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What is the difference between stochastic and random?
Wikipedia states that stochastic means random. But there are differences depending on the context. Stochastic is used as an adjective, as in stochastic process, stochastic model, or stochastic simulation, with the meaning that phenomena as analyzed has an element of uncertainty or chance (random element). If a system is not stochastic, it is deterministic. I may consider a phenomena is a random process and analyze it using a stochastic simulation model. When we generate numbers using a probability distribution, these are called random numbers, or pseudo random numbers. They can also be called random deviates. See related links.
What is the difference between 'stochastic' and 'deterministic'?
These words are used to describe ways of modeling or understanding the world. "Stochastic" means that some elements of the model or description are thought of as being random. (The word "Stochastic" is derived from an ancient Greek word for random.) A model or description that has no random factors, but conceivably could, is called "deterministic." For example, the equation Q = VC where Q = charge, V = voltage, and C = capacitance, is a deterministic physical model. One stochastic version of it would be Q = VC + e where e is a random variable introduced to account for or characterize the deviations between the actual charges and the values predicted by the deterministic model.
What is a GARCH model?
A GARCH model is employed to help predict volatility (i.e. of stocks, XE rates etc) based on historical values through model fitting. Recent data is given more significance than older data. Compare to the least squares approach, which weights all the data equally. Since volatility is not the same across the entire data set (periods of volatility cluster together), this assumption is not valid. The related link provides greater detail and an Excel spreadsheet
How do you calculate implied volatility using solver?
To calculate implied volatility using Solver, you need an options pricing model (such as Black-Scholes) and market data (including the option price, strike price, underlying asset price, risk-free rate, time to expiration, and any dividends). Build the pricing model in a spreadsheet, input the market data, and set the initial volatility value in Solver. Set the objective to match the calculated option price with the market price by changing the volatility cell. Run Solver to find the implied volatility that minimizes the difference between the calculated and market option prices.
What is the difference between the stochastic error term and the residual?
Ah, the stochastic error term and the residual are like happy little clouds in our painting. The stochastic error term represents the random variability in our data that we can't explain, while the residual is the difference between the observed value and the predicted value by our model. Both are important in understanding and improving our models, just like adding details to our beautiful landscape.
