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The Bachelier model (normal model) assumes the underlying follows an arithmetic Brownian motion with normally distributed returns, rather than the lognormal distribution of Black-Scholes. It allows negative prices and is used for interest rate options and spread options.
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Key takeawayBachelier (normal) volatility quotes are standard for interest rate options and were used for crude oil options when prices went negative in 2020. Premium sellers in commodities should know whether quotes use normal or lognormal vol to avoid mispricing their positions.
💡 Why It Matters
The Bachelier model became critical in 2020 when crude oil went negative, breaking Black-Scholes (which assumes lognormal prices that cannot be negative). Premium sellers in commodities must know which volatility convention their market uses.
⚙ How It Works
Bachelier assumes prices follow arithmetic Brownian motion with normally distributed prices (not returns). Volatility is quoted in absolute terms (e.g., $5 per barrel) rather than percentage terms (e.g., 30%). The model allows negative prices, making it suitable for interest rates and certain commodities.
📋 Example
WTI crude oil at $70/barrel with Bachelier vol of $15/barrel. This means the one-sigma 30-day expected range is roughly $55-$85 ($70 +/- $15/sqrt(12)). The same vol in lognormal terms would be approximately 21% ($15/$70). Premium sellers must use the correct convention when comparing vol across markets.
⚠ Common Mistakes
Traders compare Bachelier (normal) vol directly to Black-Scholes (lognormal) vol. Bachelier vol of $5 on a $100 stock is not the same as 5% lognormal vol. The conversion depends on the price level and is approximately: normal vol = lognormal vol * forward price. Mixing up conventions leads to mispriced trades.
❓ FAQ
What is Bachelier Model?
The Bachelier model (normal model) assumes the underlying follows an arithmetic Brownian motion with normally distributed returns, rather than the lognormal distribution of Black-Scholes. It allows negative prices and is used for interest rate options and spread options.
Why does Bachelier Model matter for premium sellers?
Bachelier (normal) volatility quotes are standard for interest rate options and were used for crude oil options when prices went negative in 2020. Premium sellers in commodities should know whether quotes use normal or lognormal vol to avoid mispricing their positions.
How does Bachelier Model work?
Bachelier assumes prices follow arithmetic Brownian motion with normally distributed prices (not returns). Volatility is quoted in absolute terms (e.g., $5 per barrel) rather than percentage terms (e.g., 30%). The model allows negative prices, making it suitable for interest rates and certain commodities.
What are common mistakes with Bachelier Model?
Traders compare Bachelier (normal) vol directly to Black-Scholes (lognormal) vol. Bachelier vol of $5 on a $100 stock is not the same as 5% lognormal vol. The conversion depends on the price level and is approximately: normal vol = lognormal vol * forward price. Mixing up conventions leads to mispriced trades.
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