Questions tagged [equivalent-measure]

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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 ...
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0answers
62 views

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 ...
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1answer
70 views

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....
6
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0answers
61 views

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 (...
1
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1answer
66 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 ...
1
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0answers
45 views

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 ...
2
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0answers
89 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 $(W)_{t\in[0;T]}$ ...
2
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1answer
96 views

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 ...