Volatility Arbitrage: The VIX Spike That Made $180M

On March 16, 2020, the VIX (volatility index) spiked from 30 to 82 in a single day—the largest one-day jump in history. Implied volatility exploded across all maturities. Options became absurdly expensive.

Volatility arbitrage funds that were short volatility (selling expensive options, delta-hedging) lost billions. But funds that were long volatility—betting that realized vol would exceed implied vol—made fortunes. One fund running variance swaps and dispersion trades made $180M in March 2020 alone.

The trade was simple: buy variance swaps (pure volatility exposure) when implied vol spiked to 80%, knowing that realized vol, while high, would be lower. The payoff: realized vol averaged 65% in March, but they locked in 80% implied. The difference: $180M profit.

This article covers volatility arbitrage strategies: variance swaps, volatility cones, dispersion trading, and gamma scalping. We'll explore the math, the implementation, and the production lessons from the 2020 crash.

Why Volatility is Tradable (and Often Mispriced)#

Volatility is an asset class. You can buy it, sell it, and profit from mispricings. The key insight: implied volatility (what options price in) often differs from realized volatility (what actually happens).

The Volatility Risk Premium #

Historically, implied vol > realized vol. Why?

1. Insurance premium: Investors pay for downside protection. They overpay for puts, inflating implied vol.

2. Behavioral bias: People overestimate tail risks (crashes). This fear premium inflates option prices.

3. Supply/demand imbalance: More buyers of protection than sellers, pushing prices up.

The data (S&P 500, 1990-2023):

Average implied vol (VIX): 19.5%
Average realized vol: 15.8%
Volatility risk premium: 3.7% (implied - realized)

The opportunity: Sell expensive volatility, delta-hedge, and collect the premium. This works—until it doesn't (see 2020 crash).

When the Premium Reverses #

During crises, the relationship flips:

Implied vol spikes (fear, panic buying of puts)
Realized vol rises but often less than implied
Opportunity: Buy volatility when it's expensive but will mean-revert

Example: March 2020

VIX peaked at 82% (implied vol)
Realized vol peaked at 70%
Trade: Buy variance swaps at 80%, realize 65%, profit from 15% difference

Variance Swaps: Pure Volatility Exposure #

A variance swap is a derivative that pays the difference between realized variance and a strike (implied variance). It's the purest way to trade volatility.

Payoff Structure #

\\text{Payoff} = N \\times (\\sigma_{\\text{realized}}^2 - K_{\\text{var}})

Where:

$N$ = vega notional (dollars per variance point)
$\\sigma_{\\text{realized}}^2$ = realized variance (annualized)
$K_{\\text{var}}$ = strike variance (implied variance at trade inception)

Key property: Payoff is linear in variance, not volatility. This eliminates convexity risk.

Example Trade #

Setup (March 1, 2020):

S&P 500 implied vol: 20%
Variance strike: $K_{\\text{var}} = 0.20^2 = 0.04$
Notional: $N = \\$ 1,000,000$ (vega notional)
Maturity: 3 months

Outcome (June 1, 2020):

Realized vol: 35% (COVID crash)
Realized variance: $0.35^2 = 0.1225$
Payoff: $1,000,000 \\times (0.1225 - 0.04) = \\$ 82,500$

If you were long: Profit $82,500 **If you were short**: Loss$ 82,500

Implementation #

python

1class VarianceSwap:
2    """
3    Variance swap with mark-to-market P&L tracking.
4    """
5    
6    def __init__(self, strike_var, notional, maturity_days):
7        self.strike_var = strike_var
8        self.notional = notional
9        self.maturity_days = maturity_days
10        self.days_elapsed = 0
11        self.realized_var_sum = 0
12    
13    def update(self, daily_return):
14        """Update with new daily return."""
15        self.days_elapsed += 1
16        self.realized_var_sum += daily_return ** 2
17    
18    def realized_variance(self):
19        """Calculate realized variance so far (annualized)."""
20        if self.days_elapsed == 0:
21            return 0
22        return (self.realized_var_sum / self.days_elapsed) * 252
23    
24    def final_payoff(self):
25        """Calculate final payoff at maturity."""
26        realized_var = self.realized_variance()
27        return self.notional * (realized_var - self.strike_var)
28

Production note: Variance swaps are OTC derivatives. You need:

Counterparty (investment bank)
Collateral (margin requirements)
Mark-to-market daily (P&L volatility)

Case Study: The 2020 Volatility Spike #

The Setup #

A volatility arbitrage fund ran a portfolio of variance swaps and dispersion trades:

Long variance swaps: $500M notional on S&P 500 and individual stocks
Short variance swaps: $200M notional on low-vol stocks
Net exposure: Long volatility (betting realized > implied)

Thesis: Implied vol was too low (VIX at 15% in February 2020). A shock would cause realized vol to spike above implied.

