Comments (17)

• banker

  My favorite explanation for the usefullness of derivatives:

  First, recognize that financial securities are just pieces of paper giving the holder the right to future cash flows. Money payed now, more money received later. There are different types of financial securities (all are used for financing). They fall under two categories: debt and equity. One is loaning and the other is stock investment (colloquially known as).

  Risk: the chance that something bad will happen (like not get payed promised money)

  Return: the compensation (profit of transaction usually measured in percent of principle invested per unit time) for giving up money now for money later

  Risk aversion: a very simple and truthful assumption that given two securities with identical returns the investor will pick the one with lower risk

  Risk/return: more return -> more risk (very simple though ppl sometimes forget)

  Different financial securities have different risk return profiles. Investors (ppl investing savings) have different risk/return preferences. Investees* (ppl needing external financing also have different risk/return preferences.

  Long story short, using derivatives (like futures, options, etc) it is easier to match risk/return profiles of securities to invester/investee preferences by embedding derivative contracts into the security.

  Example forth coming.

  Published: December 13, 2006 8:25 AM

• Person

  I wanted to point out there that that guy who posts here a lot, Mike_Sproul, draws some additional (and controversial) implications from the American/European option equivalence. Specifically, he claims that money can be fully-backed even under extremely constrained convertibility conditions. Maybe he'll drop by and stir up the blog again.

  Published: December 13, 2006 11:46 AM

• adi

  Person, Mike doesnt seem to care that in his theory people wouldnt care if bank has some kind of unilateral right to redeem bank deposit (in reality this is not an deposit, it's loan from the customers to bank) in other form that it originally was. So you might not get 200oz silver (if silver is numeraire) back from your deposit: in its place you might get a title to the farm.

  Some more exotic derivatives seem to very difficult to valuate properly and their liquidity is also a problem. For me some of those stochastic differential equations in the Hull's book appears to be very intimidating.

  Published: December 13, 2006 1:08 PM

• Person

  adi: Person, Mike doesnt seem to care that in his theory people wouldnt care if bank has some kind of unilateral right to redeem bank deposit (in reality this is not an deposit, it's loan from the customers to bank) in other form that it originally was.
  
  Well, I think under his theory a bank could maintain the market price of its currency so that you don't care that you can't redeem it because you can, just the same, buy the good you want on the market at the same price that a physical conversion would have yielded. (Hayek pondered a similar proposal, and Robert_P._Murphy wrote a Daily Article here about it.)
  
  It's tempting to dismiss Mike_Sproul as a crank (and I think he does overstate the conclusions that would be justified by his reasoning), but I still think he has something important to say. After all, if physical convertibility really is so important, why can you still buy anything with US Dollars?
  
  Like Mike_Sproul said, it's obvious that physical convertibility suspension won't matter if it's e.g., overnight. The fact that the bank isn't open 24 hours doesn't affect the value of its notes. Nor, if it required them to be redeemed only in large quantities. The big leap Mike_Sproul makes is when he says, okay, as long the bank conducts open market operations and dumps its assets on the market whenver its notes are trading too cheaply, the dollars can maintain value *as if* they were physically convertible. There's an interesting discussion on Wikipedia's Fiat Currency talk page about this.

  Published: December 13, 2006 2:28 PM

• Dan Ust

  Minor detail and perhaps I missed something, but there are also typical costs involved in an option: the option price, the brokerage fee, and, of course, if you're using borrowed money to buy them, interest. (Taxes might also apply.) So, profit would not be figured out purely by the difference between the strike price and the actual asset price, but by substracting that difference from the cost. It's often the case that an call, e.g., might seem in the money (be profitable) when the costs actually place it out of the money (make it unprofitable to exercise) -- assuming one is exercising purely to realize this profit.

  Published: December 13, 2006 3:57 PM

• RPM

  Minor detail and perhaps I missed something, but there are also typical costs involved in an option: the option price, the brokerage fee, and, of course, if you're using borrowed money to buy them, interest. (Taxes might also apply.) So, profit would not be figured out purely by the difference between the strike price and the actual asset price, but by substracting that difference from the cost.

