19. Black-Scholes Formula, Risk-neutral Valuation
The Black–Scholes pricing formula in the quantum context
Du kanske gillar. Spara som favorit. Skickas inom vardagar. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergraduate and MBA option pricing at Indiana University winning many teaching awards , was an independent consultant to the New York Stock Exchange, worked as an asset management practitioner in London, and has traded options for over 15 years. This unique mixture of learning, teaching, consulting, practice, and trading is reflected in every page.
An option is a financial contract whose value depends on that of an underlying asset such as a company stock. The Black-Scholes model for option pricing, published in , revolutionized the financial industry by introducing a no-arbitrage paradigm for valuing uncertainty and hedging against risk. This simple model assumes that the underlying stock price follows a stochastic Brownian motion process with a constant variance rate, or volatility. This assumption restricts the stock price to follow a log-normal distribution. To allow for more flexible stock price distributions observed in the real market, several new methods have been recently proposed. Jarrow and Rudd  proposed to price options based on an estimated future profile for the stock price distribution. Rubinstein  introduced a binomial tree model of possible stock price movements consistent with current market prices.