Black-Scholes Financial Crisis

Math Online Tom Circle

Black-Scholes Equation (1997 Nobel Economics)

Use: Pricing Derivatives (Options): calculate the value of an option before it matures.

1/2 (σS)².∂²V/∂S² + rS.∂V/∂S + (∂V/∂T – rV) =…

Without last 2 terms=> heat equation !

Time T
Price S of the commodity
Price V of the derivative
Risk free interest r (govt bond)
Volatility = σ of the stock = standard deviation

Assumptions: (Arbitrage Pricing Theory)
No transaction costs
No limit on short-selling
Possible to borrow/lend at risk-free rate

Market prices behave like Brownian motion: constant in rate of drift and market volatility

Put option: right to sell at a specific time for an agreed price if you wish.
Call option: right to buy at a specific time for an agreed price if you wish.

One Black-Sholes formula each for Put and Call respectively.

Derivative was invented in 1900 by Mr. Bachelier, a French PhD student of Poincaré, the Mathematics…

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