  Well, I wasn't talking about profit, I was talking about the value of the option at exercise. So yeah, of the stuff you listed I guess broker's fees would count, but other than that it's the difference between spot and strike.

  Published: December 13, 2006 4:31 PM

• Pete Canning

  No mention of a naked straddle?

  Hahaha, an options joke.

  Published: December 13, 2006 6:35 PM

• Mike Davis

  Such reasoning is dead wrong. Rather than exercising his option early, Jones can short sell a share of Microsoft and hold this position (as well as his call) until Friday.
  
  Robert:
  
  I hestitate to nit-pick such a good article. However, by selling short and holding a call, Jones now holds an out-of-the money put with a $20 strike, plus a $15 cash position. If you use B/S with 5% risk free and 25% volatility, the theoretical price of the option is about $15.01 - Jones can always sell it back to the market as an alternative to exercising. (This is also true for European options that have no early exercise provision.) The way out of the money put option, bought for pennies, is what generates the large return if the stock drops to $8.
  
  
  It is also misleading to frame option pricing in terms of probabilities of up or down movement. The follow (contrived) question is a standard interview trap:
  
  A stock is trading at $100. Tomorrow, there is a 90% chance it will close at $101 and a 10% chance it will close a $99. Assuming a risk-free rate of zero, what is the theoretical price of a 1-day expiration at-the-money call?

  
  
  

  Published: December 13, 2006 7:38 PM

• David C

  I hope it is understood here that there are 377 Trillion with a T in outstanding derivatives and that the system is getting ready to collapse, and when it does the US economy is going to collapse right along with it into the worst great depression ever. Not even the Fed can monetize that kind if a default (without hyperinflation).

  I hope it is also understood that everyone is going to cry out that the free market has failed us when it happens.

  The truth is that derivatives are not safe when they are constantly loaning freshly printed up money into the economy all the time, because it leads to massive speculation that creates massive instabilities. They are even less safe when the fed bails out leveraged collapses (like LTCM), because now everyone has a green light to engage in reckless speculation that has the effect of transferring all risks into systemic risks. IMHO, it is only a matter of time before the last straw breaks the camels back and the whole damn system collapses, causing a run on the US dollar and it's near immediate death as a currency.

  Published: December 13, 2006 7:50 PM

• M E Hoffer

  Pete,

  "No mention of a naked straddle?"

  It's been said that: "America's problem is that its only interest, when it comes to "Naked Straddles", is when they involve 'Celebrities' or Politicians."

  Published: December 13, 2006 9:12 PM

• rtr

  Why not examine the "social function" of lotteries?

  Why not examine the "social function" of "reckless speculation"?

  Why not examine the "social function" of "systemic risk"?

  Derivatives spread risk out to a greater pool than otherwise would be the case without derivatives. That's the exact opposite of increasing "systemic risk". LTCM was far less of a debacle than the fall of the rubles and pesos. And that larger debacle was somewhat absorbed by LTCM. And how would the debacle of LTCM be any different than say a debacle of Meteorite Insurance Ltd. if a destructive meteorite were to hit?

  Published: December 13, 2006 9:20 PM

• RPM

  Mike Davis wrote:

  I hestitate to nit-pick such a good article. However, by selling short and holding a call, Jones now holds an out-of-the money put with a $20 strike, plus a $15 cash position. If you use B/S with 5% risk free and 25% volatility, the theoretical price of the option is about $15.01 - Jones can always sell it back to the market as an alternative to exercising. (This is also true for European options that have no early exercise provision.) The way out of the money put option, bought for pennies, is what generates the large return if the stock drops to $8.

  If I understand your concern, then I think it's unwarranted. Did you read the footnotes? I wasn't claiming that Jones should engage in the shorting strategy; I was rather claiming that he shouldn't exercise, because the shorting strategy weakly dominates it. And here I wasn't inventing the argument, but just repeating it from standard textbook exercises.

