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1answer
35 views

Option with payoff $K^2/S^2$

Given the dynamics of the risky asset ( with dividend $q$ ), $$ \frac{dS_t}{S_t}=(\mu-q)dt + \sigma dW_t $$ Consider a european option with payoff, $$ P_0(S) = \begin{cases} 1, & \text{if ...
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3answers
119 views

Understanding $N(d_1)$ and how to use the stock itself as the numeraire?

Assume the stock price follows a geometric Brownian motion Then in Black-Scholes pricing model, $N(d_2)$ is the risk-neutral probability that the option expires in-the-money. However, it is said that ...
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1answer
94 views

Change of numeraire and reference asset

Learning about change of numeraire, and came across this statement: The price of any asset divided by a reference asset (called numeraire) is a martingale (no drift) under the measure associated ...
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0answers
62 views

Value of an option to exchange an asset for another

I'm working out the examples in the paper "Changes of Numeraire, Changes of Probability Measure and Option Pricing", corollary 3. An option of exchanging asset 2 against asset 1 at time T, its time-0 ...
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2answers
169 views

Libor Market Model: numeraire change

I am currently studying the Libor forward market model, and although I get the mechanics behind the main arguments, I still do not have an intuitive idea of what's exactly the objective behind ...
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1answer
272 views

Dealing with the stock numeraire

I don't understand how to express the stock dynamics in the stock numéraire I have $dS_t/S_t = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs ...
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1answer
185 views

Numéraire — couldn't understand the wiki explanation

I'm trying to understand Numéraire concept so am reading the wiki page: I couldn't understand the last formula's 2nd equation: $$ ...
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1answer
356 views

Baye's rule for conditional expectations (Proof review)

The Baye's rule for conditional expectations states $$ E^Q[X|\mathcal{F}]E^P[f|\mathcal{F}]=E^P[Xf|\mathcal{F}] $$ With $f=dQ/dP$ - thus being the Radon-Nikodyn derivative and $X$ being ...
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2answers
500 views

T-Forward Price on risk-neutral measure

i have and question concerning the T-forward price definition on the Robert J.Elliot's book : Mathematics of Financial Markets. On his chapter 9, definition 9.1.3 p.249. He give the formula without ...