@@ -19,16 +19,16 @@ The stochastic differential equation (SDE) of the Vasicek model is shown on the
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### Input
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- - ` r0 ` ... float, starting interest rate of the Vasicek process.
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- - ` a ` ... float, speed of reversion" parameter that characterizes the velocity at which such trajectories will regroup around b in time.
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- - ` lam ` ... float, long term mean level. All future trajectories of r will evolve around this mean level in the long run.
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- - ` sigma ` ... float, instantaneous volatility measures instant by instant the amplitude of randomness entering the system.
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- - ` T ` ... integer, end modelling time. From 0 to T the time series runs.
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- - ` dt ` ... float, increment of time that the process runs on. Ex. dt = 0.1 then the time series is 0, 0.1, 0.2,...
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+ - ` r0 ` ( float): starting interest rate of the Vasicek process.
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+ - ` a ` ( float): speed of reversion" parameter that characterizes the velocity at which such trajectories will regroup around b in time.
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+ - ` lam ` ( float): long term mean level. All future trajectories of r will evolve around this mean level in the long run.
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+ - ` sigma ` ( float): instantaneous volatility measures instant by instant the amplitude of randomness entering the system.
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+ - ` T ` ( integer): end modelling time. From 0 to T the time series runs.
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+ - ` dt ` ( float): increment of time that the process runs on. Ex. dt = 0.1 then the time series is 0, 0.1, 0.2,...
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### Output
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- - ` interest_rate_simulation ` N x 2 DataFrame with a sample path as values and modelling time as index.
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+ - N x 2 Pandas DataFrame with a sample path as values and modelling time as index.
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## Getting started
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@@ -38,11 +38,11 @@ import pandas as pd
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from Vasicek_one_factor import simulate_Vasicek_One_Factor
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r0 = 0.1 # The starting interest rate
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- a = 1.0 # speed of reversion parameter
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- lam = 0.1 # long -term mean interest rate level correction
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- sigma = 0.2 # instantaneous volatility
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- T = 52 # end modelling time
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- dt = 0.1 # increments of time
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+ a = 1.0 # Speed of reversion parameter
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+ lam = 0.1 # Long -term mean interest rate level correction
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+ sigma = 0.2 # Instantaneous volatility
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+ T = 52 # End modelling time
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+ dt = 0.1 # Increments of time
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print (simulate_Vasicek_One_Factor(r0, a, lam, sigma, T, dt))
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```
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