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The concept of capturing the risk tolerance of an investor by documenting how much risk is acceptable for a given return may be applied to a variety of decision analysis problems. MPT uses historical variance as a measure of risk, but portfolios of assets like major projects do not have a well-defined "historical variance".
CBOE Volatility Index (VIX) from December 1985 to May 2012 (daily closings) In finance, volatility (usually denoted by "σ") is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices.
Volatility risk is the risk of an adverse change of price, due to changes in the volatility of a factor affecting that price. It usually applies to derivative instruments , and their portfolios, where the volatility of the underlying asset is a major influencer of option prices .
The investor's utility function is concave and increasing, due to their risk aversion and consumption preference. Analysis is based on single period model of investment. An investor either maximizes their portfolio return for a given level of risk or minimizes their risk for a given return. [2] An investor is rational in nature.
Volatility is the most important input in risk management models and pricing models. Uncertainty on volatility leads to model risk. Derman believes that products whose value depends on a volatility smile are most likely to suffer from model risk. He writes "I would think it's safe to say that there is no area where model risk is more of an ...
Starting from a constant volatility approach, assume that the derivative's underlying asset price follows a standard model for geometric Brownian motion: = + where is the constant drift (i.e. expected return) of the security price , is the constant volatility, and is a standard Wiener process with zero mean and unit rate of variance.