VolatilityChapter 10RiskManagementandFinanciallnstitutions3e,Chapter10,CopyrightJohnC.Hull2012
Volatility Chapter 10 Risk Management and Financial Institutions 3e, Chapter 10, Copyright © John C. Hull 2012 1
Definition of VolatilitySuppose that S, is the value of a variable onday i. The volatility per day is the standarddeviation of ln(S, /Si-1) Normally days when markets are closed areignored in volatility calculations (see BusinessSnapshot 10.1, page 207) The volatility per year is /252 times the dailyvolatilityVariance rate is the square of volatility2RiskManagementandFinancialInstitutions3e,Chapter10,CopyrightJohnC.Hull 2012
Definition of Volatility ⚫ Suppose that Si is the value of a variable on day i. The volatility per day is the standard deviation of ln(Si /Si-1 ) ⚫ Normally days when markets are closed are ignored in volatility calculations (see Business Snapshot 10.1, page 207) ⚫ The volatility per year is times the daily volatility ⚫ Variance rate is the square of volatility Risk Management and Financial Institutions 3e, Chapter 10, Copyright © John C. Hull 2012 2 252
ImpliedVolatilities Of the variables needed to price an optionthe one that cannot be observed directly isvolatility We can therefore imply volatilities frommarket prices and viceversa3RiskManagementandFinancialInstitutions3e,Chapter10,CopyrightJohnC.Hull2012
Implied Volatilities ⚫ Of the variables needed to price an option the one that cannot be observed directly is volatility ⚫ We can therefore imply volatilities from market prices and vice versa Risk Management and Financial Institutions 3e, Chapter 10, Copyright © John C. Hull 2012 3
ViXIndex:AMeasureoftheImpliedVolatility of the S&P500 (Figure10.1, page208)9080706050403020W100Jan-2005Jan-2008Jan-2010Jan-2004Jan-2006Jan-2007Jan-2009Jan-2011RiskManagementandFinancialInstitutions3e,Chapter10,CopyrightJohnC.Hull20124
VIX Index: A Measure of the Implied Volatility of the S&P 500 (Figure 10.1, page 208) Risk Management and Financial Institutions 3e, Chapter 10, Copyright © John C. Hull 2012 4
AreDailyChangesinExchangeRatesNormally Distributed? Table 10.1, page 209Real World (%)Normal Model (%)>1 SD31.7325.045.274.55>2SD1.340.27>3SD0.290.01>4SD>5SD0.080.000.030.00>6SD5RiskManagementandFinancial Institutions3eChapter10,CopyrightJohnC.Hull2012
Are Daily Changes in Exchange Rates Normally Distributed? Table 10.1, page 209 Real World (%) Normal Model (%) >1 SD 25.04 31.73 >2SD 5.27 4.55 >3SD 1.34 0.27 >4SD 0.29 0.01 >5SD 0.08 0.00 >6SD 0.03 0.00 Risk Management and Financial Institutions 3e, Chapter 10, Copyright © John C. Hull 2012 5