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Tuesday, March 18, 2008

The Black-Scholes Formula is Wrong! - Part 11/12 - Other Options

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

Up to this point, I've been primarily discussing stock options. Other types of options have the same defect.

Bond Options

Bond options suffer from the same defect as equity options.

A stock options trading account can be opened for $5k or less. The bond options market isn't accessible unless you have a lot more capital and are a lot more knowledgeable.

Bond options are also priced as if the expected gain in the bond equals the risk-free interest rate, due to the put/call parity formula. The expected return from bonds is always greater than the risk-free interest rate. Even Treasury Bonds have an expected return slightly higher than the average future Fed Funds Rate, because otherwise there would be an arbitrage opportunity for banks.

Banks and hedge funds are allowed to use higher leverage ratios when investing in bonds compared to stocks. For stocks, leverage ratios are usually restricted to 7x. For high-quality investment-grade bonds, leverage ratios over 100x are allowed. For other bonds, I believe leverage ratios of 10x-20x are allowed. I don't know the full details.

The same error that applies for stock options applies for bond options. Banks receive the same massive government subsidy trading bond options that they receive trading stock options.

Gold, Oil, and Commodity Options

Gold, Oil, and other commodity options suffer same from the same defect. The options are priced as if the expected gain in price equals the Fed Funds Rate. Commodities actually rise in price much higher, according to the true inflation rate.

I considered opening a gold options account, but I couldn't find a good online broker. The market for online stock options trading is much more advanced than the market for online commodity options.

If you buy a long-term commodity option or future, you are making a leveraged bet that there WILL be inflation. As with stock options, the long-term out-of-the money options are the best deal.

You could also buy a futures contract. When you buy a futures contract, the future price equals the current spot price plus interest accumulated at the Fed Funds Rate. I think that a futures option is a better deal, but futures themselves are a good deal. The interest rate priced into the futures contract is the Fed Funds Rate, but any tangible asset will appreciate faster than the Fed Funds Rate.

I don't know what the retail customer margin rules are for futures contracts and futures options. I haven't found any detailed description of the margin rules applied to retail customers. My guess is that directly buying futures has unfavorable margin rules. Future options might be a good deal.

Convertible Preferred Stock

Convertible preferred stock contains an embedded call option as a component of the price. Typically, hedge funds will buy convertible preferred stock and short sell the underlying stock. I haven't tried to price convertible preferred stock. Each issue is different and you would have to read the fine print. The same pricing error that applies for the Black-Scholes formula applies to pricing convertible preferred stock.

Incentive Stock Options

Corporations issue incentive stock options to their executives. There is a recent accounting requirement for corporations to expense their options.

However, the options prices are calculated using the same defective Black-Scholes formula. They are priced as if the expected gain in the stock price equals the risk-free interest rate. The incentive stock options are typically VERY LONG TERM options, usually 10 years. This means that these options are INCREDIBLY mispriced. Stocks typically go up 10%-15%/year, close to the true inflation rate. Incentive stock options are expensed as if the expected gain is only 5%.

Most corporate annual statements are filled with this contradiction. In one section they say "We expect to grow earnings at a rate of 10%-15% per year", which is very easy since that's the true inflation rate. In another section they price their incentive stock options as if the stock will only go up at a rate of 5%/year.

Even though the management of a corporation is able to loot the shareholders by granting themselves options, stocks still are a good investment. For a large corporation, management can't grant themselves options worth more than 1% of the corporation each year, without seeming too greedy. If inflation is 10%, this 1% theft turns a 10% return into a 9% return, which still is an attractive inflation hedge.

1 comment:

Anonymous said...

Dear FSK or whatever,
It is interesting how smart people can often be incredibly stupid.
Once again, at the risk of being called a troll feeder or whatever, I would like to point out that in the cause that you and I have chosen in common, PRIVACY is the most important thing, web statistics and other conveniences simply fade in comparison.
You betray all of us by bugging your own blog to the benefit of the red/pink organizations.
Sure, you say with a righteous finger pointing up, they already know everything! WRONG. They don't know everything, and the less YOU give them the less they know.
So why don't you help the ignorant fools who don't know that one must run NoScript in their browser and block cookies to STOP FEEDING THE TROLLS, and better yet, stop feeding them yourself!
Here is a parting shot for your reading pleasure:
Remember, Red organizations actually have nothing better to do than sift through mountains of data, simply to keep their jobs.
Paranoid Bastard

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