Calculate The Value of A Put with A Call Price

Introduction

In options trading, puts and calls are two types of options contracts that give the holder the right, but not the obligation, to buy or sell an underlying asset at a specified price (the strike price) by a certain date (the expiration date).

The price of a put option is influenced by several factors including the underlying asset's price, volatility, time to expiration, interest rates, and the strike price. Similarly, the price of a call option is affected by the same factors.

Understanding the relationship between put and call prices is crucial for options traders. This relationship can help in hedging strategies, arbitrage opportunities, and risk management.

Relationship Between Put and Call Prices

The put-call parity theory establishes a fundamental relationship between the prices of European-style put and call options. According to put-call parity, the price of a put option (P) plus the price of the underlying asset (S) should equal the price of a call option (C) plus the present value of the strike price (K) discounted at the risk-free interest rate (r) and time to expiration (T).

This relationship holds true in an efficient market with no arbitrage opportunities. It provides a theoretical framework for understanding how changes in one option's price might affect the other.

In practice, put-call parity can be used to identify mispriced options or to design hedging strategies. For example, if the put-call parity is violated, it might indicate an arbitrage opportunity or a market inefficiency.

How to Calculate Put Value from Call Price

Using the put-call parity formula, you can calculate the theoretical value of a put option given the price of a call option. Here's a step-by-step guide:

1. Determine the current price of the underlying asset (S).
2. Identify the strike price (K) of the options.
3. Find the risk-free interest rate (r) and the time to expiration (T) in years.
4. Obtain the price of the call option (C).
5. Plug these values into the put-call parity formula to solve for the put option price (P).

This calculation provides a theoretical value for the put option. In reality, market prices may differ due to factors like transaction costs, bid-ask spreads, and market imperfections.

Worked Example

Let's consider a practical example to illustrate how to calculate the value of a put option using the price of a call option.

Example Scenario:

• Current price of the underlying asset (S): $100
• Strike price (K): $105
• Risk-free interest rate (r): 5% or 0.05
• Time to expiration (T): 6 months or 0.5 years
• Price of the call option (C): $8.50

Using the put-call parity formula:

The calculated value of the put option is $10.80. This means, according to put-call parity, the put option should be priced at $10.80 given the current market conditions.