Table of Contents
Part 1 - Overview and Background
Part 2 - Axioms
Part 3 - Formula Derivation
Part 4 - The Put/Call Parity Formula
Part 5 - The Volatility Smile
Part 6 - The Contradiction
Part 7 - Resolving the Contradiction
Part 8 - The Kelly Criterion
Part 9 - How FSK Trades Options
Part 10 - Only Fools and Hedge Funds Write Covered Calls
Part 11 - Other Options
Part 12 - Summary
The problem with the Black-Scholes formula is not that the underlying Mathematics is wrong. The axioms don't model reality. Options are priced as if the expected return in the underlying asset equals the risk-free interest rate. The expected return of stocks exceeds the risk-free interest rate. The expected return of bonds and commodities also exceeds the risk-free interest rate.
The entire options market feeds off negative real interest rates, sponsored by the Federal Reserve. In an options trade, the two parties to the transaction experience different interest rates. Banks can borrow cheaper than retail customers. Banks can lend at a better rate than retail customers. Banks get much more favorable terms for short sales and investing the short sale proceeds.
Under a gold standard, you can't have a large derivatives market. Negative real interest rates are needed to funnel money to banks and hedge funds. Complicated derivative transactions allow this interest rate subsidy to be packaged and sold.
Options traders do not notice that every listed option is mispriced because they adopt a hedged position and the errors in the pricing model work in favor of professional traders. If you are willing to adopt an unhedged position, you can profit from this structural defect in the economic system.
As a retail customer, you shouldn't make a short stock bet unless you have specific information that a stock is going to tank. Similarly, you should avoid writing calls or buying puts. Statistically, the odds for those trades are very poor because you are betting AGAINST inflation. A retail customer shouldn't short naked puts, because of the margin rules. Long-term deep out-of-the-money calls are extremely attractively priced for a retail customer.
A retail customer can't normally borrow at the Fed Funds Rate to buy stock. When you buy a call option, the interest rate priced into the call option is the Fed Funds Rate, making the purchase very lucrative. This trade is useless to banks and hedge funds, who have other more reliable ways to make money.
Buying out-of-the-money call options risks a 100% loss certain times. A banker or hedge fund manager won't risk losing his job by adopting a strategy that might lose money. Their managers and shareholders want a trading system that *ALWAYS* makes money. The Kelly Criterion tells individual investors approximately how much of their savings they can risk buying options.
When you buy an unhedged call option, it's like you're making a leveraged bet that there WILL be inflation. According to my calculations, some options are mispriced by as much as 200%. The edge from the trade is a lot greater than the transaction costs and capital gains taxes.
Commodity futures are mispriced, because the interest rate priced into the future is the Fed Funds Rate and not the true inflation rate. Bond options and commodity options are also similarly mispriced, although I haven't analyzed the details fully. I couldn't find a reliable online resource for prices and quotes. There are many online brokers that offer stock option trades. I couldn't find a decent online broker for commodity option trades. I've been considering buying some gold, silver, or oil commodity options, but haven't found a good broker or information source.
Analyzing the Black-Scholes formula and its contradictory axioms led me to discover the fundamental structural flaw in the US monetary system. This is a good information source, because all the "official" axioms for the Black-Scholes formula can be found in many economics books. Mainstream economists have a strange ability to simultaneously believe contradictory axioms. I'm lucky that I didn't study economics much in school. I avoided economics because I sensed that there was some funny business going on. I learned to think before I started studying economics.
Saturday, March 22, 2008
Table of Contents
Posted by FSK at 12:00 PM