Put Call Arbitrage Calculator

Put Call Arbitrage is a strategy in options trading where investors simultaneously buy a put option and sell a call option on the same underlying asset. This calculator helps you determine the potential arbitrage opportunities by analyzing the price differences between put and call options.

What is Put Call Arbitrage?

Put Call Arbitrage is a trading strategy that exploits the mispricing between put and call options on the same underlying asset. The strategy involves buying a put option and selling a call option with the same strike price and expiration date.

The key idea is that the put and call options should be priced in a way that creates an arbitrage opportunity. If the sum of the premiums paid for the put and received from the call is positive, there's an arbitrage opportunity.

This strategy is most effective in markets with low volatility and when the underlying asset is not expected to move significantly in the near term.

How to Calculate Put Call Arbitrage

The calculation involves comparing the premiums of put and call options with the same strike price and expiration date. The formula for calculating the arbitrage opportunity is:

Arbitrage Opportunity = (Call Premium) - (Put Premium) - (Strike Price × e^-rT)

Where:

Call Premium - The price of the call option
Put Premium - The price of the put option
Strike Price - The strike price of both options
r - The risk-free interest rate
T - The time to expiration in years

The result will be positive if there's an arbitrage opportunity, indicating that buying the put and selling the call is profitable.

Example Calculation

Let's consider an example where:

Call Premium = $2.50
Put Premium = $1.80
Strike Price = $50
Risk-free rate (r) = 5% (0.05)
Time to expiration (T) = 30 days (0.0821 years)

Using the formula:

Arbitrage Opportunity = $2.50 - $1.80 - ($50 × e^{-0.05×0.0821})

= $2.50 - $1.80 - ($50 × 0.96)

= $2.50 - $1.80 - $48

= -$45.30

In this case, the arbitrage opportunity is negative ($-45.30), meaning there's no profitable arbitrage opportunity with these option prices.

FAQ

What is the difference between Put Call Arbitrage and Call Spread?

Put Call Arbitrage involves buying a put and selling a call with the same strike and expiration, while a Call Spread typically involves selling a call and buying another call with a higher strike price. The objectives and risk profiles are different between the two strategies.

Is Put Call Arbitrage always profitable?

No, Put Call Arbitrage is not always profitable. It depends on the current pricing of the options and the underlying asset. The calculator helps you determine when there's a potential arbitrage opportunity.

What are the risks of Put Call Arbitrage?

The main risks include market volatility, changes in interest rates, and the potential for the arbitrage opportunity to disappear if option prices adjust. It's important to monitor the positions closely.