# Tagged Questions

0answers
37 views

### Transform the American cash-or-nothing call into a linear complementarity problem for the diffusion equation

Transform the American cash-or-nothing call into a linear complementarity problem for the diffusion equation and show that the transformed payoff is g(x,τ) = be^[(1/2)((k+1)^2)τ+(1/2)(k−1)x]H(x), ￼￼ ...
2answers
225 views

### Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE and the Mass/Material Balance PDE have similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive the ...
3answers
978 views

### What tools are used to numerically solve differential equations in Quantitative Finance?

There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
10answers
2k views

### Using Black-Scholes equations to “buy” stocks

From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
1answer
3k views

### Transformation from the Black-Scholes differential equation to the diffusion equation - and back

I know the derivation of the Black-Scholes differential equation and I understand (most of) the solution of the diffusion equation. What I am missing is the transformation from the Black-Scholes ...