When all model parameters are piecewise constant over each observation period, This isīecause the probability distributions of the simulated and true state vectorsĪre identical only for piecewise constant parameters. General is not the exact solution to this GBM model. Specifically, it applies a Euler approach to a transformed process, which in Price paths by an approximation of the closed-form solution of separable models. In contrast, the simBySolution method providesĪ more accurate description of the underlying model. All models shipped in the simulation suite have this The Euler method is often the least accurate and most general The discrete-time approximation improves as DeltaTimeĪpproaches zero. This error is attributed to the discrepancy between theĬhoice of the dt time increment and what in theory is a This simple approximation suffers fromĭiscretization error.
Representing Market Models Using SDELD, CEV, and GBM ObjectsĬreate sdeld, cev, and gbm objects to represent the marketĪpproximation literally evaluates the stochastic differential equation directlyįrom the equation of motion, for some suitable value of theĭt time increment.
Of appropriate dimension, indicating static (non-time-varying) Identified as a callable function of time and state, Rate parameter of drift and diffusion objects is Parameters display like fields of a structure. Once again, the class of each object is clearly identified, and Required an explicit state vector to uniquely determine the Initial price of each index is as a scalar Thus, the dimensionality is more easily resolved. Two input objects that provide more information than the two functionsįrom step 4 of Representing Market Models Using SDE Objects. Representing Market Models Using SDEDDO ObjectsĬreate an sdeddo object using sdeddo to represent the marketĬlass SDEDDO: SDE from Drift and Diffusion Objects The SDE engine has assigned theĭefault simulation method, simByEuler, to the You resolve the dimensionality by specifying an initial state Unambiguously the dimensionality of the state vector and Brownian In this case, this information is insufficient to determine Two inputs: a drift-rate function and a diffusion-rate function, bothĪccessible by passing the sample time and the corresponding state vector Simulation: simulation method/function simByEulerĪdditional information to determine the dimensionality of the model,īecause the functions passed to the sde object are known only Class SDE: Stochastic Differential Equationĭiffusion: diffusion rate function G(t,X(t))
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