INVESTMENTS 投资学 （博迪BODIE, KANE, MARCUS）Chap021 Option Valuation_精品.pptVIP

21-* Figure 21.10 Profit on a Protective Put Strategy 21-* Figure 21.11 Hedge Ratios Change as the Stock Price Fluctuates 21-* Hedging On Mispriced Options Option value is positively related to volatility. If an investor believes that the volatility that is implied in an option’s price is too low, a profitable trade is possible. Profit must be hedged against a decline in the value of the stock. Performance depends on option price relative to the implied volatility. 21-* Hedging and Delta The appropriate hedge will depend on the delta. Delta is the change in the value of the option relative to the change in the value of the stock, or the slope of the option pricing curve. Delta = Change in the value of the option Change of the value of the stock 21-* Example 21.6 Speculating on Mispriced Options Implied volatility = 33% Investor’s estimate of true volatility = 35% Option maturity = 60 days Put price P = $4.495 Exercise price and stock price = $90 Risk-free rate = 4% Delta = -.453 21-* Table 21.3 Profit on a Hedged Put Portfolio 21-* Example 21.6 Conclusions As the stock price changes, so do the deltas used to calculate the hedge ratio. Gamma = sensitivity of the delta to the stock price. Gamma is similar to bond convexity. The hedge ratio will change with market conditions. Rebalancing is necessary. 21-* Delta Neutral When you establish a position in stocks and options that is hedged with respect to fluctuations in the price of the underlying asset, your portfolio is said to be delta neutral. The portfolio does not change value when the stock price fluctuates. 21-* Table 21.4 Profits on Delta-Neutral Options Portfolio 21-* Empirical Evidence on Option Pricing The Black-Scholes formula performs worst for options on stocks with high dividend payouts. The implied volatility of all options on a given stock with the same expiration date should be equal. Empirical test sho