The differential-equations tag has no wiki summary.
7
votes
1answer
245 views
Connections between random walk and heat equation (Material for ~)
I am preparing an undergraduate lecture in quantitative finance and I am looking for material that combines the topics:
random walk and
heat equation
The material should be accessible ...
6
votes
0answers
127 views
How to get an analytic result for option price based on this model?
I defined such a model for stock price
(1)....
$$dS = \mu\ S\ dt + \sigma\ S\ dW + \rho\ S(dH - \mu) $$
, where $H$ is a so-called "resettable poisson process" defined as
(2)....
$$dH(t) = ...
4
votes
1answer
170 views
Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?
Both the Black-Scholes PDE and the Mass/Material Balance PDE have similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive the ...
8
votes
3answers
714 views
What tools are used to numerically solve differential equations in Quantitative Finance?
There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
4
votes
1answer
263 views
An equation for European options
So, any European type option we can characterize with a payoff function $P(S)$ where $S$ is a price of an underlying at the maturity.
Let us consider some model $M$ such that within this model ...
6
votes
10answers
1k views
Using Black-Scholes equations to “buy” stocks
From what I understand, Black-Scholes equation in finance is used to price options which are a contract between a potential buyer and a seller. Can I use this mathematical framework to "buy" a stock? ...
8
votes
3answers
584 views
Deterministic interpretation of stochastic differential equation
In Paul Wilmott on Quantitative Finance Sec. Ed. in vol. 3 on p. 784 and p. 809 the following stochastic differential equation: $$dS=\mu\ S\ dt\ +\sigma \ S\ dX$$ is approximated in discrete time by ...
21
votes
1answer
2k views
What is the role of stochastic calculus in day-to-day trading?
I work with practical, day-to-day trading: just making money. One of my small clients recently hired a smart, new MFE. We discussed potential trading strategies for a long time. Finally, he expressed ...
13
votes
1answer
1k 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 ...
