Black-Scholes model
Also called: Black-Scholes-Merton, Black Scholes formula
The Black-Scholes model is a formula for the fair price of a European option using five inputs: the stock price, strike, time to expiry, risk-free interest rate and volatility.
Published by Fischer Black and Myron Scholes in 1973, with Robert Merton, it earned the 1997 Nobel prize in economics. It assumes prices move randomly with constant volatility, which real markets break during crashes, but it remains the standard starting point.
Formula
C = S·N(d1) − K·e^(−rT)·N(d2), where d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d2 = d1 − σ√T
In Journey Shares
Journey Shares prices its options with Black-Scholes, using each person's own measured volatility.
Related terms
- Option premium: An option's premium is the price paid to buy it.
- Implied volatility: Implied volatility is the size of future price swings that an option's market price implies.
- Risk-free rate: The risk-free rate is the return on an investment with no default risk, usually taken as the yield on short-term US Treasury bills.
- Call option: A call option is a contract that gives its buyer the right, but not the obligation, to buy a stock at a set price (the strike) before or at a set date.
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