Sidebar on Black-Scholes for Risk Management
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Description: Working paper by Philip H. Dybvig and William J. Marshall.
Sidebar on Black-Scholes for Risk Management Working Paper by Dybvig and Marshall the Good, the Bad, and the Ugly Philip H. Dybvig and William J. Marshall The Black-Scholes Option Pricing Model The precursor of all modern option pricing models was developed by Fischer Black and Myron Scholes.//footnote: Black, F. and M. Scholes, "The Pricing of Options and Corporate Liabilities" Journal of Political Economy 81, 1973, 637-654.// The main result is an option-pricing formula based on simple and reasonable assumptions in a continuous-time model. The remarkable thing about the result is that it relies on the absence of arbitrage, and part of the proof is a formula that specifies a trading strategy in the underlying stock and the riskless bond that will replicate the payoff of the option at the end.//footnote: For more discussion of why this makes sense, see Rubinstein, M. and H. Leland, ``Replicating Options with Positions in Stock and Cash,'' Fianancial Analysts Journal, Jan-Feb 1995, 149-160.// If the option is priced differently in the economy, buying or selling the option and following either the trading strategy or the trading strategy in reverse will make money! Using the same sort of analysis gives the trading strategy that will hedge the financial risk in a firm's cash flows.
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