Risk-neutral measure

Quantitative Finance Glossary

Probability measure mathbbQ — equivalent to the physical measure mathbbP but reweighted — under which the discounted price of every traded asset is a martingale: S_t / B_t = mathbbE^mathbbQ[S_T / B_T mid mathcalF_t], where B_t is the money-market numeraire. By FTAP-I, mathbbQ exists iff the market is arbitrage-free; by FTAP-II it is unique iff the market is complete. Constructed via Girsanov by shifting GBM drift from μ to r with Radon-Nikodým density involving the market price of risk θ = (μ - r)/σ. Not the 'true' measure — a pricing artefact under which risk premia are absorbed into the numeraire.

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