Wilson Mongwe's Statistics and Quantitative Finance Blog
Asian options are path-dependent options whose payoff depends on the average value of the underlying asset during a specific set of dates across the life of the option. Because the payoff of the Asian options depends on the average value Continue reading Pricing Arithmetic Asian Options using Moment Matching
Determining the correct parameter values to be used in a Jump-Diffusion model is not a trivial process (as outlined here). In this blog post we will be using the biologically inspired differential evolution technique to calibrate a Jump-Diffusion model using Continue reading Calibrating Jump Diffusion Models using Differential Evolution
Over the past decade there has been an increase in the amount of digital information that is available. In particular, there is now vasts amount of data that is available on social media platform such as twitter and Facebook that Continue reading Analyzing A South African Financial News Twitter Corpus using a Topic Model
Traditionally, asset returns have been modeled using diffusion processes. Diffusion processes assume that the sample path of the process being modeled is continuous. However, empirical evidence suggests that there are jumps that occur in asset returns, such as those that Continue reading Calibrating Financial Models using a Non-Parametric Technique
In the previous article we looked at how one can use Neural Networks to detect jumps present in returns of a particular stock. In this blog post, we build on the thinking established in the previous article and use a Continue reading A Random Forest Test For Jumps in Stock Markets Using R
Delta hedging is a technique used by trades to reduce the directional risk of a position. This delta hedging strategy results in the reduction of the variability of the profit and loss (pnl) of the position. A position that is Continue reading An Interactive Dynamic Delta Hedging Example in R
Modelling of financial markets is usually undertaken using stochastic processes. Stochastic processes are collection of random variables indexed, for our purposes, by time. Examples of stochastic processes used in finance include GBM, OU, Heston Model and Jump Diffusion processes. For Continue reading A Test for the Presence of Jumps in Financial Markets using Neural Networks in R
Maximum Likelihood Estimation (MLE) is often the preferred method when it comes to the estimation of statistical models. It is preferred due to the "nice" properties that the estimators from this estimation algorithm have (e.g. estimators are asymptotically normal). This MLE Continue reading Understanding the EM Algorithm
This post is the first part in a series of posts where we will be discussing jump diffusion models. In particular, we will first introduce diffusion and jump diffusion processes (part 1/3), then we will look at how to asses if Continue reading Introduction to Diffusion and Jump Diffusion Processes