Table of Contents
What kind of models do quants use?
Quant models may include: Alpha Model – Determines the potential return of securities, aka the firm’s ‘secret sauce’. Risk Model – Evaluates relationships between assets to measure and mitigate risk. Trading Model – Automates the trading of a highly impactful and costly trading list.
What is stochastic calculus used for?
Stochastic calculus is the mathematics used for modeling financial options. It is used to model investor behavior and asset pricing. It has also found applications in fields such as control theory and mathematical biology.
Is the Ito integral a martingale?
We give one and a half of the two parts of the proof of this theorem. If b = 0 for all t (and all, or almost all ω ∈ Ω), then F(T) is an Ito integral and hence a martingale. If b(t) is a continuous function of t, then we may find a t∗ and ǫ > 0 and δ > 0 so that, say, b(t) > δ > 0 when |t − t∗| < ǫ.
Why do we need stochastic calculus in quantitative finance?
Instead, a theory of integration is required where integral equations do not need the direct definition of derivative terms. In quantitative finance, the theory is known as Ito Calculus. The main use of stochastic calculus in finance is through modeling the random motion of an asset price in the Black-Scholes model.
What is the difference between stochastic calculus and ordinary calculus?
The fundamental difference between stochastic calculus and ordinary calculus is that stochastic calculus allows the derivative to have a random component determined by a Brownian motion. The derivative of a random variable has both a deterministic component and a random component, which is normally distributed.
Are stochastic processes always differentiable?
Many stochastic processes are based on functions which are continuous, but nowhere differentiable. This rules out differential equations that require the use of derivative terms, since they are unable to be defined on non-smooth functions.