## Variance Swap

**Variance Swap**

A variance swap is a financial instrument used for calculating the difference between an expected return and an actual return. It is a type of over-the-counter derivative that offers the holder to speculate or hedge their exposure on the magnitude of the future price volatility of an underlying asset. Variance swap includes exchange rates, interest rates, or an index price.

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**What Is Variance Swap?**

A variance swap is a type of financial derivative that offers the holder to speculate on the future price movement and it offers the hedger to hedge their exposure to the magnitude of the possible future price movements of the underlying asset. In simple words, variance swaps are used to measure the difference between an expected return and an actual return. It is similar to a plain vanilla swap and the major benefit of using a variance swap is that the investors don’t have to take directional exposure of the underliers.

**How Is Variance Swap Used?**

Variance swaps are similar to plain vanilla swaps. There are two parties involved in the variance swap transaction. The transaction takes place as follows

- One party involved in the transaction is supposed to pay an amount based on the actual price variance of the underlying asset.
- The other party involved will pay a fixed amount. This fixed amount is also known as the strike price, it is the predetermined rate i.e., it is specified at the beginning of the contract.
- The strike price is set in such a way that the net present value of they pay off becomes zero.
- At maturity, the contract will be settled in cash. The payoff of the counterparties will be determined by multiplying the difference between the variance and fixed price volatility by the theoretical amount.
- In case of any margin requirements specified in the contract, the netting of payments may take place during the life of the contract.

**Mathematical Terms:**

Since you have a basic understanding of how variation swap works. One must be familiar with the mathematical expressions used in variance swap. A variance swap is expressed as the arithmetic average of the differences from the mean value after it’s squared.

**Example And The Payoff Of Variance Swap:**

Variance swaps can be used to hedge the tail risk. Following is an illustration of a variance swap.

- The above illustration consists of two parties A & B at time 0.
- Mr. A and B are at time 0 where the current price volatility of an option is trading at
**20%,**so the variance is the square of volatility**(20%^2).** - Mr. A thinks that the variance is too low or Mr. A wants to hedge against the possibility of an increase in the volatility. This is the hedge of tail risk.
- Mr. A can enter into a variance swap where he is supposed to pay the above forward rate or the fixed variance of
**20%^2.**Once Mr. A has entered into a transaction for a period of 60 days and he will be receiving the actually realized price variance at the maturity of the contract. - The actually realized price variance will not be known to the parties at
**time 0**but will be known after**60 days.**i.e., at maturity of the contract. - After 60 days the actual price variance will be determined for example it is calculated to be
**40%**volatile which is**40%^2**variance.

- As per the illustration, Mr. A is going to pay a fixed variance of
**(20%^2) i.e. 400 units**and will be receiving the realized variance i.e**. (40%^2) i.e. 1600 units.** - To simplify the payment process. The amount will be netted i.e. Mr. A will receive
**1200 units**from Mr. B. Mr. B will incur a loss of**1200 units**. - In case, If the volatility would have been lower than
**20%**then Mr. A would be paying the counterparty, Mr. B. - To summarise, if the price of the forward rate would have been
**$20**per unit then Mr. A would have received the difference between the fixed variance and actual variance multiplied by the price i.e.**1200 units x $20 per unit = $24,000.**

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**Bottom Line:**

Variance swaps refer to an over-the-counter financial derivative instrument. A variance swap is similar to a plain vanilla swap. It can be used to speculate and hedge future price volatility. It is a two-party contract and the major benefit of using variance swap is that the investors don’t have to take directional exposure of the underliers. The payoff of variance swap will be greater than the volatility swap because the payoff of these products is at variance rather than the standard deviation.

**Author – Divyashri Kadam**

**About The Author – **Divyashri is a Bachelor’s Degree Holder in Accounting and Finance. Also, a Certified Financial Modeling and Valuation Analyst (FMVA). She is enthusiastic to learn more about financial markets, financial analysis, and anything relating to stocks.

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