7.1 Properties of Stock Option Prices Chapter 7 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 7.1 Properties of Stock Option Prices Chapter 7
72 Notation European call C: American Call option option price price p: European put P: American Put option option price prIce So: Stock price today ST: Stock price at time T X: Strike price D: Present value of T: Life of option dividends during options :Motl波动率)ofe stock price r: Risk-free rate for maturity T with cont comp Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 7.2 Notation • c : European call option price • p : European put option price • S0 : Stock price today • X : Strike price • T : Life of option • : Volatility(波动率) of stock price • C : American Call option price • P : American Put option price • ST :Stock price at time T • D : Present value of dividends during option’s life • r : Risk-free rate for maturity T with cont comp
73 Effect of Variables on Option Pricing (Table 7. 1, page 169) Variable c P 十 T 十 D 十 十 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 7.3 Effect of Variables on Option Pricing (Table 7.1, page 169) Variable c p C P S0 X T r D + + – + ? ? + + + + + + + – + – – – – + – + – +
7.4 American vs European Options An American option is worth at least as much as the corresponding European option P≥ Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 7.4 American vs European Options An American option is worth at least as much as the corresponding European option C c P p
7.5 Upper bound for Options prices It should be relatively easy to see that C<So and c≤S Otherwise, you could make a risk-less profit by buying the stock and selling the option Likewise p≤ Xe-ri and P≤X Otherwise, you could make a risk-less profit by selling the option and investing the proceeds at r Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, Shanghai Normal University 7.5 Upper Bound for Options Prices • It should be relatively easy to see that c S0 and C S0 Otherwise, you could make a risk-less profit by buying the stock and selling the option • Likewise, p Xe-rT and P X Otherwise, you could make a risk-less profit by selling the option and investing the proceeds at r