# Questions tagged [girsanov]

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### change of measure expectation

How to find expectation of this stochastic process? Also, to show that the expectation of a stochastic process expression [Xt - St] in one measure is equal to expectation of another expression (of the ...
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### Change of numeraire in options with currency exchange features

FV of an EUR denominated option under "COP" risk measure is given by: $$V_t^{COP} = D^{COP} \mathbb{E}_t^{COP} \left[X_T(S_T -K)^+\right]$$ where $X_T$ is the exchange rate COP/EUR. Pricing the ...
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### Equivalent Martingale Measure result Hull?

I've been reading Hull's chapter about Martingales and measures where he states that if you have the dynamics of two securities as follows: \begin{align} \frac{df}{f} = (r + \lambda \sigma_f) dt + \...
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### Why do we need $dS_t=r S_tdt+\sigma S_tdW_t^Q$?

Suppose $S_t$ is the stock price and follows the dynamics $$dS_t=\mu S_tdt+\sigma S_tdW_t$$. According to Girsanov, we can apply change of measure and obtain $dS_t=r S_tdt+\sigma S_tdW_t^Q$, this ...
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### Ito, Stochastic Exponential and Girsanov

This is a two-part question relating to the change of measure density used in Girsanov and secondly to the Stochastic Exponential. Whilst reading notes relating to Girsanov it is stated that the ...
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I am going through the derivation of CMS convexity from the notes of Lesniewski There is a transformation from $T_p$ forward measure to annuity measure $Q$ as $$P(0,T_p)E^{Q_{T_p}}\left[S(T_0,T)\... 1answer 146 views ### Bivariate Black-Sholes Model Let us propose bivariate Black-Sholes Model. Assume, we have an arbitrage-free complete market. r_{f} is risk-free rate. Under real-world measure P: dS_{1} (t)=S_{1} (t) [\mu_{1}dt+\sigma_{1}... 1answer 3k views ### Radon-Nikodym derivative and risk natural measure I need help with my understanding of changing probability measure. Im not a mathematician so I hope for answers that are not too technical. As shown in this Wikipedia article http://en.wikipedia.org/... 1answer 2k views ### Girsanov Theorem and Quadratic Variation Girsanov theorem seems to have many different forms. I've got a problem matching the form in wiki to the one in Shreve's book, due to the difficulty of quadratic variation calculation. Below is the ... 2answers 1k views ### Uniqueness of equivalent martingale measure in Black Scholes-Model Let's consider standard Black-Scholes model with price process S_t satisfying SDE$$dS_t = S_t(bdt + \sigma dB_t), where $B_t$ is standard Brownian Motion for probability $\mathbb{P}$. I ...
Suppose $B(t)$ is a standard Brownian motion, and $B_{1}(t)$ is given by $dB_{1}(t)=\mu dt+dB(t)$. Suppose $P$ is the Wiener measure induced by $B(t)$ on the $C[0,\infty)$, and $P_{1}$ is the Law ...
Assume that we want to calculate the time $t=0$ price of a bond: $B(0,T) = E_P[\exp(-\int_0^T r_s ds)]$, where $r$ is the interest rate following the SDE \$dr_t=k(\theta-r_t)dt+\sigma dB_t=b(r_t)dt+\...