Bachelier Model Call
Computes the price of a call option with the Bachelier model, which assumes the price follows normal (arithmetic) motion instead of lognormal. Because it allows negative prices, it came back into fashion for pricing options on assets that can go negative, as happened with oil in 2020 and with some spreads. The volatility here is absolute, in price units, not a percentage. The premium is e^(−rT)·[(F−K)·N(d) + σ√T·φ(d)]. Enter the forward price, the strike, the interest rate, the normal volatility and the term.
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Bachelier Model Call
Computes the price of a call option with the Bachelier model, which assumes the price follows normal (arithmetic) motion instead of lognormal. Because it allows negative prices, it came back into fashion for pricing options on assets that can go negative, as happened with oil in 2020 and with some spreads. The volatility here is absolute, in price units, not a percentage. The premium is e^(−rT)·[(F−K)·N(d) + σ√T·φ(d)]. Enter the forward price, the strike, the interest rate, the normal volatility and the term.
The model that accepts negative prices
For decades, the Bachelier model was treated as a historical curiosity, the 1900 work that preceded Black-Scholes but used an assumption considered wrong: prices that move normally, not lognormally. The problem, it was said, is that this allows negative prices. Until April 2020, when oil actually went negative, and the Bachelier model came back from retirement.
The central difference is in the volatility. In Bachelier it's absolute, measured in price units, not a percentage. That makes it the natural choice for pricing options on spreads, rates and any asset that can cross zero, situations where Black-Scholes simply breaks by not allowing negative values.
Enter the forward price, the strike, the interest rate, the normal volatility in price units and the term. The tool returns the call premium. Note that when the forward equals the strike, the price depends almost entirely on volatility and time, in a much simpler form than the lognormal model's.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.