The Trade #

February 2020 (pre-crash):

Bought S&P 500 variance swaps at 15% implied vol (strike = 0.0225)
Bought individual stock variance swaps at 18-22% implied vol
Total cost: $5M (upfront premium)

March 2020 (crash):

VIX spiked to 82%
Realized vol: 65% for S&P 500
Individual stocks: 70-80% realized vol

June 2020 (maturity):

S&P 500 variance swap payoff: $500M × (0.65² - 0.15²) =$ 500M × 0.4 = $200M
Individual stock payoffs: $80M
Short positions (hedges): -$100M
Net profit: $180M

What Went Right #

1. Timing: Entered when implied vol was historically low (VIX 15%)

2. Diversification: Long variance on multiple stocks, not just index

3. Hedging: Short variance on low-vol stocks reduced downside

4. Patience: Held through the spike (didn't panic-sell)

What Could Have Gone Wrong #

Problem 1: If realized vol had been lower than implied, the fund would have lost money.

Example: If realized vol was 12% instead of 65%, the loss would have been:

$500M × (0.12² - 0.15²) =$ 500M × (-0.0081) = -$4M

Problem 2: Margin calls during the spike

When VIX hit 82%, mark-to-market P&L swung wildly. The fund needed $50M in additional collateral to avoid forced liquidation.

Lesson: Maintain ample liquidity. Variance swaps have massive intra-period P&L volatility.

Problem 3: Counterparty risk

If the investment bank (counterparty) had failed, the fund would have lost the entire position.

Lesson: Diversify counterparties. Use central clearing when possible.

Dispersion Trading: Long Stocks, Short Index #

Dispersion trading exploits the correlation risk premium: index implied vol includes a premium for correlation. When correlation drops, individual stocks become more volatile relative to the index.

The Strategy #

Trade: Long variance on individual stocks, short variance on index

Payoff drivers:

Correlation: When correlation drops, stocks move independently → higher individual vol, lower index vol
Volatility of volatility: Individual stocks have higher vol-of-vol than index

Example #

Setup:

Long variance swaps on 10 S&P 500 stocks (equal-weighted)
Short variance swap on S&P 500 index
Notional: $1M per stock,$ 10M on index (delta-neutral)

Scenario 1: Correlation drops (50% → 30%)

Individual stocks realize 25% vol each
Index realizes 18% vol (lower due to diversification)
Profit: Individual stocks pay more than index costs

Scenario 2: Correlation spikes (50% → 80%)

Individual stocks realize 22% vol
Index realizes 21% vol (high correlation = index vol approaches stock vol)
Loss: Index costs more than individual stocks pay

Production Results #

Backtest (2015-2023):

Average annual return: 6.2%
Sharpe ratio: 0.85
Max drawdown: -12% (March 2020, correlation spiked)
Win rate: 68% of months profitable

Key insight: Dispersion works in normal markets but fails during crises when correlation spikes to 1.0.

Gamma Scalping: The Delta-Hedging Game #

Gamma scalping is the active management of a long volatility position. You buy options, delta-hedge continuously, and profit from realized vol exceeding implied vol.

The Mechanics #

1. Buy options (long gamma, long vega) 2. Delta-hedge (sell stock to neutralize directional risk) 3. Rehedge daily (as stock moves, delta changes) 4. Profit from gamma (rehedging captures realized vol)

The Math #

Gamma P&L (per day):

\\text{Gamma P&L} = \\frac{1}{2} \\times \\Gamma \\times (\\Delta S)^2

Where:

$\\Gamma$ = option gamma
$\\Delta S$ = stock price change

Theta cost (per day):

\\text{Theta cost} = \\Theta

Net P&L:

\\text{Net P&L} = \\text{Gamma P&L} - \\text{Theta cost}

Breakeven: Gamma P&L = Theta cost when realized vol = implied vol

Profit: Realized vol > implied vol → Gamma P&L > Theta cost

Example #

Setup:

