# Volatility Arbitrage

Volatility arbitrage is a trading strategy that tries to profit from the difference between the forecasted or implied volatility of an asset and its actual future volatility.

## Key Takeaways – Volatility Arbitrage

Market Neutral Strategy

- Volatility arbitrage tries to profit from the difference between expected and actual volatility.
- Options are typically used to create market-neutral positions.
Implied vs. Realized Volatility

- Success depends on accurately predicting the gap between implied volatility (market expectation) and realized volatility (actual market movement).

Here’s a detailed explanation of how volatility arbitrage works:

## Key Concepts

### Volatility

**Implied Volatility (IV)**– The market’s forecast of a likely movement in an asset’s price. It is often derived from the prices of options, using standard deviation or similar.**Realized Volatility**– The actual volatility of the asset observed over a specific period.

### Options

Financial derivatives that give the buyer the right, but not the obligation, to buy (call option) or sell (put option) an asset at a predetermined price before or at the option’s expiration date.

Options are heavily used in volatility arbitrage, given volatility is a material part of how they’re priced.

## How Volatility Arbitrage Works

### 1) Identify the Discrepancy

Traders look for assets where the implied volatility (derived from options prices) is significantly different from what they believe the actual future volatility (realized volatility) will be.

### 2) Constructing the Trade

- If a trader believes that the implied volatility is too high compared to expected future volatility, they might sell options (as options are overpriced).
- Conversely, if they believe the implied volatility is too low, they might buy options (as options are underpriced).

### 3) Delta Hedging

- To isolate the volatility component and minimize exposure to the asset’s price movements, traders often use a technique called delta hedging.
- This involves continuously adjusting the position in the underlying asset to remain delta-neutral – i.e., the portfolio’s value remains unaffected by small price changes in the asset.

### 4) Profit Realization

- The goal is for the actual volatility to match the trader’s expectations.
- If implied volatility was overestimated and the trader sold options, the options will expire worthless or lose value, allowing the trader to buy them back cheaper or keep the premium.
- If implied volatility was underestimated and the trader bought options, the options will gain value as the market realizes the higher volatility.

## Practical Example of Volatility Arbitrage

### Assumption

A trader notices that the implied volatility of a stock’s options is significantly higher than the trader’s forecast of the stock’s future volatility.

### Strategy

- The trader sells options (call or put) to capitalize on the high implied volatility.
- Simultaneously, the trader delta hedges by taking an opposite position in the underlying stock to protect against price movements.

### Execution

- If the trader’s forecast is correct and the actual realized volatility is lower than the implied volatility, the options will lose value.
- The trader profits from the difference between the premium received from selling the options and the cost of maintaining the delta-hedged position.

## More Specific Example of Volatility Arbitrage

Let’s go through a specific example of volatility arbitrage using exact instruments and amounts to make it easy to follow.

### Scenario Setup

**Stock**: XYZ Corp**Current Stock Price**: $100**Options**: 1-month at-the-money (ATM) call options**Implied Volatility (IV)**: 30%**Trader’s Forecasted Realized Volatility**: 20%

### Instruments and Quantities

**Options Sold**: 10 ATM call options (Each option contract typically covers 100 shares of the stock)**Delta Hedging**: Initial position in the underlying stock to maintain delta neutrality.

### Step-by-Step Process

**1) Sell Options**:

- The trader sells 10 ATM call options on XYZ Corp with a strike price of $100.
- Given the implied volatility of 30%, the option premium (price) might be $5 per share per option contract.
- Total premium received = 10 options * 100 shares per option * $5 = $5,000.

**2) Delta Calculation**:

- The delta of an ATM call option is approximately 0.5.
- To be delta neutral, the trader needs to hold an opposite position in the underlying stock.
- Total delta for 10 options = 10 * 100 shares * 0.5 = 500 shares.

**3) Delta Hedging**:

- To hedge, the trader needs to short 500 shares of XYZ Corp.
- Current stock price is $100, so the trader shorts 500 shares, receiving $100 * 500 = $50,000.

### Maintaining Delta Neutrality

- As the stock price moves, the delta of the options will change. The trader needs to continuously adjust the position in the underlying stock to maintain delta neutrality.
- For example, if the stock price increases and the delta of each option increases to 0.6, the new total delta is 10 * 100 * 0.6 = 600 shares.
- The trader now needs to short an additional 100 shares (600 total – 500 initially shorted) to maintain delta neutrality.

### Profit and Loss

**If Realized Volatility is Lower than Implied Volatility**:

- The trader’s forecast of 20% realized volatility is correct, and the actual stock movement is less than expected by the market.
- The options will lose value faster than anticipated because the actual stock price fluctuations are smaller.
- The trader buys back the options at a lower price (say $2 per option).
- Cost to buy back = 10 options * 100 shares per option * $2 = $2,000.
- Profit from options = $5,000 (premium received) – $2,000 (cost to buy back) = $3,000.

**Adjusting the Hedge**:

- Throughout the month, the trader adjusts the delta hedge, incurring some transaction costs.
- Assume total transaction costs are $500.
- Net profit = $3,000 (from options) – $500 (transaction costs) = $2,500.

### Summary

**Initial Action**: Sold 10 ATM call options, shorted 500 shares of XYZ Corp.**Premium Received**: $5,000.**Options Bought Back**: $2,000.**Transaction Costs**: $500.**Net Profit**: $2,500.

By maintaining a delta-neutral position and correctly predicting lower realized volatility, the trader profits from the discrepancy between implied and realized volatility, while adjusting for changes in the delta and managing transaction costs.

## Risks and Considerations

**Model Risk –**The strategy heavily relies on accurate forecasting of future volatility. Incorrect models or assumptions can lead to losses. This strategy requires volatility expertise.**Execution Risk –**Delta hedging requires continuous rebalancing. This can be challenging and costly in volatile markets. This makes it more of a professionals strategy, who has the software/algorithmic setup to do this in a more accurate and cost-efficient way.**Liquidity Risk –**Large trades or illiquid markets can make it difficult to enter and exit positions without affecting the market price.**Market Risk –**Unanticipated market events can cause sudden changes in volatility and lead to losses.

## Conclusion

Volatility arbitrage is a complex but potentially profitable strategy for experienced traders who can accurately forecast volatility and efficiently manage the risks associated with options and delta hedging.

Individual traders can pursue vol arb, but for best results it generally requires sophisticated software, continuous monitoring, and an understanding of both the options market and the underlying asset.