Paul Wilmott on Quantitative Finance, Chapter 1.2, Time Value of Money

In chapter 1.2, I learned the time value of money. I show a derivation of the formula for continuous compounding from discrete compounding using a Taylor series expansion.

Category:

Education

Tags:

• math
• finance
• quantitative finance
• interest
• taylor series
• nathan's lessons

[papipoet]

I believe that should be "ln" and not just "log" which implies base 10.

[NathanWhitehead]

@papipoet I'm a mathematician, I use "log" to mean base e logarithm. Down with the ln heretics!

[steerox]

Nice video, although at 3.10 I think there are missing parentheses around $\delta x$ in the $\delta x^2$ of the second order term.

[NathanWhitehead]

@steerox

Thanks! In the video I'm thinking of \delta x as a single value, so it's just a single values squared. But you could imagine there is some delta of x^2 as well, so it would be clearer with extra parentheses. Consider them virtually added.

[greek300]

can you do those equations on excell?

[pm51ok]

great explanation! clear and simple~ thanks

[Donk696]

Method short cutting taylor series. m*ln(1+r/m) =r*[ln(1+r/m) - ln(1)]/(r/m) as m -> inf the rhs is just r*derivative of ln(x) evaluated at x= 1, which is just r.

[Faiman1000]

Cool stuff!

[steerox]

Yeah, I realized that after I watched a few more videos. It just looked funny to me at first because I'm reading through McDonald's Derivatives Markets book, in which \delta by itself represents a lease rate (eg dividends).

Thanks for the video notes, by the way. I watched them all yesterday, and they really helped clear up some points of confusion regarding how discrete random walk models relate to the geometric Brownian motion model. These are great!