MathLiveBlack–Scholes equation
A partial differential equation that the price of a European option must satisfy under the Black–Scholes model, where the option value depends on the underlying asset price and time. Solving it with the appropriate terminal condition gives the option's fair value.
\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2}+rS\frac{\partial V}{\partial S}-rV=0What the symbols mean
| price of the option as a function of underlying asset price S and time t | |
| time | |
| price of the underlying asset | |
| volatility of the underlying asset's returns | |
| risk-free interest rate |
About this formula
- FieldEconomics and finance
- TopicOption pricing
- LevelUniversity
- Also calledBlack–Scholes PDE, Black-Scholes partial differential equation, option pricing PDE, European option pricing equation, Black-Scholes differential equation, option price PDE
- SourceWikidata Q17005676
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