Questions tagged [equivalent-measure]

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Why the Esscher transform is the right transform for pricing formula?

A Wiener process has infinitely many states of the world at any time step. Does that not mean that there are infinitely many EMM's for any model that uses the Wiener process? But then if there is only ...
user53249's user avatar
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7 votes
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Let $\mathbb{P} \sim \mathbb{Q} \sim \mathbb{R}$ be equivalent probability measures on some measurable space

Let $\mathbb{P} \sim \mathbb{Q} \sim \mathbb{R}$ be equivalent probability measures on some measurable space $(\Omega, \mathcal{F})$, and let $\mathcal{G} \subset \mathcal{F}$ be a sub- $\sigma$-...
codelearner's user avatar
2 votes
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Equivalent local martingale measure vs. equvalent martingale measure in a Brownian setup

Assume you have the standard financial market built up of a Brownian motion. I have seen some books say that an equivalent local martingale measure imples no arbitrage, and some say that an equivalent ...
user394334's user avatar
4 votes
2 answers
233 views

Poisson process under equivalent martingale measure

I have a stochastic process $N(t)$ which is equal to $n$ with probability $P\{N(t) = n\}=\frac{\left(\lambda t \right)^{n}}{n!}e^{-\lambda t }$ where $t$ represents the time period. In other words, ...
user9875321__'s user avatar
5 votes
1 answer
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Is first order stochastic dominance conserved under change of measure?

As the title states, my question is whether first order stochastic dominance is conserved under change of measure, for instance from the $\mathbb{P}$ measure to $\mathbb{Q}$ measure and change of ...
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3 votes
2 answers
203 views

Change of measure for a stochastic process to be a martingale

$\text { Give a measure change so that } X_{t}=e^{B_{t}}\left(B_{t}-t / 2\right) \text { is a martingale, } 0 \leq t \leq T$ My attempt Using Ito's lemma on $X_{t}$ we get: $-\frac{e^{B t}}{2} d t+\...
codelearner's user avatar
3 votes
1 answer
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EMM for Bachelier model

The stock price is assumed to evolve as $S_{t}=S_{0}+\mu t+\sigma B_{t}$, where $S_{0}>0, \mu>0$ and the process $B_{t}$ is Brownian motion. The saving account is assumed to be $\beta_{t}=e^{r t}...
codelearner's user avatar
1 vote
1 answer
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How to prove that the following is still a Brownian motion [closed]

Given a Brownian motion $B_t$ on a filtered probability space, how can I prove that $W_t=B_t+\alpha t$ is still a Brownian motion, with $\alpha \in \mathbb{R}$? Is it always true? Do I need necessarly ...
RedLapm's user avatar
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3 votes
0 answers
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Is $E_t^{Q}(g(Y))=E_t^{Q^Z}(g(Y))$?

Consider $$Z(t)=\left(\frac{S(t)}{H}\right)^p$$where $S$ has a standard Black-scholes Dynamics for a stock, $H$ is a postive constant and $p =1 - \frac{2r}{\sigma^2}$ and a simple claim with a pay-off ...
Pedro Gomes's user avatar
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What's the price of a lookback call option in the arbitrage-free CRR-model?

If we consider the CRR-model in two periods, i.e. T=2. Let $S^1$ be the risky asset with $S_0^1=100$ and $S^0$ the bond with $S_0^0=1$. Furthermore, we assume the model is arbitrage-free with $y_b=-0....
stats19's user avatar
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Can the risk-neutral measure depend on the option type?

In an ideal Black-Scholes setting, the Risk-Neutral measure $Q$ is unique and so, obviously, does not depend on what derivative instrument we want to price. Assume some deviation from perfect markets (...
Dmitry Makarov's user avatar
1 vote
1 answer
73 views

We have a two LIBOR contracts, how to compare their values by change of change of numeraire

We have two LIBOR contracts: contract 1 pays $L\left(T_{1},\:T_{2}\right)-K$ at time $T_{1}$ contract 2 pays $L\left(T_{1},\:T_{2}\right)-K$ at time $T_{2}$. Now, $F_{1}$ is the par strike such that ...
Lithium's user avatar
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1 vote
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Replicating portfolio of an option and to find inital price

I am very new to financial math so I am not sure how to do with this question. A friend sent me this question to practice but I am unsure how to begin. I read about call option . Can that be used for ...
starfire's user avatar
2 votes
0 answers
138 views

Last step step in Girsanov's theorem proof

I consider the version of Girsanov's theorem presented in this question. Let us take the particular case that $\mathbb{F}$ is the filtration generated by standard Brownian motion $(W)_{t\in[0;T]}$ ...
fwd_T's user avatar
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Market Price of Risk for Consumption Asset - Hull's Example 28.1

In Hull's Options, Futures, and Other Derivatives, he gives an example 28.1 as below. Consider a derivative whose price is positively related to the price of oil and depends on no other ...
LaTeXFan's user avatar