# Mathematics of Finance, Fall 2015

## Resources and source material

### Review session

Room 517 at 11:05

### Resources on the web

Some materials that complement the textbooks

The yield curve, based on US Treasuries

• Charts of the yield curve, you choose the day. Interest rates have been very low since 2008. The yield curve was very flat in December 2005. It was inverted in December 2000.

Some interesting and famous books related to quantitative finance.

### R and coding practice

There are many web pages on R programming. I have selected my two favorites, but you should feel free to surf the web looking for others. R is similar to Matlab and Python, but the documentation is worse.

Classes that use R have pages with links (like this one).

Style in programming is important, particularly if you want your code to work. Programmers argue about style conventions, but good programmers all have them. Look at their code and see. Much of the R code posted on the web as examples has awful style. You should have higher professional standards than these hackers. This course does not use the "object oriented" parts of R. You don't have to read up on classes with style.

### News and blog articles

Here are news articles and blog posts that might be interesting to math finance students. It's a good idea to read and think about them even if you're not interested. This is the kind of thing interviews love to ask about. You will see that most of them come from just a few sources. You might want to follow a few sources directly.

• Treasury forwards.: A forward contract is an agreement today to buy (or sell) a specified asset at a specified time and price in the future. The market price of a forward contract (futures contract, probably) reflects "the market" view of what the price will be in the future, sort of. Now, the market thinks the interest rate on US Treasury will go up slowly over the next year or two.

• VIX.: "Volatility" is a parameter in the Black Scholes option price formula. The price is a function of the volatility. If the option is traded and has a market price, the "implied volatility" ("implied vol") is the volatility parameter in Black Scholes that gives the market price. VIX is a forward contract on the implied volatility at some point in the future. The VIX price today reflects what "the market" thinks implied vol will be in the future.

• Transperency is important for financial markets. One form of transperency is accurately reporting risks associated to investments. This is important in "mortgage backed securities", which are bundles of mortgages. One way to invest money is to lend it to a home buyer as a mortgage. Banks used to do this. Now, they "bundle" mortgages, so an investor can buy a small percentage of a pool of mortgages and get the appropriate percentage of the mortgage payments. Bundlers can cheat and put high risk mortgages into low risk pools. The economy allows high risk assets, but it strongly depends on low risk assets being safe.

• The Gaussian copula is a model of the correlation between defaults. It has a parameter R that controls the amoung of correlation. If you have a basket of many bonds or loans, the correlation determines the risk, which is uncertainty in the total number of defaults. If there is no correlations, then the number of defaults is very nearly the default probability multiplied by the number of bonds or loans. One way to invest money is to lend it to a home buyer as a mortgage. Banks used to do this. Now, they "bundle" mortgages, so an investor can buy a small percentage of a pool of mortgages and get the appropriate percentage of the mortgage payments. Bundlers can cheat and put high risk mortgages into low risk pools. The economy allows high risk assets, but it strongly depends on low risk assets being safe. This famous article blamed the parameter R rather than the people who set it too low.

• The Economist defends the Gaussian copula. It's in the "all models are wrong, some models are useful" camp. Some model is better than no model. Of course, that's true only if people understand the limitations of the model. It's especially important that MBA holders not be allowed to manipulate the parameters in the model to get the outcomes they prefer.

• Noah Smith (at Bloomberg) describes the current state of financial engineering. "Engineering" means creating complex rules for who gets how much money under which situations. For example, there can be a pool of corporate bonds from many shaky companies. We know some of them will default, so the coupon stream from the pool will be less (maybe a lot less) than the promised stream. If we feel confident that at least half of the stream will actually come in, we can sell that half as being relatively safe. Then we can sell the much more risky second half at a big discount. That way we strip out and sell off the risky part of the asset.