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 The code I've shared here can be tested to confirm that negative prices do not exist in the simulation.Class SDE: Stochastic Differential Equationĭiffusion: diffusion rate function G(t,X(t)) The other examples, will return negative prices with negative expected returns. If tested with a negative log expected return, the price should not fall below zero. # Notice, with many samples this nearly matches our initial log E and stdev(r) Plot(P, type = "b", xlab = "Forward End of Month Prices", ylab = "Expected Price from Log E", ylim = c(0,max(P))) I see you already have an answer and ColonelBeauvel might have more domain knowledge than I (assuming this is business or finance homework.) I approached it a bit differently and am going to post a commented transcript. One of the classical model (which does not mean this model is realistic) assumes the observed log return are following a normal distribution. Here is the result for the first 1000 values of P, representing 4 years: plot(1:1000, P) Be carefull to check that prod(rate) will not return Inf. Your configuration for the return price you mention ( mean=0.01 and sd=0.05) will however lead to exploding stock price (unrealistic model and parameters). 005)Īssuming the model you mentioned, you can get the serie of the prices P (containing 100001 elements, I will take P=100 - change it with your own value if needed): factor = 1 + r
With these hypothesis, you can get a series of daily return in R with: r = rnorm(100000. huge!) and t moves along a day range of 252 days per year. I furthermore make the assumption that the mean is set for an annual basis ( 1% rate of return from one day to another is just. You are getting it wrong: from what you wrote, the mean and the sd applies on the return and not on the price.
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