14.6 DailyⅤ volatilities In option pricing we express volatility as volatility per year In VaR calculations we express volatility as volatility per day year √252 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 14.6 Daily Volatilities • In option pricing we express volatility as volatility per year • In VaR calculations we express volatility as volatility per day day year = 252
14.7 Daily volatility(continued) Strictly speaking we should define o 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 proportional change in one day 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 14.7 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 proportional change in one day
14.8 IBM EXample (p. 343) We have a position worth $10 million in IBM shares The volatility of IBM is 2% per day(about 32% per year) We use m=10and￥99 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 14.8 IBM Example (p. 343) • We have a position worth $10 million in IBM shares • The volatility of IBM is 2% per day (about 32% per year) • We use N=10 and X=99
14.9 IBM 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 2000010=S632456 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 14.9 IBM 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
14.10 IBM 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(0.01)=-233, the Var is 2.33×632456=S1,473,.621 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 14.10 IBM 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(0.01)=-2.33, the VaR is 2.33 632,456 = $1,473,621