Scaling in Financial Data and in Physics
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The Black—Scholes equation for option prices is based on a number of hypotheses and assumptions. Subsequent price changes were assumed to be statistically independent, and their probability distribution was assumed to be the normal distribution. Moreover, the risk-free interest rate r and the volatility σ were assumed constant (in the simplest version of the theory). In this chapter, we will examine financial data in the light of these assumptions, develop more general stochastic processes, and emphasize the parallels between financial data and physics beyond the realm of Brownian motion.
KeywordsStochastic Volatility Hurst Exponent Random Matrix Theory Geometric Brownian Motion Stochastic Volatility Model
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