12.1 Options on Stock Indices Currencies and futures Chapter 12 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.1 Options on Stock Indices, Currencies, and Futures Chapter 12
12.2 European Options on Stocks Paying continuous dividends We get the same probability distribution for the stock price at time T in each of the following cases 1. The stock starts at price So and provides a continuous dividend yield g The stock starts at price Soe-qn and provides no dividend yield Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.2 European Options on Stocks Paying Continuous Dividends We get the same probability distribution for the stock price at time T in each of the following cases 1. The stock starts at price S0 and provides a continuous dividend yield = q 2. The stock starts at price S0e -qT and provides no dividend yield
12.3 European Options on Stocks Paving continuous dividends (continued) We can value European options by reducing the stock price to Soe q/ and then behaving as though there is no dividend Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.3 European Options on Stocks Paying Continuous Dividends (continued) We can value European options by reducing the stock price to S0 e –q T and then behaving as though there is NO dividend
12.4 Extension of Chapter 7 Results (Equations 12.1 to 12.3) Lower Bound for calls Xe Lower Bound for puts p≥e"-So oe 9? Put Call Parity C+Xe=p+se9? Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.4 Extension of Chapter 7 Results (Equations 12.1 to 12.3) 0 qT rT c S e Xe − − − Lower Bound for calls: Lower Bound for puts 0 rT qT p Xe S e − − − Put Call Parity 0 rT qT c Xe p S e − − + = +
12.5 Extension of Chapter 11 Results(equations 12.4 and 12.5 soe g n(di-xe n(d2) where d, ln(S0/X)+(r-q+a/2)7 √T n(S/X)+(r-q-a-/2) √T Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.5 Extension of Chapter 11 Results (Equations 12.4 and 12.5) 0 1 2 2 0 1 0 1 0 2 ( ) ( ) ( ) ( ) 2 ln( / ) ( / 2) where 2 ln( / ) ( / 2) q r r T T T T q c S N d Xe N d p Xe N d S N d S X r T d T S X r T d e e q q T − − − − = − = − − − + + = + − − − =