  Am I missing something?

  It is also misleading to frame option pricing in terms of probabilities of up or down movement.

  Well you're right it may have misled, but I don't think there's anything false in the article. I only discussed option values at the time of exercise; I made a passing reference to B/S for pre-exercise values. And the stuff about probabilities had nothing to do with prices of the options, it had to do with what type of options one might want to buy/sell based on those probabilities.

  Incidentally I did try to vet those passages on wilmott.com, but nobody responded to the thread. Is there a specific thing I wrote that you think is actually wrong (as opposed to misleading)?

  Published: December 14, 2006 10:34 AM

• adi

  Does anyone know about history of derivatives? In Hull's book it was said that somekind of future contracts were made during the 19th century when Chicago Board of Trade was founded as a gathering place for livestock and grain trading.

  I dont know how the people in those days could calculate prices for European put and call - options. Did ordinary people know how to solve Fourier-Stieltjes transformations of partial differential equations ? :)

  Published: December 14, 2006 2:41 PM

• rtr

  Well they didn't have to know complicated mathematics back in the day even if they could put on iron butterflies for arbitrage credits. Bid/Ask spreads were generally much larger for local market makers. Of course, there was a limited time when using Black-Scholes pricing models was advantageous to those who possessed that knowledge before it became widely diseminated. Fading large orders was simple supply and demand pricing adjustment. The important thing is that information was gathered through the market process to the benefit of farmers, ranchers, traders, and speculators. "Reminiscenses of a Stock Operator" has some commodities futures early 20th century escapades in it I believe.

  Published: December 14, 2006 2:57 PM

• Mike Davis

  Robert
  
  Your point is well taken. I did not mean to pour cold water over what I thought was an excellent series of posts.
  Let's see if I can make my point more clearly.
  Jones's portfolio is equivalent to the following portfolio:
  
  100 Shares Microsoft bought at $20
  
  1 put option strike $20.
  
  The key point is that by exercising early, you forgo the time premium. However, since the option is deep in the money, the time premium is negligible. If fact, it is very close to the value of a put option struck at $35 with a strike of $20.
  
  To put it mathematically, for a deep in the money call option, the call price is approximately S - K *exp(-rt). By exercising at S-K, Jones leaves K*(1 -exp(-rt)) on the table. Using your example, Jones pockets $15 and leaves about $0.014 on the table. What I was suggesting was misleading (not wrong) was that the $0.014 left on the table (which is approximately equal to the value of a $20 strike put option struck at $35 for r = 0.05% and a wide range of volatility) could turn into $12. Again, your argument is not wrong. However, from a model perspective the probability of this event is even less than the six sigma event described by Henry, Nassim's quant in "Fooled by Randomness".
  
  The point I suggest you make is that in your example essentially gives you a "free option". When reality deviates substantially from theory and one of these "zero probability" events occurs, one of these options can pay out big. In fact, this is a common option pit (and portfolio) strategy. It works on the hypothesis that by looking at the distribution of actual moves, the market underestimates the probaililty of large moves - it assigns a zero probaility to possible moves that have not been observed.
  This is what Nassim refers to as "the black swan paradox". Or in more rhetorical terms " just because you have never viewed me in a dead state does not mean that I am immortal!"
  
  To summarize all this waffle, your example would have been better had you not chosen an example where to call was so far in the money.
  
  

  Published: December 15, 2006 12:16 AM

• RPM

  Mike,

  I realize I sound defensive and unwilling to tolerate light criticism, but I really don't follow you. At first you seemed to be saying that my example is misleading because the probability of a stock dropping so much in five days is virtually negligible. But then you seemed to make the point that in the real world, we shouldn't treat such moves as negligible.
  

  Published: December 15, 2006 9:44 PM

• Deniel

  Hahaha, an options joke.

  Published: December 20, 2006 9:36 AM