medium · Quantitative Finance stochastic
Girsanov's Theorem identifies the 'market price of risk' as θ = (μ - r)/(σ).
What is the effect of applying the Girsanov transformation to the drift of a stock process?
- It turns a mean-reverting process into a pure driftless random walk under any measure.
- It defines the 'volatility drag' subtracted from the arithmetic to get the geometric mean.
- It removes the risk premium from the drift, shifting it from the physical μ to the risk-neutral r.
- It raises the process's volatility term to compensate for the investor's degree of risk aversion.
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