课件希腊字母第15章例子一家银行以30万美元价格出售了10万股不.pdf

The Greek Letters Chapter 15 Options, Futures, and Other Derivatives, 6th Edition, Copyright © John C. Hull 2005 15.1 Example ⚫ A bank has sold for $300,000 a European call option on 100,000 shares of a nondividend paying stock ⚫ S0 = 49, K = 50, r = 5%, s = 20%, T = 20 weeks, m = 13% ⚫ The Black-Scholes value of the option is $240,000 ⚫ How does the bank hedge its risk to lock in a $60,000 profit? Options, Futures, and Other Derivatives, 6th Edition, Copyright © John C. Hull 2005 15.2 Naked Covered Positions Naked position Take no action Covered position Buy 100,000 shares today Both strategies leave the bank exposed to significant risk Options, Futures, and Other Derivatives, 6th Edition, Copyright © John C. Hull 2005 15.3 Stop-Loss Strategy This involves: ⚫ Buying 100,000 shares as soon as price reaches $50 ⚫ Selling 100,000 shares as soon as price falls below $50 This deceptively simple hedging strategy does not work well Options, Futures, and Other Derivatives, 6th Edition, Copyright © John C. Hull 2005 15.4 Delta (See Figure 15.2, page 345) ⚫ Delta (D) is the rate of change of the option price with respect to the underlying Option price Slope = D B A Stock price Options, Futures, and Other Derivatives, 6th Edition, Copyright © John C. Hull 2005 15.5 Delta Hedging ⚫ This involves maintaining a delta neutral portfolio ⚫ The delta of a European call on a stock paying dividends at rate q is N (d 1)e– qT ⚫ The delta of a European put is