This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 Valuing Stock Options: The BlackScholesMerton Model Chapter 13 1 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The BlackScholesMerton Random Walk Assumption Consider a stock whose price is S In a short period of time of length t the return on the stock ( S / S ) is assumed to be normal with mean t and standard deviation is expected return and is volatility t 2 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Lognormal Property These assumptions imply ln S T is normally distributed with mean: and standard deviation : Because the logarithm of S T is normal, S T is lognormally distributed T S ) 2 / ( ln 2  + T 3 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Lognormal Property continued where [ m , v ] is a normal distribution with mean m and variance v [ ] [ ] T T S S T T S S T T 2 2 2 2 , ) 2 ( ln , ) 2 ( ln ln   + or 4 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Lognormal Distribution E S S e S S e e T T T T T ( ) ( ) ( ) = =  2 2 2 1 var 5 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 The Expected Return The expected value of the stock price is S e T The return in a short period t is t But the expected return on the stock with continuous compounding is 2 /2 This reflects the difference between arithmetic and geometric means 6 Fundamentals of Futures and Options Markets, 7th Ed, Ch 13, Copyright John C. Hull 2010 7 Mutual Fund Returns (See Business Snapshot 13.1 on page 294)Snapshot 13....
View
Full
Document
This note was uploaded on 08/22/2011 for the course FINANCE 422 taught by Professor Jiang during the Spring '11 term at University of Arizona Tucson.
 Spring '11
 Jiang
 Derivatives, Options

Click to edit the document details