Buy 100 ATM call options on SPY (strike $400, 30 days to expiry)
Implied vol: 20%
Gamma: 0.02
Theta: -$50/day per contract
Delta-hedge: Short 5,000 shares of SPY

Day 1: SPY moves from $400 to$ 405 (+$5)

Gamma P&L: $0.5 × 0.02 × 100 × 5² =$ 250$
Theta cost: $50 × 100 =$ 5,000$
Net P&L: $250 -$ 5,000 = - $4,750$ (theta dominates on low-vol days)

Day 2: SPY moves from $405 to$ 395 (-$10)

Gamma P&L: $0.5 × 0.02 × 100 × 10² =$ 1,000$
Theta cost: $5,000$
Net P&L: $1,000 -$ 5,000 = - $4,000$ (still losing, but less)

Over 30 days: If realized vol averages 25% (higher than 20% implied), cumulative gamma P&L exceeds cumulative theta cost → profit.

Production Lessons #

Lesson 1: Transaction Costs Kill Gamma Scalping #

Problem: Rehedging daily costs money. Bid-ask spreads, commissions, and market impact add up.

Example: Rehedging 10,000 shares daily at 1 bp bid-ask = $10/day. Over 30 days =$ 300. This eats into gamma P&L.

Solution: Optimize rehedging frequency. Don't rehedge every tick—rehedge when delta exceeds a threshold (e.g., 0.1).

Lesson 2: Implied Vol Changes Hurt #

Problem: You buy options at 20% implied vol. Next day, implied vol drops to 18%. Your options lose value (vega loss).

Solution: Hedge vega exposure. Sell other options to neutralize vega. Focus on pure gamma scalping, not vega speculation.

Lesson 3: Variance Swaps Are Cleaner Than Options #

Problem: Options have theta decay, vega risk, and strike selection issues. Variance swaps have none of these.

Solution: Use variance swaps for pure volatility exposure. Use options only when variance swaps are unavailable (small-cap stocks, exotic underlyings).

Conclusion: Volatility is Profitable But Dangerous #

Volatility arbitrage offers attractive returns:

Volatility risk premium: 3-4% annually (sell expensive vol)
Crisis opportunities: $180M profit in 2020 (buy cheap vol before spikes)
Dispersion trades: 6% annual return (exploit correlation premium)

But the risks are real:

Tail risk: Short vol strategies blow up in crashes (see LTCM, 2008, 2020)
Margin calls: Variance swaps have massive intra-period P&L swings
Transaction costs: Gamma scalping is expensive (rehedging costs)

Best practices:

Use variance swaps for pure vol exposure (avoid theta/vega complications)
Diversify: Long and short vol positions, multiple underlyings
Maintain liquidity: Margin calls are inevitable during spikes
Optimize rehedging: Balance gamma P&L vs transaction costs
Monitor correlation: Critical for dispersion trades

The 2020 case study shows both sides: $180M profit for long vol funds, billions in losses for short vol funds. Choose your side wisely.

Volatility Arbitrage: The VIX Spike That Made $180M

Why Volatility is Tradable (and Often Mispriced)#

The Volatility Risk Premium #

Historically, implied vol > realized vol. Why?

1. Insurance premium: Investors pay for downside protection. They overpay for puts, inflating implied vol.

2. Behavioral bias: People overestimate tail risks (crashes). This fear premium inflates option prices.

3. Supply/demand imbalance: More buyers of protection than sellers, pushing prices up.

The data (S&P 500, 1990-2023):

Average implied vol (VIX): 19.5%
Average realized vol: 15.8%
Volatility risk premium: 3.7% (implied - realized)

The opportunity: Sell expensive volatility, delta-hedge, and collect the premium. This works—until it doesn't (see 2020 crash).

When the Premium Reverses #

During crises, the relationship flips:

Implied vol spikes (fear, panic buying of puts)
Realized vol rises but often less than implied
Opportunity: Buy volatility when it's expensive but will mean-revert

Example: March 2020

VIX peaked at 82% (implied vol)
Realized vol peaked at 70%
Trade: Buy variance swaps at 80%, realize 65%, profit from 15% difference

Variance Swaps: Pure Volatility Exposure #

A variance swap is a derivative that pays the difference between realized variance and a strike (implied variance). It's the purest way to trade volatility.

