Overview

Vasicek


{% dr = (b - a r) dt + \sigma dW %}

Topics


Calibration


There are three parameters to the Vasicek model. Therefore, unless the parameters are pre-sepcified, it will require three zero coupon bond prices to fit the model.

However, while the model may fit the 3 selected prices, it will not fit the entire curve, only the selected bonds. This limits the ability of the modeler to calibrate the vasicek model to a given curve. For some applications, this lack of fit may be acceptable.

Bond Option Formula


(see bjork pg 386)

Monte Carlo Simulations


Fixed Income analysis is a complex subject. The davinci library contains a number of differenct tool for analyzing cash flows from fixed income instruments. This corner goes through some simple examples.

copy 

let ito = await import('/lib/statistics/simulations/v1.0.0/ito.mjs');

let a = 0.1;
let b = 0.1;
let sigma = 0.1;

let dt = function(points){
    return b - a*points[points.length-1]
}

let data = [];
for(let i=0;i<5;i++){ let sims=ito.generate(300, dt, ()=>sigma, 0.5)
  sims=sims.map(p =>{
    return {
      value:p,
      sim:(i+1).toString()
    }
  });
  data = [...data,...sims]
}

$val.set('data',data);
Try it!

Extended Vasicek Model


Extended Vasicek Model - The Vasicek model was extended by Hull and White in order to create a model that can be calibrated to the entire curve.
{% dr = (b(t) - ar)dt + \sigma dW %}

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