Sep
30
Entries Vasicek estimation and Vasicek model in binomial tree introduced how to estimate Vasicek model parameters, how to implement Vasicek interest rate model in binomial tree, which can be further used to price option on bonds, for instance. Here i share another two excel files demonstrating how to calibrate a Vasicek model to a given term structure and simulate Vasicek zero bond prices and the path of the short rate.
Download at http://www.mathematik.uni-kl.de/~korn/korn2b.htm, besides Vasicek short rate model, CIR, Dothan and Exponential Vasicek are also included in one file.
Download at http://www.mathematik.uni-kl.de/~korn/korn2b.htm, besides Vasicek short rate model, CIR, Dothan and Exponential Vasicek are also included in one file.
Sep
29
Basically there are two types of finite difference methods: explicit finite difference method and implicit finite difference method. Other types are just the derivation of these two types, for example, Crank-Nicolson method is an average of the explicit method and implicit method.
Two sample Matlab files to compare the performance of solving PDE via implicit and explicit method. http://frontera.bu.edu/MathFn.html
Two sample Matlab files to compare the performance of solving PDE via implicit and explicit method. http://frontera.bu.edu/MathFn.html
Sep
28
Asian options are securities with payoff which depends on the average of the underlying stock price over certain time interval. Since no general analytical solution for the price of the Asian option is known, a variety of techniques have been developed to analyze arithmetic average Asian options.
A simple and numerically stable 2-term partial differential equation characterizing the price of any type of arithmetically averaged Asian option is given. The approach includes both continuously and discretely sampled options and it is easily extended to handle continuous or discrete dividend yields.
The paper "Unified Asian Pricing", Risk, Vol. 15, No. 6, 113-116 and its Mathematica nb file can be downloaded at http://www.stat.columbia.edu/~vecer/.
A simple and numerically stable 2-term partial differential equation characterizing the price of any type of arithmetically averaged Asian option is given. The approach includes both continuously and discretely sampled options and it is easily extended to handle continuous or discrete dividend yields.
The paper "Unified Asian Pricing", Risk, Vol. 15, No. 6, 113-116 and its Mathematica nb file can be downloaded at http://www.stat.columbia.edu/~vecer/.
Sep
27
This is the algorithm involved on the use of the non-linear forecast of asset's prices based on the nearest neighbour method.
The basic idea of the NN algorithm is that the time series copies it's own past behavior, and such fact can be used for forecasting purposes. On the zip file there are two functions: one is the univariate version of NN (nn.m) and the other is the multivariate approach, also called simultaneous NN (snn.m).
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=9396&objectType=file
The basic idea of the NN algorithm is that the time series copies it's own past behavior, and such fact can be used for forecasting purposes. On the zip file there are two functions: one is the univariate version of NN (nn.m) and the other is the multivariate approach, also called simultaneous NN (snn.m).
Quotation
The nearest neighbor method is defined as a non-parametric class of regression. Its main idea is that the series copies its own behavior along the time. In other words, past pieces of information on the series have symmetry with the last information available before the observation on t+1. Such way of capturing the pattern on the times series behavior is the main argument for the similarity between NN algorithm and the graphical part of technical analysis, charting.
The way the NN works is very different than the popular ARIMA model. The ARIMA modeling philosophy is to capture a statistical pattern between the locations of the observations in time. For the NN, such location is not important, since the objective of the
algorithm is to locate similar pieces of information, independently of their location in time. Behind all the mathematical formality, the main idea of the NN approach is to capture a nonlinear dynamic of self-similarity on the series, which is similar to the fractal dynamic of a chaotic time series.
The way the NN works is very different than the popular ARIMA model. The ARIMA modeling philosophy is to capture a statistical pattern between the locations of the observations in time. For the NN, such location is not important, since the objective of the
algorithm is to locate similar pieces of information, independently of their location in time. Behind all the mathematical formality, the main idea of the NN approach is to capture a nonlinear dynamic of self-similarity on the series, which is similar to the fractal dynamic of a chaotic time series.
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=9396&objectType=file
Sep
26
The Black-Scholes formula, one of the major breakthroughs of modern finance, allows for an easy and fast computation of option prices. But some of its assumptions, like constant volatility or log-normal distribution of asset prices, do not find justification in the markets. More complex models, which take into account the empirical facts, often lead to more computations and this time burden can become a severe problem when computation of many option prices is required, e.g. in calibration of the implied volatility surface. To overcome this problem Carr and Madan (1999) developed a fast method to compute option prices for a whole range of strikes.
Fast Fourier transform (FFT) is applied for this purpose, the use of the FFT is motivated by two reasons. On the one hand, the algorithm offers a speed advantage. This effect is even boosted by the possibility of the pricing algorithm to calculate prices for a whole range of strikes. On the other hand, the cf of the log price is known and has a simple form for many models considered in literature, while the density is often not known in closed form.
Fast Fourier transform (FFT) is applied for this purpose, the use of the FFT is motivated by two reasons. On the one hand, the algorithm offers a speed advantage. This effect is even boosted by the possibility of the pricing algorithm to calculate prices for a whole range of strikes. On the other hand, the cf of the log price is known and has a simple form for many models considered in literature, while the density is often not known in closed form.
Quantitative Finance Collector is simply a record of my financial engineering learning journey as a master in quantitative finance, a PhD candidate in finance and a Quantitative researcher, with most of the entries written at school. 
