16.6 Time horizon Instead of calculating the 10-day, 99% VaR directly analysts usually calculate a 1-day 99% VaR and assume 10- day VaR=√10×1- day VaR This is exactly true when portfolio changes on successive days come from independent identically distributed normal distributions Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.6 Time Horizon • Instead of calculating the 10-day, 99% VaR directly analysts usually calculate a 1-day 99% VaR and assume • This is exactly true when portfolio changes on successive days come from independent identically distributed normal distributions 10 - day VaR = 10 1- day VaR
16.7 Historical simulation (See Table 16.1 and 16.2) Create a database of the daily movements in all market variables The first simulation trial assumes that the percentage changes in all market variables are as on the first day The second simulation trial assumes that the percentage changes in all market variables are as on the second day and so on Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.7 Historical Simulation (See Table 16.1 and 16.2) • Create a database of the daily movements in all market variables. • The first simulation trial assumes that the percentage changes in all market variables are as on the first day • The second simulation trial assumes that the percentage changes in all market variables are as on the second day • and so on
16.8 Historical simulation continued Suppose we use m days of historical data Let vi be the value of a variable on day i There are m-1 simulation trials The ith trial assumes that the value of the market variable tomorrow (i.e, on day m+1)is Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.8 Historical Simulation continued • Suppose we use m days of historical data • Let vi be the value of a variable on day i • There are m-1 simulation trials • The ith trial assumes that the value of the market variable tomorrow (i.e., on day m+1) is i−1 i m v v v
169 The Model-Building Approach The main alternative to historical simulation is to make assumptions about the probability distributions of return on the market variables and calculate the probability distribution of the change in the value of the portfolio analytically This is known as the model building approach or the variance-covariance approach Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.9 The Model-Building Approach • The main alternative to historical simulation is to make assumptions about the probability distributions of return on the market variables and calculate the probability distribution of the change in the value of the portfolio analytically • This is known as the model building approach or the variance-covariance approach
16.10 Daily 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, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 16.10 Daily Volatilities • In option pricing we express volatility as volatility per year • In VaR calculations we express volatility as volatility per day 252 year day =