## Archive for the ‘finance’ Category

### Python Monte Carlo graphs

Wednesday, November 16th, 2011

I wanted to plot the paths of my Monte Carlo simulation of Black Scholes in my previous post. Using iPython started with the --pylab flag, it's pretty easy. [sourcecode language=Python] from math import exp from random import gauss St0=41.75 rate=.0535 vol=.34 trials=100 for trials in range(trials): prices=[St0] for day in range(time): ...

### Black Scholes Monte Carlo in Python

Wednesday, November 16th, 2011

The Black Scholes formula is a partial differential equation that can be used to price the present value of an option under certain assumptions. As with everything, you can read all about it in Wikipedia. It turns that that figuring out the present value of an option is also a ...

### Bootstrapping Zero Curves

Sunday, June 8th, 2008

A yield curve is a representation of what interest rates you could lock in today for investments over different periods. It's effectively a set of yields for securities of different maturities (typically cash rates at the short end, futures and then swaps at the longer maturities - see the ...

### The “Mathematical Constant” and Continuously Compouding Interest

Sunday, June 8th, 2008

One of the (many) aspects of the "Mathematical Constant" $$e$$ is that: $$\lim_{x\to\infty} (1+\frac{1}{x})^x = e$$ This property makes $$e$$ very useful for working on compounding interest problems. How so? Let's start with the basic time value of money formula giving the relationship between the PV (present value) and FV (future value) given R (the ...