# Tagged Questions

stochastic processes is a collection of random variables representing the evolution of some system of random values over time.

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### State of Art - Nelson Siegel Modeling

My idea is to work with dynamic Nelson Siegel models(DNS) on my master's thesis. As I am finishing undergraduation this year I started researching on the subject. I wonder what is being discussed in ...
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### Does No arbitrage(NA) imply efficient markets (EMH)?

The EMH states that stocks are traded at its fair values. This means there is no arbitrage strategy in efficient markets. However, if the market is no arbitrage, can we conclude the market is ...
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### Why is it useless to model stochastic volatility when pricing Vanilla style derivatives?

With respect to the answer by user AFK in Ideas about Stochastic volatility models. I am specifically interested in interest rate options (IR Caps/Floors and Swaptions).
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We got the stochastic process for stock price of n stocks at continues time. We can find if there is a arbitrage trading strategy or dominant trading strategy. I wonder if we cannot find such ...
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### Any idea of compound Poisson processes in betting? [closed]

Any suggestions on compound poisson processes in bets of a customer?
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### Modelling commodity price uncertainty with brownian motion - time period impacts

background I have two separate models of a metals resources company. Each model produces a series of accounting and cashflows forecast for different assets, and consolidates these to a overall ...
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### Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
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### Relationships between white noise and random walk

I would like to ask 5 questions about relations between these processes. 1) Could white noise be also a random walk? 2) Could random walk be also a white noise? 3) Could white noise be stationary? ...
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### Interpreting and scaling of Realized Variance with sample data

I have some question about realized variance(RV) and I have some sample prices below to work with. You can run the R code below to build a vector of log returns. Three are 78 5-minute buckets in a ...
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### Monte Carlo simulating Cox-Ingersoll-Ross process

The CIR process is given by the SDE $$\mathrm dr_t = \theta(\mu-r_t)\mathrm dt + \sigma\sqrt{r_t}\mathrm dW_t$$ where $W_t$ is a Brownian motion. I am interested in finite-difference schemes of ...
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### Jump-Diffusion Processes

This last quarter of college for senior project, I will be doing research on the application of jump-diffusion processes to pricing derivatives. I was wondering if anyone could recommend any resources ...
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### Discounted Stock Price

I have the following Question : Prove that under the risk-neutral probability p the stock and the banjaccount have the same average rate of growth. In other words, if $S_0 , S_N$ are the initial ...
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### Provide a bond pricing differential equation and invoke Feynman-Kac Theorem

Grateful for any assistance. Consider the process: $dZ=r(t)Z\,dt$ , where $r(t)$ is stochastic interest rate and $Z=Z(r,t;T)$ is a zero coupon bond Price. Provide a bond pricing partial ...
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### Stationary distribution for square root process

Consider the process, $$dX_t=(-aX_t+b(1-X_t))dt + \sqrt{X_t(1-X_t)}dW_t$$ How do I show that the stationary distribution for the transition density is a beta distribution? I tried expanding the ...
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### How to estimate parameters of geometric brownian motion with time-varying mean?

Does anyone know how to estimate $A$, $\sigma_1$,$\sigma_2$ from the following system? $$dx = \mu_t x dt + \sigma_1 x dB_x$$ $$d\mu = A(\bar\mu - \mu) dt + \sigma_2 dB_\mu$$ Variation in $x$ could ...
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### Why is Brownian motion merely 'almost surely' continuous?

Why is Brownian motion required to be merely almost surely continuous instead of continuous? For example, this is stated as condition 2 in this article in section 1, Characterizations of the Wiener ...
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### Is a stationary process necessarily mean-reverting?

Intuitively, a stationary stochastic process needs to be mean-reverting. This should follow immediately from the definition of stationarity: the mean of the process needs to be constant over time, so ...
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### Complete Multiperiod Binomial model

I have the following deifnition of a Complete multiperiod binomial model: A multi period binomial model can be called complete if every derivative security can be replicated by trading in the ...
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### Transformation into Martingale

If $f$ is some function of BV on $\mathbb{R}$ and $dZ_t = f(W_t)dW_t + \mu_t dt$ ($W_t$ is a $1$-dimensional standard Brownian Motion), then what choice of real valued function $F$ makes: \begin{...
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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 ...
I want to correctly simulate a $\mathcal{Q}$ - martingale $S$, which is a geometric Brownian motion and an exponential of a process $X$, X_t = X_0 + \mu t + \sigma B_t = X_{t-\Delta t}...