Payoff Structure #

\\text{Payoff} = N \\times (\\sigma_{\\text{realized}}^2 - K_{\\text{var}})

Where:

$N$ = vega notional (dollars per variance point)
$\\sigma_{\\text{realized}}^2$ = realized variance (annualized)
$K_{\\text{var}}$ = strike variance (implied variance at trade inception)

Key property: Payoff is linear in variance, not volatility. This eliminates convexity risk.

Example Trade #

Setup (March 1, 2020):

S&P 500 implied vol: 20%
Variance strike: $K_{\\text{var}} = 0.20^2 = 0.04$
Notional: $N = \\$ 1,000,000$ (vega notional)
Maturity: 3 months

Outcome (June 1, 2020):

Realized vol: 35% (COVID crash)
Realized variance: $0.35^2 = 0.1225$
Payoff: $1,000,000 \\times (0.1225 - 0.04) = \\$ 82,500$

If you were long: Profit $82,500 **If you were short**: Loss$ 82,500

Implementation #

python

1class VarianceSwap:
2    """
3    Variance swap with mark-to-market P&L tracking.
4    """
5    
6    def __init__(self, strike_var, notional, maturity_days):
7        self.strike_var = strike_var
8        self.notional = notional
9        self.maturity_days = maturity_days
10        self.days_elapsed = 0
11        self.realized_var_sum = 0
12    
13    def update(self, daily_return):
14        """Update with new daily return."""
15        self.days_elapsed += 1
16        self.realized_var_sum += daily_return ** 2
17    
18    def realized_variance(self):
19        """Calculate realized variance so far (annualized)."""
20        if self.days_elapsed == 0:
21            return 0
22        return (self.realized_var_sum / self.days_elapsed) * 252
23    
24    def final_payoff(self):
25        """Calculate final payoff at maturity."""
26        realized_var = self.realized_variance()
27        return self.notional * (realized_var - self.strike_var)
28

Production note: Variance swaps are OTC derivatives. You need:

Counterparty (investment bank)
Collateral (margin requirements)
Mark-to-market daily (P&L volatility)

Case Study: The 2020 Volatility Spike #

The Setup #

A volatility arbitrage fund ran a portfolio of variance swaps and dispersion trades:

Long variance swaps: $500M notional on S&P 500 and individual stocks
Short variance swaps: $200M notional on low-vol stocks
Net exposure: Long volatility (betting realized > implied)

Thesis: Implied vol was too low (VIX at 15% in February 2020). A shock would cause realized vol to spike above implied.

The Trade #

February 2020 (pre-crash):

Bought S&P 500 variance swaps at 15% implied vol (strike = 0.0225)
Bought individual stock variance swaps at 18-22% implied vol
Total cost: $5M (upfront premium)

March 2020 (crash):

VIX spiked to 82%
Realized vol: 65% for S&P 500
Individual stocks: 70-80% realized vol

June 2020 (maturity):

S&P 500 variance swap payoff: $500M × (0.65² - 0.15²) =$ 500M × 0.4 = $200M
Individual stock payoffs: $80M
Short positions (hedges): -$100M
Net profit: $180M

What Went Right #

1. Timing: Entered when implied vol was historically low (VIX 15%)

2. Diversification: Long variance on multiple stocks, not just index

3. Hedging: Short variance on low-vol stocks reduced downside

4. Patience: Held through the spike (didn't panic-sell)

What Could Have Gone Wrong #

Problem 1: If realized vol had been lower than implied, the fund would have lost money.

Example: If realized vol was 12% instead of 65%, the loss would have been:

$500M × (0.12² - 0.15²) =$ 500M × (-0.0081) = -$4M

Problem 2: Margin calls during the spike

When VIX hit 82%, mark-to-market P&L swung wildly. The fund needed $50M in additional collateral to avoid forced liquidation.

Lesson: Maintain ample liquidity. Variance swaps have massive intra-period P&L volatility.

Problem 3: Counterparty risk

If the investment bank (counterparty) had failed, the fund would have lost the entire position.

Lesson: Diversify counterparties. Use central clearing when possible.

Dispersion Trading: Long Stocks, Short Index #

Dispersion trading exploits the correlation risk premium: index implied vol includes a premium for correlation. When correlation drops, individual stocks become more volatile relative to the index.

