# Questions tagged [girsanov]

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### SDE simulation: P or Q?

Let's take a GBM under $P$: $dS=\mu dt+\sigma dW_{t}^{P}$ and then under $Q$ $dS=r dt+\sigma dW_{t}^{Q}$, where $dW_{t}^{Q} = dW_{t}^{P} + (\mu - r)/\sigma dt$ Now, let's say that I have ...
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### 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/...
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 ...
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+\...