There are three main volatility models in the finance: constant volatility, local volatility and stochastic volatility models.

Before the stock market crash of 1987, the Black-Scholes (B-S) model which was built on geometric Brownian motion (GBM) with constant volatility and drift was the dominant model. In this model, stock price is the only source of randomness and it can be hedged with the underlying stock with a return distribution as log-normal. In the B-S model, the stock price S is described by the following stochastic differential equation (SDE), where W is a standard Brownian motion:

The above Stochastic Differential Equation…

Endgame for “AI Winter”

In the early 1980s, Winter was coming for Artificial Intelligence (AI) with a period of reduced funding and interest in AI research, which will later be called the “AI Winter”!

During this cold-weather period which lasted until the mid-2000s, almost no research paper on Neural Nets was published because of the lost interest in the field. The reason was simple: no effective algorithms had been put forward against the traditional ones.

Karger’s algorithm back in town (with Python code)

Are you ready for dividing and slicing? Let’s start with networks. We like dense networks, otherwise even if a very single edge or wire is disconnected, a large portion of the network can be down — a situation definetely not desired ! There are generally clusters, unevenly distributed segments, within networks. While dealing with separation of these segments or “clusters” efficiently, we look for edges between them such that the number of edges are minimum.