## What is Volatility Arbitrage?

Volatility arbitrage refers to a type of statistical arbitrage strategy that is implemented in options trading. It generates profits from the difference between the implied volatility of options and the forecasted volatility of underlying assets.

The values of options are impacted by the volatility of their underlying assets. Higher volatility of the underlying asset leads to a higher value of the option. Therefore, the different implied volatility of the option and forecasted volatility of the asset will generate a difference between the expected price and market price of the option.

### Summary

**Volatility arbitrage profits from the difference between the implied volatility of options and the forecasted volatility of the prices of the underlying assets.****It is generally implemented in a delta-neutral portfolio with an option and its underlying asset.****Risks exist in volatility arbitrage, with the uncertainty in the implied volatility estimate, timing of the holding positions, and the price change of the underlying asset.**

### Volatility Arbitrage and Delta-Neutral Portfolio

Volatility arbitrage is generally implemented in a delta-neutral portfolio that consists of an option and its underlying asset. Delta is a measure of the sensitivity of the derivative price to the change of its underlying asset price.

The delta of a call option ranges from 0 to 1, as an increase in the asset price leads to a higher value for the corresponding call option. The delta of a put option ranges from -1 to 0, as a higher asset price leads to a lower value of the corresponding put option. An options trader can create a delta-neutral portfolio with a total delta of zero by balancing the positive and negative deltas of the positions.

Since the delta of an option changes over time, the portfolio requires frequent rebalancing to keep delta neutral. The options trader can thus make profits through these re-balancing trades by implementing a volatility arbitrage strategy.

The value of a delta-neutral portfolio remains constant with small price changes in the underlying assets. Therefore, as long as trading with a delta-neutral strategy, volatility arbitrage is a speculation in the volatility instead of the price of the underlying asset.

### How Volatility Arbitrage Works

Traders who implement a volatility arbitrage strategy look for options with implied volatility significantly higher or lower than the forecasted price volatility of the underlying assets. If a trader thinks that implied volatility of a stock option is underestimated (option is underpriced), the trader can open a long position for the call option and short the underlying asset to hedge.

This forms an arbitrage position, which keeps the portfolio delta neutral. The trader is said to “long volatility.” With the unchanged stock price, when the implied volatility increases later and the option moves up to the fair value, the trader profits.

If a trader thinks that a stock option is overpriced due to its overestimated implied volatility, the trader can short volatility by opening a short position for the call option and hedge the position by buying the underlying asset. If the stock price does not change and the trader’s forecast is correct, the option moves down to its fair value. Thus, the trader profits from his forecast on the volatility.

According to the put-call parity (as shown in the formula below), holding a long European put and a long underlying asset is equivalent to holding a long European call for the same class and a long bond with a face value of the strike price, matured at the expiration date of the options.

Therefore, the option positions for the volatility arbitrage strategy can be either calls or puts. When a trader wants to long/short volatility, he can long/short either a call or a put, and it gives the same result.

**P + S = C + PV[K]**

Where:

**P**= Price of a European put option**S**= Price of the underlying asset (at the same class with the European put)**C**= Price of a European call option**PV[K]**= Present value of the strike price (K), discounted at the risk-free rate from the expiration date of the options

### Volatility Arbitrage – Concerns

To some extent, volatility arbitrage is not a “real” arbitrage that provides an opportunity to generate risk-free profits. Risks still exist in the volatility arbitrage strategy. In order to profit from such a strategy, a trader must be correct in multiple assumptions. It includes the overvalue or undervalue of the option, the proper timing for holding the positions, and the price change of the underlying asset.

Incorrect estimates can cause time value erosion and expensive strategy adjustments. They may counteract the gains.

Also, the volatility arbitrage strategy in a portfolio provides diversification in volatility risk. However, “black swan” events can significantly impact the returns, especially when the portfolio contains implied volatilities correlated among assets.

Hedge fund management firm Long Term Capital Management (LTCM) used to implement the volatility arbitrage strategy and some other arbitrage strategies. Since arbitrage provides a low level of returns, LTCM traded with high leverage. As a result of its high leverage and a “black swan” event – the default on its domestic local currency bonds by the Russian government – LTCM failed in 1998.

### Additional Resources

CFI is the official provider of the global Commercial Banking & Credit Analyst (CBCA)™ certification program, designed to help anyone become a world-class financial analyst. To keep advancing your career, the additional resources below will be useful: