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Research Library: When You Cannot Hedge Continuously: The Corrections to Black-Scholes (1998)

March 18, 2012 by MoneyScience   Comments (0)

Emanuel Derman Goldman Sach Quantitative Strategies Research Notes Introduction The insight behind the Black-Scholes formula for options valuation is the recognition that, if you  know the future volatility of a stock, you can  replicate an option payoff exactly by a continuous  rebalancing of a portfolio  consisting of the  underlying stock and a risk-free bond. If no  arbitrage is possible, then the value of the option  should be the cost of the...

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Research Library: On the Black-Scholes Equation: Various Derivations (pdf)

March 18, 2012 by MoneyScience   Comments (0)

Manabu Kishimoto Abstract One of the significant equations in financial mathematics is the Black-Scholes equation, a partial differential equation that governs the value of financial derivatives, such as options. In this paper, various derivations of the Black-Scholes equation are illustrated. Throughout these derivations, core concepts in financial mathematics, such as Ito’s lemma, the replicating portfolio, the CAPM, arbitrage pricing, risk-neutral pricing, and put-call parity, are...

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Research Library: The Pricing of Options and Corporate Liabilities (pdf, 1973)

March 18, 2012 by MoneyScience   Comments (0)

Fischer Black University of Chicago Myron Scholes Massachusetts Institute of Technology Journal of Political Economy, 1973 Abstract If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and underlying stocks. Using this principal, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the...

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The Black-Scholes Formula: A Documentary

March 18, 2012 by MoneyScience   Comments (0)

This documentary from the BBC's Horizon program charts the history behind perhaps the most important formula in finance: the Black-Scholes-Merton options pricing model. Two of its creators were awarded the Nobel Prize in Economics in 1997 and only a year later their hedge fund Long Term Capital Management (LTCM) had collapsed with staggering losses of $100 billion due to significant leverage of the strategy. The Black-Scholes Formula was derived by observing that an investor can...

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