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Jul
19
revised How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$?
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Jul
19
comment How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$?
Richard: thanks for pointing out the typo. If $X \sim \mathcal{N}(\mu, \sigma^2)$, $\mathbb{E}\left[e^X\right] = e^{\mu + \frac{1}{2} \sigma^2}$.
Jul
2
awarded  Necromancer
Jun
7
comment Modelling driftless stock price with geometric Brownian motion
user7056: you should complain to stack exchange as they won't let me edit my comments!
Jun
3
revised Modelling driftless stock price with geometric Brownian motion
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Jun
2
revised Modelling driftless stock price with geometric Brownian motion
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Jun
2
comment Modelling driftless stock price with geometric Brownian motion
The superscript $Q$ indicates that the expectation is taken over the risk-neutral probability measure [en.wikipedia.org/wiki/Risk-neutral_measure]. To compute $\mathbb{E}^Q\left[ e^{\sigma W_t} \right]$, note that, for $X \sim \mathcal{N}(\mu, \sigma^2)$, $\mathbb{E}\left[ e^X\right] = e^{\mu+\sigma^2/2}.$
Jun
2
answered Modelling driftless stock price with geometric Brownian motion
Apr
21
comment How to calculate the expected value of a function of a standard brownian motion (Wiener process)
If the OP is not comfortable with using $\cos x = \Re \{ e^{i x} \} $, let $\cos x = \frac{e^{i x} + e^{-i x}}{2}$ and proceed from there.
Mar
31
answered Simulating the short rate in the Hull-White model
Jan
27
revised Time-zero price of two specific contingent claims
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Jan
27
comment Time-zero price of two specific contingent claims
@user8: i see, but then I think your answer is wrong, since $\frac{V_0}{B_0} = \mathbb{E}^Q \left[ \frac{V_T}{B_T} \middle\vert \mathcal{F}_0\right] = \mathbb{E}^Q \left[ \frac{\int_0^T S_u \; du}{B_T} \middle\vert \mathcal{F}_0\right]$. In other words, the factor $e^{r u}$ appears in the integrand; it's not canceled out by $B_T = e^{r T}$.
Jan
27
comment Time-zero price of two specific contingent claims
@user8: Although your answer agrees with mine if we take the limit of $r \rightarrow 0$ in my expression, why are you assuming that $r=0$?
Jan
26
comment Time-zero price of two specific contingent claims
I think your expression for $S_t =S_0 e^{\sigma W^Q_t-\frac{1}{2}\sigma^2t}$ is wrong. Under the risk-neutral measure $Q$, $S_t= S_0 e^{(r-\sigma^2/2)t + \sigma W_t}$.
Jan
26
answered Time-zero price of two specific contingent claims
Dec
19
answered How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$?
Dec
17
revised A Question from “Mathematical Methods for Financial Markets” Chapter 2
LaTex formatting
Dec
17
suggested suggested edit on A Question from “Mathematical Methods for Financial Markets” Chapter 2
Nov
26
revised Risk Neutral Evaluation - Exchange/Spread Options
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Nov
24
revised Risk Neutral Evaluation - Exchange/Spread Options
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