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Risk-Neutral Pricing

Value discounted payoffs under a measure that removes risk premia.

Reviewed 2026-08-10TheQuantBateman ResearchReading note
01Intuition

Build the mental model first.

Change the probability lens so tradable assets grow at the funding rate after carry. Then discount the expected payoff.

ONE-LINE DEFINITION

Value discounted payoffs under a measure that removes risk premia.

02Mathematics

Now make it exact.

Vt=BtEQ[BT1XTFt]V_t=B_t\,\mathbb{E}^{\mathbb{Q}}[B_T^{-1}X_T\mid\mathcal{F}_t]
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Every model has a price.

01

Educational conventions are stated explicitly and may simplify market quotation or settlement details.

02

Rates are continuously compounded unless the section says otherwise.

03

Inputs are deterministic in the base model.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Why a quant cares.

This is the common pricing spine of derivatives desks, not a claim that investors are actually risk neutral.

IntuitionMathematicsImplementationDesk risk
05Desk view
FRONT OFFICE VIEW

The hedge has opinions.

Start with the quote convention, then ask which Foundations risk survives the hedge. A number without its convention is merely well-dressed ambiguity.

Ask Bateman about this model
06Related

Continue through the graph.