medium · Quantitative Finance stochastic
In the Heston model, the variance process v_t is not a traded asset.
How does this affect the Girsanov change of measure to the risk-neutral measure Q?
- An additional market price of risk for the variance must be assumed or calibrated, as it is not uniquely determined by the stock price.
- The market price of risk attached to variance is automatically zero under any correctly specified arbitrage-free model.
- The variance process itself becomes fully deterministic once we switch over from mathbbP to the risk-neutral pricing measure Q.
- The variance drift stays exactly the same as under mathbbP, since only directly traded assets have their drifts shifted by Girsanov's theorem.
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