# Tag Info

Accepted

### Does numeraire have to be a tradable asset

This is an interesting question that I have asked myself. Below is my take. Let us consider an economy $(\Omega,\mathcal{F},P)$ equipped with a filtration $(\mathcal{F})_{t \geq 0}$ consisting on a ...
• 8,119
Accepted

### How do we determine the "correct measure"?

Recall that any traded asset divided by a numéraire is a martingale under the measure associated to that numéraire. For the 3 interest rates you mention, the natural measure (namely the one that makes ...
• 8,119

### Intuition for Stock Price Numeraire Drift

The drift is the expectation of the return over an infinitesimal interval. Let $Q$ be the risk-neutral measure and $Q^S$ be measure associated with the stock price numeraire defined by \begin{align*} \...
• 21.2k
Accepted

### Intuition for Stock Price Numeraire Drift

As a general principle, I would be wary of economic or financial interpretations of change of measure techniques. Changing numéraires is merely a mathematical tool to ease pricing, see for example the ...
• 8,119
Accepted

### Numeraire correlated to the traded asset

As @ilovevolatility explains, the seminal reference for this matter is Geman, El Karoui & Rochet (1995). We assume none of the assets are dividend paying, and they are strictly positive. There are ...
• 8,119
Accepted

• 1,906

### Change of numeraire to the forward measure in the Vasicek model

Let's assume you are working with 1-dimensional Brownian motion, the instantaneous correlation matrix $\rho$ drops to 1. $C$ and $C'$ both are 1. Now, referring to Proposition 2.3.1, in particular ...
• 31
Accepted

### On Girsanov Theorem to switch from Risk-Neutral to Stock Numeraire

(I might not be answering your question, but I feel this clarification is needed.) A random variable $X$ of $(\Omega, \mathcal{F})$ is a $\mathcal{F}$-measurable function $X : \Omega → \mathbf{R}$. So,...
• 5,043

### Caplet "in arrears" pricing formula

Case I Let us consider a derivative with a payoff $H(L(T_{f},T_{S},T_{E}))$ which is paid at time $T_{p}$. Note that: $T_{f}$ - LIBOR fixing date; $T_{S}$ - LIBOR start date; $T_{E}$ - LIBOR maturity ...
• 83
### Where does the term $\gamma$ come from when moving from measure $\mathbb Q^{N}$ to $\mathbb Q^{M}$?
From your assumption that \begin{align*} dX(t)\cdot d\frac{M(t)}{N(t)} &= \frac{M(t)}{N(t)}X(t)\gamma(t)dt,\\ dX(t) &= X(t)\big(\mu(t)dt+\sigma(t)dW(t)\big), \end{align*} under $\mathbb Q^{M}$,...