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How do you derive the main PDE in the Heston stochastic volatility model?
Wiki User
∙ 13y ago
It is not possible to reproduce the equations on this website, however you can find a detailed derivation at the related link.
Wiki User
∙ 13y ago
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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 are the main defects of the Black and Scholes model?
Black-Scholes makes the following assumptions (which are not valid in reality)constant volatility (not valid in the long term),efficient markets (hence no room for artbitrage),constant interest rates,log-normal returns,the option are imlicitly European and can only be exercized on their expiration dateno commission or transaction costs,and perfect market liquidity.
Did charlton heston work as a model?
Yes. At one point Charlton Heston worked as a male model.
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 major difference between a mathematical model and an econometric model?
Mathematical model is exact in nature.it has Beta zero and Beta one and no stochastic or disturbance variables. Econometric model represents omitted variable, error in measurement and stochastic variables.
What is a stochastic error?
In a statistical model, variations in the dependent variable can be attributed to independent variables. However, there is a random element that is not accounted for and this is the stochastic error.
What is stochastic calculus?
The mathematical theory of stochastic integrals, i.e. integrals where the integrator function is over the path of a stochastic, or random, process. Brownian motion is the classical example of a stochastic process. It is widely used to model the prices of financial assets and is at the basis of Black and Scholes' theory of option pricing.
What has the author Lode Li written?
Lode Li has written: 'A stochastic theory of the firm' -- subject(s): Accessible book 'Optimal operating policies for multi-plant stochastic manufacturing systems in a changing environment' 'A stochastic model of resource flexibility' -- subject(s): Accessible book
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 has the author Tuula Hakala written?
Tuula Hakala has written: 'A stochastic optimization model for multi-currency bond portfolio management' -- subject(s): Mathematical models, Interest rates, Risk, Stochastic programming
What has the author H M Scoging written?
H. M. Scoging has written: 'A stochastic model of daily rainfall simulation in a semi-arid environment' -- subject(s): Mathematical models, Rain and rainfall, Stochastic processes
What is stochastic disturbance term?
A stochastic disturbance term is a random variable included in a statistical model to account for unexplained variability or uncertainty in the data. It represents the effects of unobserved factors that are not explicitly modeled but can influence the outcome of an analysis. By incorporating this term, the model can better capture the randomness or unpredictability in the data.
What is stochastic error term?
A Stochastic error term is a term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included Xs. It is, in effect, a symbol of the econometrician's ignorance or inability to model all the movements of the dependent variable.
What has the author Yanguang Shan written?
Yanguang Shan has written: 'A stochastic spray model for radio frequency inductively coupled plasmas'
