衍生工具与风险管理第5章课件.pptVIP

D. M. Chance An Introduction to Derivatives and Risk Management, 6th ed. Chapter 5: Option Pricing Models:The Black-Scholes Model When I first saw the formula I knew enough about it to know that this is the answer. This solved the ancient problem of risk and return in the stock market. It was recognized by the profession for what it was as a real tour de force. Merton Miller Trillion Dollar Bet, PBS, February, 2000 Important Concepts in Chapter 5 The Black-Scholes option pricing model The relationship of the model’s inputs to the option price How to adjust the model to accommodate dividends and put options The concepts of historical and implied volatility Hedging an option position Origins of the Black-Scholes Formula Brownian motion and the works of Einstein, Bachelier, Wiener, It? Black, Scholes, Merton and the 1997 Nobel Prize The Black-Scholes Model as the Limit of the Binomial Model Recall the binomial model and the notion of a dynamic risk-free hedge in which no arbitrage opportunities are available. Consider the AOL June 125 call option. Figure 5.1, p. 131 shows the model price for an increasing number of time steps. The binomial model is in discrete time. As you decrease the length of each time step, it converges to continuous time. The Assumptions of the Model Stock Prices Behave Randomly and Evolve According to a Lognormal Distribution. See Figure 5.2a, p. 134, 5.2b, p. 135 and 5.3, p. 136 for a look at the notion of randomness. A lognormal distribution means that the log (continuously compounded) return is normally distributed. See Figure 5.4, p. 137. The Risk-Free Rate and Volatility of the Log Return on the Stock are Constant Throughout the Option’s Life There Are No Taxes or Transaction Costs The Stock Pays No Dividends The Options are European A Nobel Formula The Black-Scholes model gives the correct formula for a European call under these assumptions. The model is derived with complex mathematics but is easily understandable. The