# Questions tagged [numeraire]

Numeraire is a unit of account in which all other assets in a given model are denominated. Most importantly, one can borrow and lend at the Numeraire rate.

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### Convexity adjustment when payment if after interest natural term?

I've been working with a convexity adjustment for an interest rate payoff and the next question came to me: The usual problem that gives rise to the convexity adjustment I'm referring to is as ...
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### Is the money market account (MMA) numeraire and the forward measure equivalent?

Suppose we have a risk-neutral measure $\tilde{\mathbb{P}}$. The money market account is given as $M(t) = e^{\int^t_0 R(s) ds}$, while the price of the zero-coupon bond at time $t$ that matures at $T$ ...
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### The relation between exchange rate SDE and respective interest rates

The exchange rate between a domestic currency money market and a foreign currency money market can be expressed as $$dQ(t) = (r_d - r_f)Q(t)dt + \sigma Q(t)d\tilde{W}(t)$$ where $r_d$ is the ...
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### Deriving Black Scholes PDE under stock as a numeraire

There are many ways to derive the Black Scholes PDE. The Martingale way would be to demand the option price is driftless according to particular measures. Below I derive the correct PDE using the bank ...
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### Is the delta of a call option a martingale using the stock numeraire?

For example in the Black_scholes case the delta N(d1) does appear to be equal to the expectation (under the stock measure) of the delta at expiration, which is the expectation of I(S(T)>K). Is ...
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