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12 votes
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Hyperbolic and Elliptic PDEs in Quant Finance

PDE Classification (Background) Linear second-order PDEs can be classified as either elliptic, parabolic or hyperbolic. A general PDE in two dimensions for $u=u(x,y)$ would look like $$Au_{xx}+2Bu_{xy}...
Kevin's user avatar
  • 16k
6 votes
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Any book which is intro to PDEs but prioritises techniques useful for solving Black-Scholes?

Ok I'll answer this from a practioner's perspective rather than a purist's (which I am solidly not). Below are the books that influence my understanding of this space, listed in chronological order of ...
James Spencer-Lavan's user avatar
4 votes
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Pricing PDE of Asian option by Shreve

Intuitively, once a stock hits value zero the underlying company is bankrupt and the value remains zero (this might not be true in the real world but it's a common assumption). So, once $S_t$ is zero ...
Bob Jansen's user avatar
  • 8,562
3 votes

Canonical text on numerical PDEs in finance

I got a lot of mileage out of Daniel Duffy's Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach.
river_rat's user avatar
  • 1,010
3 votes

What are the parallels between the Black-Scholes equation and the heat equation?

For heat equation, it describes how heat diffuses (usually measured by temperature) through the length of the material and over time. For Black Scholes, it describes how the value of the option ...
mirmo's user avatar
  • 131
2 votes
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Power option's PDE

As mentioned by James, the expansion of the ${\frac {1}{2}}\sigma ^{2}S^{2}{\frac {\partial ^{2}V}{\partial S^{2}}}$ term yields: $$ \frac {\partial ^{2}V}{\partial S^{2}} = \frac {\partial}{\partial ...
userPrimeNumber's user avatar
2 votes
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Is stochastic control with the HJB equation used in market making/algo trading at institutions?

I would say that there are two things that we can talk about: Research purpose Real Trading Those models are a good thing to start when you try to build something that has to have characteristics of ...
ltrd's user avatar
  • 501
1 vote

Kou model — solving PIDE for European and American options in Python

The issue I described in my initial question is linked to the integral term. In the paper, this term is multiply by $ \theta \Delta \text{t} $ but this is only the "implicit" part of the ...
pierrot's user avatar
  • 96
1 vote

When to use total derivative and when not to?

If I understand your questions correctly, $\xi$ is a function of $\tau$ so you need to apply chain rule. Therefore, the rate of change of $U$ wrt $\xi$ also depends on the rate of change wrt $\tau$. ...
THATS MY QUANT MY QUANTITATIVE's user avatar
1 vote

What is the PDE for this interest rate derivative?

You can work out the specific PDE by applying the multi-dimensional Itô formula to the (sufficiently smooth) value function $\Pi_t = f(t, r, \sigma)$. Follow the steps from the regular Heston PDE ...
quant_son's user avatar
1 vote

Any book which is intro to PDEs but prioritises techniques useful for solving Black-Scholes?

It depends on the degree of technicality you are seeking. Here are two books that might be relevant for an analysis based on Green’s function, although they are quite technical (the exposition of the ...
Daneel Olivaw's user avatar
1 vote

Any book which is intro to PDEs but prioritises techniques useful for solving Black-Scholes?

I like the book "Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing (Springer Verlag)" from Norbert Hilber. Very easy to read and exhaustive. The ...
pierrot's user avatar
  • 96
1 vote
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Trying to measure "radius of diffusion" in the stock market

Answer was given by noob2. The property can be checked by a "Variance ratio test of market efficiency" (Lo & MacKinley). Here's a nice methodology I found: https://mingze-gao.com/measures/...
Azur's user avatar
  • 131

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