12.6 The Expected Return The expected value of the stock price is T e The expected return on the stock is T 儿-2/2 hnE(S/S)]=u Options, Futures, and Other Derivatives, Sth Edition C 2002 by John C. Hull 6
12.6 Options, Futures, and Other Derivatives, 5th Edition © 2002 by John C. Hull 6 The Expected Return • The expected value of the stock price is S0 e mT • The expected return on the stock is m – s 2 /2 = m = m −s ln ( / ) ln( / ) / 2 0 2 0 E S S E S S T T
127 The volatility The volatility of an asset is the standard deviation of the continuously compounded rate of return in 1 year As an approximation it is the standard deviation of the percentage change in the asset price in 1 year Options, Futures, and Other Derivatives, Sth Edition C 2002 by John C. Hull
12.7 Options, Futures, and Other Derivatives, 5th Edition © 2002 by John C. Hull 7 The Volatility • The volatility of an asset is the standard deviation of the continuously compounded rate of return in 1 year • As an approximation it is the standard deviation of the percentage change in the asset price in 1 year
128 Estimating volatility from Historical Data (page 239-41) Take observations So, Sy on at intervals ofτ years 2. Calculate the continuously compounded return in each interval as u =n 3. Calculate the standard deviation s of the u. s y The historical volatility estimate is: 0= Options, Futures, and Other Derivatives, Sth Edition C 2002 by John C. Hull
12.8 Options, Futures, and Other Derivatives, 5th Edition © 2002 by John C. Hull 8 Estimating Volatility from Historical Data (page 239-41) 1. Take observations S0 , S1 , . . . , Sn at intervals of t years 2. Calculate the continuously compounded return in each interval as: 3. Calculate the standard deviation, s , of the ui ´ s 4. The historical volatility estimate is: u S S i i i = − ln 1 t s = s ˆ