# Questions tagged [numerairechange]

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### Risk neutral measure & change in numeraire

There are two questions about risk neutral and change in numeraire I am not so sure if my answer is correct. Question 01: Risk neutral Let says I have 2 risky asset A and B. Each has stochastics ...
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### Change of numéraire for non-Normal distributions

I'm looking for a resource, a book or an article, that describes the framework of change of numéraire in a broader context than just Brownian motions or Normal distributions. I'm only really ...
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### Hull Martingales and measures problem 27.16 7e?

Here's a question from Hull's Options Futures and Other derivatives which I'd appreciate if someone helped me to clarify. The question is from the chapter "Martingales and Measures" Suppose that the ...
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### Show a process is Martingale

$$Z(t)=(\frac{S(t)}{H})^p$$where $S$ has a standard Black-scholes Dynamics for a stock, $H$ is a postive constant and $p =1 - \frac{2r}{\sigma^2}$. How can I show that $Z(t)/Z(0)$ is a postive Q-...
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### Equivalent Martingale Measure(EMM) of Inverse of Stock Price

I met this question says how to price a vanilla call option $C(St,t,T,K) = \frac{1}{S_T}$which pays the inverse of a stock $V_{t} = \frac{1}{S_{t}}$ at maturity if the stock price follows a geometric ...
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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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### 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 ...
### How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?
I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs $$(S_T f(S_T))^+$$ How do I express the stock dynamics using the ...