# Tagged Questions

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### Confidence Intervals of Stock Following a Geometric Brownian Motion

In preparation for my Options, Future's and Risk Management examination next week, I have been presented with a series of questions and their answers. Unfortunately, my lecturer, one of the less ...
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### Lipschitz condition in mathematical finance

I am interested in a rigorous explanation on why the Lipschitz condition plays a major part in stochastic calculus, most significantly in mathematical finance. To be specific, suppose we want to ...
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### Sums of random variables and independence

I'm having troubles with this proof: Let $\{Z_i\}_{i\in\mathbb{Z}}$ be i.i.d. random variables with zero mean and unit standard deviation. For $(a_0, a_1, ..., a_r)$ a sequence of $r$ real numbers ...
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### pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
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### Direct use of implied volatility

I am not sure to understand exactly the direct use of implied volatility. Let's take an example: if an instrument has a daily volatility of $\sigma$, there is a 68% probability that its value will be ...
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### probability question about brownian motion

Assume $W_{t}$ is a standard Brownian Motion, calculate the the probability that $W_{t}*W_{2t}$ is negative, i.e., $P(W_{t}*W_{2t}<0)$. I find it tricky to calculate the probability.Thank you.
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### probability that the stock price is below the strike price

How can I prove that under the risk-neutral probability: $\mathbb{P}[S_{t}<K]=-\frac{\partial{C}}{\partial{K}}(K,T)$ where $S_{t}$ is the stock price, K is the strike price, C is the call ...
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### Transition densities in the Heson model

Knowing the Characteristic function $\Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t]$ (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ...
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### arbitrage opportunity in a two period model

I have a little problem evaluating an european call. I Suppose the following: in $$t=0 : S_0 = 10$$ $$t = 1 : S_1 = \{10,11\}~with ~p=0.5$$ riskless rate : $(1+r)=\beta=1.049$ Strike ...
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### If the risk neutral probability measure and the real probability measure should coincide

Sorry if this may be a stupid question. I have not had that much mathematical finance, I've only learned about discrete time models. But lets for the argument say that you have a stochastic process ...
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### To lump or not to lump

Suppose I have a very simple asset whose price takes only three possible values: $X_t\in \{-1,0,1\}$. I also got some discrete time series $X = (X_t)_{t\geq 0}$ and I would like to come up with a ...
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### Physical Option Implied Distribuition

So I got risk neutral probabilities from stock option prices. How can I then map them to a physical measure?