Questions tagged [wienerprocess]
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11
questions with no upvoted or accepted answers
3
votes
0
answers
75
views
Feymann Kac pde with correlated process
I have to solve the following PDE:
\begin{equation}
\begin{cases}
\dfrac{\partial F}{\partial t}+\dfrac{1}{2}\dfrac{\partial^2 F}{\partial x^2}+\dfrac{1}{2}\dfrac{\partial^2 F}{\partial y^2}+\dfrac{1}{...
2
votes
0
answers
130
views
The distribution of the jump diffusion process
In the Merton jump diffusion model the process of the share price can be expressed as $$S_{t}=S_{0}\cdot\exp\left\{ X_{t}\right\} ,$$ where $$X_{t}=\mu t+\sigma W_{t}+\sum_{i=1}^{N_{t}}Y_{i}.$$
Here $...
2
votes
0
answers
161
views
Expected value of a wiener process on an infinite time horizon with a barrier
Say I have a wiener process with $X(0) = X_0>0$ and the dynamics
\begin{equation}
dX(t) =
\begin{cases}
-\mu dt + \sigma X(t) dW(t)^{\mathbb{Q}} & \mathrm{for\ } X(t)>0\\
0 & \mathrm{...
1
vote
0
answers
45
views
Sample Wiener process constrained to open (initial), high (max), low (min), close (final)
With a Brownian bridge, one can sample a Wiener process constrained to a specified initial value and a final value.
Can the same be done when the process is constrained also to have a specified ...
1
vote
0
answers
90
views
Is this the right way to accelerate my Monte-Carlo Simulation
I am trying to develop a pricer for Call VS Call and I'm using MonteCarlo method to do so because my stocks are correlated between each others.
Basically my inputs are ...
1
vote
0
answers
131
views
Value of trading strategy
A trading strategy is defined as follows: starting capital $v_0 = 5$ and 1 risky asset holdings $\varphi_t = 3W_t^2-3t$ where $W$ is a Wiener process.
The problem is to find the probability of the ...
1
vote
1
answer
222
views
Why the Esscher transform is the right transform for pricing formula?
A Wiener process has infinitely many states of the world at any time step. Does that not mean that there are infinitely many EMM's for any model that uses the Wiener process?
But then if there is only ...
1
vote
0
answers
696
views
CIR model. Is there a closed-form solution or even a good proxy of analytical solution?
Is there a closed-form (analytical) solution for the Cox-Ingersoll-Ross SDE
\begin{equation}
dr_t=k_r(\theta_r-r_t)dt+\sigma_r\sqrt{r_t}dW_t\tag{1}
\end{equation}
?
Notice that $\{r_t\}$ is our ...
1
vote
0
answers
45
views
How to expand lognormal approximation of Brownian motion
How can we expand this sum? $\sum_{i=1}^n (e^{rt_i-\frac{1}{2}\sigma^2t_i+\sigma w_{t_i}})^2$ where: $w_{t_i}$ is a standard Brownian motion.
If we let $m_t=e^{-\frac{1}{2}\sigma^2t_i+\sigma w_{t_i}}$...
1
vote
0
answers
67
views
Solving for roots of a stochastic pay-off function
I have a pay-off function for a derivative which is defined by the Heaviside difference between $G$ and $B$ shifted by $-F$. To find the value of $V_{t=0}$, I need to find $\tau$ when $\frac{dV}{dt} = ...
0
votes
0
answers
61
views
How to simulate a conditional expectation given a filtration
I had a question regarding how to simulate a certain conditional expectation. I am given two processes $X_1(t), X_2(t)$ which both follow their own SDE, but both are of the form
\begin{equation*}
dX_i(...