the option can be exercised. The relationship between the strike price and stock price determines the option’s intrinsic value.
- Time to Expiration: The longer the time until expiration, the more time value an option has, increasing the price of both puts and calls.
- Volatility: Higher expected volatility of the underlying stock increases the chance of the option finishing in-the-money, thus increasing the price of both puts and calls.
- Interest Rates: Higher interest rates tend to increase call prices and decrease put prices. This is because higher rates reduce the present value of the strike price, a benefit for call holders.
- Dividends: Expected dividends paid by the underlying stock decrease call prices and increase put prices, as the stock price is expected to drop by the dividend amount on the ex-dividend date.
Frequently Asked Questions (FAQ)
1. Does put-call parity apply to American options?
No, put-call parity in its strict form only applies to European options, which cannot be exercised before the expiration date. Because American options have the feature of early exercise, their pricing relationship is more complex and can deviate from this formula.
2. What is a synthetic call option?
Using the put-call parity formula, you can create a position that mimics the payoff of a call option. This is called a synthetic call option and is constructed by buying a put, buying the underlying stock, and borrowing the present value of the strike price.
3. What does it mean if the calculator’s price is different from the market price?
If the calculated price is different from the market price, it signifies a potential arbitrage opportunity. For example, if the calculator shows a call should be $5 but it’s trading at $4, it’s considered underpriced. An arbitrageur could theoretically buy the call, and sell the synthetic equivalent, for a risk-free profit.
4. Why does the full formula use the “Present Value” of the strike price?
Money has time value. The strike price is a cash amount that will be exchanged in the future. Therefore, its value today is lower than its face value. The full formula discounts the strike price using the risk-free interest rate to find its present value (PV), providing a more accurate theoretical price.
5. Are transaction costs included in this calculation?
No, the put-call parity model assumes a frictionless market with no transaction costs, commissions, or bid-ask spreads. In the real world, these costs can often eliminate small arbitrage opportunities.
6. How do dividends affect the formula?
If the underlying stock pays a dividend, the formula must be adjusted. The present value of the expected dividends is subtracted from the stock price side of the equation: C + PV(K) = P + (S – PV(Div)). This is because the stock price is expected to drop by the dividend amount.
7. What is a “protective put”?
A protective put is a strategy where an investor holds the underlying stock and buys a put option on it. The put-call parity shows that the portfolio (P + S) is equivalent to holding a call option and a risk-free bond (C + PV(K)).
8. What is the risk-free interest rate?
It’s the theoretical rate of return of an investment with zero risk. In practice, the yield on short-term government securities, like a U.S. Treasury bill, is often used as a proxy for the risk-free rate.