Random Fixed Income Returns

Overview


Calculating the random returns to fixed income instruments can be difficult. This is due to the complex nature of the interest rate curve.

When modeling a retirees portfolio of fixed income assets, one must make a determination of how long the maturities of the assets are. If the maturities are all long, then there is not real randomness in the portfolio because all the interest payments are fixed. (although, if the retirement plan involves selling bonds in the portfolio, the market price of each bond will fluctuate).

If one decides to model the randomness of the term structure, one will have to utilize a Term Structure Model. To simplify matters, one could just assume a flat discount curve and implement a single rate model using any of a number of the common short rate models

Simulating an Ito Process


Vasicek 

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]
}
Try it!

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