Drift Lives in the Measure: An Intuitive Look at Girsanov's Theorem

Wed, 06 May 2026 00:00:00 +0000

Why This Matters

We want to price a derivative. Under the real world measure $\mathbb{P}$, we face two problems. First, we do not know the true drift $\mu$ of the underlying, and historical estimates are notoriously unreliable. Second, even if we knew $\mu$, taking the expected payoff under $\mathbb{P}$ would still not give the market price. Risky cash flows must be discounted more heavily than guaranteed ones because investors are risk averse. Pricing under $\mathbb{P}$ requires both the true probabilities of outcomes and a model for how the market prices risk. Both are fundamentally unobservable. So what can we do?

How Randomness Solves a Deterministic Equation: An Intuitive Look at the Feynman–Kac Theorem

Tue, 28 Apr 2026 00:00:00 +0000

Why This Matters

The first time I encountered the Feynman-Kac theorem, I found it fascinating but unintuitive. The theorem claims that a deterministic PDE and the expectation of a stochastic process are two representations of the same object. A PDE is smooth and deterministic. A stochastic expectation involves randomness, probability measures, and averaging over infinitely many paths. How could these be the same thing? I understood the steps of the proof, but I still didn’t have a clear intuition for why this equivalence should exist.

Risk-Neutral Pricing on Inflection Quant

Drift Lives in the Measure: An Intuitive Look at Girsanov's Theorem

Why This Matters

How Randomness Solves a Deterministic Equation: An Intuitive Look at the Feynman–Kac Theorem

Why This Matters