The Strategy #

Trade: Long variance on individual stocks, short variance on index

Payoff drivers:

Correlation: When correlation drops, stocks move independently → higher individual vol, lower index vol
Volatility of volatility: Individual stocks have higher vol-of-vol than index

Example #

Setup:

Long variance swaps on 10 S&P 500 stocks (equal-weighted)
Short variance swap on S&P 500 index
Notional: $1M per stock,$ 10M on index (delta-neutral)

Scenario 1: Correlation drops (50% → 30%)

Individual stocks realize 25% vol each
Index realizes 18% vol (lower due to diversification)
Profit: Individual stocks pay more than index costs

Scenario 2: Correlation spikes (50% → 80%)

Individual stocks realize 22% vol
Index realizes 21% vol (high correlation = index vol approaches stock vol)
Loss: Index costs more than individual stocks pay

Production Results #

Backtest (2015-2023):

Average annual return: 6.2%
Sharpe ratio: 0.85
Max drawdown: -12% (March 2020, correlation spiked)
Win rate: 68% of months profitable

Key insight: Dispersion works in normal markets but fails during crises when correlation spikes to 1.0.

Gamma Scalping: The Delta-Hedging Game #

Gamma scalping is the active management of a long volatility position. You buy options, delta-hedge continuously, and profit from realized vol exceeding implied vol.

The Mechanics #

The Math #

Gamma P&L (per day):

\\text{Gamma P&L} = \\frac{1}{2} \\times \\Gamma \\times (\\Delta S)^2

Where:

$\\Gamma$ = option gamma
$\\Delta S$ = stock price change

Theta cost (per day):

\\text{Theta cost} = \\Theta

Net P&L:

\\text{Net P&L} = \\text{Gamma P&L} - \\text{Theta cost}

Breakeven: Gamma P&L = Theta cost when realized vol = implied vol

Profit: Realized vol > implied vol → Gamma P&L > Theta cost

Example #

Setup:

Buy 100 ATM call options on SPY (strike $400, 30 days to expiry)
Implied vol: 20%
Gamma: 0.02
Theta: -$50/day per contract
Delta-hedge: Short 5,000 shares of SPY

Day 1: SPY moves from $400 to$ 405 (+$5)

Gamma P&L: $0.5 × 0.02 × 100 × 5² =$ 250$
Theta cost: $50 × 100 =$ 5,000$
Net P&L: $250 -$ 5,000 = - $4,750$ (theta dominates on low-vol days)

Day 2: SPY moves from $405 to$ 395 (-$10)

Gamma P&L: $0.5 × 0.02 × 100 × 10² =$ 1,000$
Theta cost: $5,000$
Net P&L: $1,000 -$ 5,000 = - $4,000$ (still losing, but less)

Over 30 days: If realized vol averages 25% (higher than 20% implied), cumulative gamma P&L exceeds cumulative theta cost → profit.

Production Lessons #

Lesson 1: Transaction Costs Kill Gamma Scalping #

Problem: Rehedging daily costs money. Bid-ask spreads, commissions, and market impact add up.

Example: Rehedging 10,000 shares daily at 1 bp bid-ask = $10/day. Over 30 days =$ 300. This eats into gamma P&L.

Solution: Optimize rehedging frequency. Don't rehedge every tick—rehedge when delta exceeds a threshold (e.g., 0.1).

Volatility risk premium: 3-4% annually (sell expensive vol)
Crisis opportunities: $180M profit in 2020 (buy cheap vol before spikes)
Dispersion trades: 6% annual return (exploit correlation premium)

But the risks are real:

Tail risk: Short vol strategies blow up in crashes (see LTCM, 2008, 2020)
Margin calls: Variance swaps have massive intra-period P&L swings
Transaction costs: Gamma scalping is expensive (rehedging costs)

Best practices:

Use variance swaps for pure vol exposure (avoid theta/vega complications)
Diversify: Long and short vol positions, multiple underlyings
Maintain liquidity: Margin calls are inevitable during spikes
Optimize rehedging: Balance gamma P&L vs transaction costs
Monitor correlation: Critical for dispersion trades

The 2020 case study shows both sides: $180M profit for long vol funds, billions in losses for short vol funds. Choose your side wisely.

NordVarg Team

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NordVarg Team

Join 1,000+ Engineers

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