Black-Scholes Financial Crisis

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) = 0

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 of Financial prediction on stock market, based on Brownian Motion Theory of gas from Einstein. Poincaré was not impressed, gave the thesis only mention honorable (credit) , not trés honorable (distinction).

The problem of this Black-Sholes formula is the assumption being too ‘academic’, assume no financial ‘Fat Tail’, but sadly everybody believes in it and uses it blindly, which causes the recent Financial Crisis.


5 thoughts on “Black-Scholes Financial Crisis

  1. Pingback: Mathematics produced IT billionaires | Math Online Tom Circle

  2. Pingback: Why do people hate mathematics? | Math Online Tom Circle

    • Black-sholes formula used quite common in the corporate world, affecting employees in various ways:

      1. When M&A (Merger & Acquisition) happens, say, your company Q being acquired by M company. Your invested Q stock option (ie not yet mature to sell) will be converted to M shares using the Black-Sholes formula.

      2. Derivatives Trading: Blindly trading causes a colleague to lose U$30 million in one night; also an oil company CEO put his oil derivatives position exposed to U$ 500 million loss. Both cases due to the Black-Sholes formula, resulting the colleague being fired and the other CEO jailed for 6 years.

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