Questions tagged [pde]

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58 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 ...
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55 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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48 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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28 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}}...
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228 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 ...
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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 ...
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80 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}{\...
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1answer
67 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, ...
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1answer
61 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 ...