https://anonfiles.com/file/69d36074de50b14ec7afa334d9a31da8
[Edit: the diagram captures the basic idea but is outdated. I am travelling now, but will release an updated version when I return
The modifications are simplifications. I.e. no changes to the basic system, but only one type of derivative instead of several and increased automation..]
Feel free to ask questions. I am also working on a text based explanation.
The amount of text is huge, so I figured a diagram is better.
Since the diagram is still arcane and any rigorous text would be much worse...
Here is explanation based on analogy:
Have you ever seen the pyramid of champagne glasses at a wedding? A giant bottle of champagne is poured into the top glass. The top glass overflows into the second tier of glasses. The second tier of glasses overflow into a third tier, and so on. Here is a video if this is completely foreign to you ...
http://www.youtube.com/watch?v=k-wXLnMTiwY
Suppose that we have one bitcoin.
Think of the volume of cheap champagne you can purchase with one bitcoin. This volume fluctuates over time.
Think of the pyramid of glasses. Suppose each glass can hold one USD worth of champagne before it overflows. In the future, maybe a bitcoin will be worth enough to fill a whole pyramid of glasses
... or maybe just a single glass 
.Now suppose we commit to buying 1 bitcoin worth of champagne one year from today. We also commit to pouring the champagne we buy into a pyramid of glasses.
The blockchain enforces these commitments as txn rules. There is no trust involved at all.
Now suppose we sell off ownership of each individual glass in the pyramid right now. We won't know exactly how much each glass is worth until next year, but we can still sell them now.
Which glass would you want if you could have your pick? That's right, the top glass. It gets filled with champagne first. As long as 1 bitcoin sells for more than $1 a year from now, this glass will be worth 1 USD.
The top glass is very useful as a medium of exchange. I could agree to pay you ten top glasses next year in exchange for a USB stick. I don't have to worry about overpaying (since they are worth at most 10 USD). You don't have to worry about being short-changed (since they are highly unlikely to be worth less than 10 USD). You can set prices in terms of top glasses and not have to worry about adjusting them.
Under a free market, the glasses will all trade for different prices (all between $0.00 and $1.00).
The bottom glasses will be the cheapest. The top glass the most expensive.
The system I designed allows a bitcoin to be divided into a pyramid of glasses. The top glass always sells for about $1 as long as a bitcoin is worth more than say $10.
Glasses in the second tier also always sell for about $1 as long as a bitcoin is worth more than say $25. The lower tiers of glasses fluctuate wildly in price.
Why is this helpful? The fact that a bitcoin is worth $10 in Feburary and $200 in April and $80 in June is a big problem. It causes trouble/worry for bitcoin-focused businesses, bitcoin users, bitcoin workers, and anyone accepting bitcoin as a means of payment. If we can divide bitcoins into a pyramid of glasses worth up to 1 USD each, then we can solve this problem. Everyday users of bitcoin can exchange the top and second tier glasses only. They won't have to worry about price movements any more than if they were using paypalUSD. Moreover, they still have all the freedom, anonymity, and security from confiscation offered by bitcoin.
Storage of USD value in the blockchain also reduces dependence on the banking system. Speculative trades, for example, do not need to rely on Mt. Gox or banks with their AML/KYC rules. They can be completely decentralized.
High-risk investors can speculate in the enormously volatile bottom glasses. Average investors can just purchase and hold some bitcoin. The expanded functionality will facilitate bitcoin adoption and lead bitcoin to appreciate in value.