16.11 Daily volatility continued Strictly speaking we should define od as the standard deviation of the continuously compounded return in one day In practice we assume that it is the standard deviation of the percentage change in one day Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.11 Daily Volatility continued • Strictly speaking we should define day as the standard deviation of the continuously compounded return in one day • In practice we assume that it is the standard deviation of the percentage change in one day
16.12 Microsoft Example We have a position worth $10 million in Microsoft shares The volatility of Microsoft is 2% per day (about 32% per year We use m=10and￥99 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.12 Microsoft Example • We have a position worth $10 million in Microsoft shares • The volatility of Microsoft is 2% per day (about 32% per year) • We use N=10 and X=99
16.13 Microsoft Example continued The standard deviation of the change in the portfolio in 1 day is $200,000 The standard deviation of the change in 10 days is 200,000√10=$632,456 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.13 Microsoft Example continued • The standard deviation of the change in the portfolio in 1 day is $200,000 • The standard deviation of the change in 10 days is 200,000 10 = $632,456
16.14 Microsoft Example continued We assume that the expected change in the value of the portfolio is zero (this is OK for short time periods We assume that the change in the value of the portfolio is normally distributed Since N(2.33 =0.01, the VaR is 2.33×632456=$1.473,621 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.14 Microsoft Example continued • We assume that the expected change in the value of the portfolio is zero (This is OK for short time periods) • We assume that the change in the value of the portfolio is normally distributed • Since N(–2.33)=0.01, the VaR is 2.33 632,456 = $1,473,621