Black-76 Call Price (Options on Futures)
Works out the premium of a European call option on futures with the Black-76 model, the variant of Black-Scholes used when the underlying is a futures or forward contract. The price is e^(−rT)·[F·N(d1) − K·N(d2)], with d1 and d2 built from the futures price, the strike, the volatility and the term. Because the future already embeds the cost of carry, the discount hits both terms and the interest rate never shows up inside d1. It is the standard for options on commodities, indices and rates. Enter the futures price, the strike, the risk-free rate, the term in years and the annual volatility.
Result
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Black-76 Call Price (Options on Futures)
Works out the premium of a European call option on futures with the Black-76 model, the variant of Black-Scholes used when the underlying is a futures or forward contract. The price is e^(−rT)·[F·N(d1) − K·N(d2)], with d1 and d2 built from the futures price, the strike, the volatility and the term. Because the future already embeds the cost of carry, the discount hits both terms and the interest rate never shows up inside d1. It is the standard for options on commodities, indices and rates. Enter the futures price, the strike, the risk-free rate, the term in years and the annual volatility.
When to reach for Black-76 instead of Black-Scholes
The original Black-Scholes was built for stock options, where the spot price is what counts. But a large slice of the options market doesn't trade on spot at all, it trades on futures: oil, interest rates, the index, coffee. That's where Black-76 comes in. Fischer Black published the tweak in 1976, and the change is subtle but decisive: instead of the spot price, the formula revolves around the futures price, which already bakes in the cost of carrying the asset to expiry.
Two things shift in practice. The discount factor e^(−rT) now multiplies the whole expression, not just the strike, and the interest rate drops out of d1. What you get back is the fair call premium, roughly what the right to buy that future at the agreed strike is worth. Set that figure against what the pit is actually charging and you get a read on whether the option looks rich or cheap.
The inputs are the usual suspects for this kind of calculation: futures price, strike, risk-free rate, term in years and annual volatility. Keep in mind the model assumes constant volatility and European exercise, so treat the number as a reference rather than gospel. Real markets have a volatility smile and other quirks no closed-form formula captures in full.
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Black-76 Put Price (Options on Futures)
Works out the premium of a European put option on futures with the Black-76 model, the Black-Scholes version for when the underlying is a future or forward contract. The price is e^(−rT)·[K·N(−d2) − F·N(−d1)], where d1 and d2 come from the futures price, the strike, the volatility and the term. The future already carries the cost of carry, so the discount factor multiplies both terms and interest does not enter d1. It applies to puts on commodities, indices and rates. Enter the futures price, the strike, the risk-free rate, the term in years and the annual volatility.
Black-Scholes-Merton Call (Dividends)
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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.