Questions tagged [pde]
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10
questions
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56 views
What is the difference between “stochastic” heat equation and just heat equation?
I am trying to understand the difference between the "stochastic" heat equation and the heat equation. Will i be wrong to say the stochastic heat equation is just the heat equationg with the ...
0
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0answers
53 views
Spot the mistake in final step of BS solution via PDE approach!
Doing last step -- un-change of variable, where in my case I have
$$k = -\frac{2r}{\sigma^{2}},$$
$$v(\tau, x) = u(\tau, x) \cdot \exp\left(-\frac{1}{4}(k+1)^{2} \tau - \frac{1}{2}(k-1)x\right),$$
$$x ...
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47 views
Solution of the following PDE using European put option
I'm reading some articles about PDE and I found the following PDE, with $q_1,A >0$:
$g_t(t,y)+ \beta^2yg_y(t,y)+\frac{1}{2}\beta^2y^2g_{yy}(t,y)-q_1 g(t,y)=0 \quad (t,y) \in [0,T), \times (0,+\...
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0answers
26 views
Can we proof the boundary condition for the Black Scholes derived from a replicating Portfolio?
So for Black Scholes we know that the PDE is the follwing: ${\frac {\partial V}{\partial t}}+{\frac {1}{2}}\sigma ^{2}S^{2}{\frac {\partial ^{2}V}{\partial S^{2}}}=rV-rS{\frac {\partial V}{\partial S}}...
6
votes
1answer
205 views
Hyperbolic and Elliptic PDEs in Quant Finance
Parabolic PDEs (e.g. heat equation) are closely linked to finance via the Feynman Kac Theorem.
Do other types of PDEs appear in quant finance? Elliptic PDEs don't contain a time dimension (so perhaps ...
1
vote
0answers
42 views
boundary conditions in finite element method
In the appendix A of this paper, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.227.5073&rep=rep1&type=pdf, a finite element method is demonstrated to price a straddle. The same ...
1
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0answers
76 views
How to solve this particular PDE using Feynman-Kac formula?
I have to solve the PDE
$$
\begin{align}
\frac{\partial F}{\partial t} + \frac{1}{2}\frac{\partial^2 F}{\partial x^2} + \frac{1}{2}\frac{\partial^2 F}{\partial y^2} + \frac{1}{2}\frac{\partial^2 F}{\...
1
vote
1answer
59 views
Canonical text on numerical PDEs in finance
I am looking for a text similar to Glasserman's Monte Carlo Methods in Financial Engineering, but with a focus on numerical methods for PDEs. Glasserman's book seems to cover a lot for what is ...
2
votes
1answer
66 views
Trying to measure “radius of diffusion” in the stock market
Good evening!
I'm quite new to quantitative finance (coming from the math world!), so please excuse me if I'm not familiar with every concept!
I am currently studying the Black-Scholes equation, ...
0
votes
0answers
30 views
What PDE does the physical measure sde solve?
I have two questions:
1)
Let's say I had an estimate of $\mu$ in an sde:
$dZ = \mu Z dt + \sigma Z dW$
If I ran monte carlo I could price say an option like $Call_t = e^{-rT}E_t[(Z-k)+]$
Feynman-...
