Discrete/Continuous modelling approach-Quantitative Finance

Question

Explain the Discrete/Continuous modelling approach in Quantitative Finance.

Answer 1

Discrete/Continuous: Whether deterministic or probabilistic, the eventual model you note down can be continuous or discrete. Discrete implies that asset prices and/or time can only be incremented in finite chunks, whether a cent or a dollar, a day or year. Continuous implies that no such lower increment exists. The continuous mathematics processes is frequently easier than that of discrete ones. But when this comes to number crunching you have in any case to turn a continuous model in a discrete one.

In discrete models we end up along with difference equations. For option pricing an illustration of this is the binomial model. Time progresses in finite amounts, the time step. In continuous models we finish up with differential equations. The corresponding of the binomial model in discrete space is the Black–Scholes model that has continuous asset price and continuous time. Here binomial or Black–Scholes, both of such models come from the probabilistic assumptions regarding the financial world.