William S. Wong

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 Oct31 awarded Yearling Jul19 revised How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$? added 57 characters in body Jul19 comment How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$? Richard: thanks for pointing out the typo. If $X \sim \mathcal{N}(\mu, \sigma^2)$, $\mathbb{E}\left[e^X\right] = e^{\mu + \frac{1}{2} \sigma^2}$. Jul2 awarded Necromancer Jun7 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! Jun3 revised Modelling driftless stock price with geometric Brownian motion added 362 characters in body Jun2 revised Modelling driftless stock price with geometric Brownian motion deleted 4 characters in body Jun2 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 $X \sim \mathcal{N}(\mu, \sigma^2)$, $\mathbb{E}\left[ e^X\right] = e^{\mu+\sigma^2/2}.$ Jun2 answered Modelling driftless stock price with geometric Brownian motion Apr21 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. Mar31 answered Simulating the short rate in the Hull-White model Jan27 revised Time-zero price of two specific contingent claims added 56 characters in body Jan27 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 $B_T = e^{r T}$. Jan27 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 $r=0$? Jan26 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 $Q$, $S_t= S_0 e^{(r-\sigma^2/2)t + \sigma W_t}$. Jan26 answered Time-zero price of two specific contingent claims Dec19 answered How to compute $\mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]$? Dec17 revised A Question from “Mathematical Methods for Financial Markets” Chapter 2 LaTex formatting Dec17 suggested suggested edit on A Question from “Mathematical Methods for Financial Markets” Chapter 2 Nov26 revised Risk Neutral Evaluation - Exchange/Spread Options added 108 characters in body