Recently I have been working on pricing a high dimensional (4 dimension, actually) derivative via partial differencial equation (PDE), which can be solved numerically by Finite Element or Finite Difference method. Indeed Matlab has a PDE toolbox to use, however, as I know, this PDE toolbox can only calculate two dimensional problem, for instance, stock and time dimension as Black Scholes model does.

For your attention, I found an excellent Finite Element package named Getfem++ written in C++, as its webpage says, "The Getfem++ project focuses on the development of a generic and efficient C++ library for finite element methods. The goal is to provide a library allowing the computation of any elementary matrix (even for mixed finite element methods) on the largest class of methods and elements, and for arbitrary dimension (i.e. not only 2D and 3D problems). " what's more interesting is this library can be linked easily to Matlab.

We know Finite Element method is an alternative to Finite Difference discretization of the BS and other equations in the price resp. the log-price space variable. The advantage of FE is that it gives convergent deterministic approximations of the option price under realistic, low smoothness assumptions on the payoff function, as e.g. for binary contracts and in particular allow a higher rate of convergence that that achievable with Monte Carlo simulations.

At previous post I shared a site using R language for Vasicek estimation, as we know, Vasicek model is a term structure model describing the stochastic process of interest rates. It is a type of "one-factor model" with negative interest rate possible, despite this shortcoming, it is still applied for fixed income research and application due to its mean-reversion characteristics.

Here is another Vasicek application implemented with binomial tree in C++, the tree construction procedure is outlined in Tuckman famous book Fixed Income Securities. By providing input parameters like the initial short rate, speed of mean reversion, long-run average rate and volatility, interest rate following Vasicek evolution is constructed.

For detail check this page http://math.nyu.edu/~atm262/spring06/ircm/vasicek/.

I am not a fan of Quantitative Macroeconomics, which uses standard neoclassical theory to explain business cycle fluctuations and tries to answer the following questions, to name a few,
What are the empirical characteristics of business cycles?
What brings business cycles about?
What propagates them?
Who is most affected and how large would be the welfare gains of eliminating them?
What can economic policy, both fiscal and monetary policy do in order to soften or eliminate business cycles?
Should the government try to do so?
......

Sounds boring? I found this site when I searched "Kalman filter", click the following link for codes in Quant economics of different programming languages.
http://ideas.repec.org/s/dge/qmrbcd.html

Libor Market Model is a term structure model applied to value and hedge exotic interest rate derivatives. The model is recognized and employed largely because of its consistency with the popular market model, Black's formula. This consistency makes the calibration process easy as the Black's market prices for vanilla interest rate Options can be instantly used as an input.

The purpose of this book -Libor Market Model: Theory and Implementation is to analyze the Libor Market Model in theory and implement it practically to the evaluation of normal caps, barriers, European swaptions and ratchets, etc. The dynamic of the Libor Market Model will be derived and the whole steps of its implementation applying Monte Carlo simulation will be introduced. Implementation is accomplished via several volatility and correlation formulation. Special attention should be given when it comes to calibrate the Libor Market Model and model the forward rate volatilities and correlations since they could impact prices of interest rate derivatives substantially.

Options to exchange one asset for another arise in various contexts. An option to buy yen with Australian dollars is, from the point of view of a US investor, an option to exchange one foreign currency asset for another foreign currency asset. A stock lender offer is an option to exchange shares in one stock for shares in another stock.

Consider a European option to give up an asset worth ST at time T and receive in return an asset worth VT, the payoff from the option is
max(VT-ST,0)
A formula for valuing this option was first produced by Margrabe at his paper “The value of an option to exchange one asset for another”, Journal of Finance, a sample Matlab file can be downloaded here