Simulating Interest rates using CIR and HJM
While we can club equity, commodity and currency simulators in one category, interest rate simulators are a completely different animal. First because there is more than one way of modeling interest rates
Equilibrium models and Arbitrage free models.
An equilibrium model is based on a simplified macro model of interest rate [...]
Tag Archives: Building Monte Carlo models
Linking Monte Carlo Simulation with Binomial Trees and the Black Scholes model
A binomial tree uses the same process to generate a path that the Monte Carlo simulation model uses which is also the same model that the Black Scholes solution integrates over an infinitely small interval. From node zero to the terminal node in a [...]
Option Pricing – Building Monte Carlo Simulators in Excel for pricing vanilla & Exotic Options
My first interaction with a Monte Carlo simulation was not a very pleasant experience. It was a exam problem based on a difficult text book and an even more incomprehensible study note that I had hardly understood. But over the years [...]
We have introduced our friend mu (u) as drift and sigma as diffusion (or standard deviation or volatility or vol). In the previous session we have also gone out and built a simple excel based Monte Carlo simulation model for generating stock prices. While the process is focused right on equity securities, the same underlying [...]
Extending MC simulation models to Currencies & Commodities
Extending the original Monte Carlo (MC) Simulator for Equities to Currencies and Commodities required a few simple changes. Rather than using just r, we now use an adjusted r for the model.
In the case of currencies the adjusted yield is the interest rate differential between the domestic and [...]
Here is a slightly revised model for calculating the change in price of an equity security. We now add one more component to our generator function. While the first term works off expected return the second term will help us model uncertainty. Since in our world we drive and link uncertainly with volatility, our model also uses a factor proportional to volatility.
Pricing a financial instrument is not an exact science. There it is out there now; you can go ahead and lynch me for blasphemy.
While the formulae, the mathematics, the derivation, the proofs and the exact models would like us to believe otherwise, in essence pricing financial securities in these markets is more along the lines [...]
Principal Component Analysis and Volatility functions
(The text and methodology given below follows the content covering the subject topics in “Interest Rate Modelling” by Jessica James and Nick Webber).
Principal components analysis (PCA) is a way to analyze the yield curve. It makes use of historical time series data and implied covariances to find factors that explain [...]
Here is the cosmic code joke again. If you can read this, you will understand perfectly what the following section on calibrating the CIR (Cox, Ingersoll and Ross) model means. If you can’t you still have to take that course on computational finance. Now without further ado, here goes:
Calibration of the Cox, Ingersoll and Ross [...]
