The Quant Journey

Barrier options are options that have a payout that is dependent on the terminal stock price and whether or not they reach a barrier

CVA is the difference between the value of a portfolio which we assume is risk-free, and a portfolio where we account for default risk

Value at Risk gives an indication of how much you stand to lose on a portfolio with a given probability, over a specific time period.

Simple Model Consisting of One Stock and a Riskless Bank Account B

Equivalent local martingale measures are an integral part within continuous-time stochastic processes. They define the risk-neutral measure…

In order to understand the replication by portfolio argument, we first have to familiarise ourselves with the concept of the Standard…

In order to derive the Black Scholes PDE from the Brownian Motion using the Delta-Hedging Argument, we have to set up our self-financing…

Semi martingales are the continuous time equivalent of the Doob Decomposition Theorem.

Local Martingales play an important role in modelling the real world dynamics of the financial markets.

Understanding the quadratic variation of stochastic processes is a key component in quantitative financial modelling. This type of…

A Martingale is simply a stochastic process (a sequence of random variables) for which, given some arbitrary time s < t, the conditional…

The Brownian Bridge is a classical brownian motion on the interval [0,1] and it is useful for modelling a system that starts at some given…

The Ornstein–Uhlenbeck process is one of several approaches used to model interest rates, currency exchange rates, and commodity prices…

In this article I will give a primer on how to think about finance in terms of stochastic processes, how to solve the Geometric Brownian…