The simple online cash advance application takes just minutes to complete

ELEMENTARY PRINCIPLES OF DERIVATIVE PRICING

In this post, we take a preliminary glance at how derivative contracts are priced. First, we introduce the concept of arbitrage. Arbitrage occurs when equivalent assets or combinations of assets sell for two different prices. This situation creates an opportunity to profit at no risk with no commitment of money. Let us start with the simplest (and least likely) opportunity for arbitrage: the case of a stock selling for more than one price at a given time. Assume that a stock is trading in two markets simultaneously. Suppose the stock is trading at $100 in one market and $98 in the other market. We simply buy a share for $98 in one market and immediately sell it for $100 in the other. We have no net position in the stock, so it does not matter what price the stock moves to. We make an easy $2 at no risk and we did not have to put up any funds of our own. The sale of the stock at $100 was more ! than adequate to finance the purchase of the stock at $98. Naturally, many market participants would do this, which would create downward pressure on the price of the stock in the market where it trades for $100 and upward pressure on the price of the stock in the market where it trades for $98. Eventually the two prices must come together so that there is but a single price for the stock. Accordingly, the principle that no arbitrage opportunities should be available is often referred to as the law of one price. Recall that we mentioned in earlier posts that an asset can potentially trade in different geographic markets and, therefore, have several spot prices. This potential would appear to violate the law of one price, but in reality, the law is still upheld. A given asset selling in two different locations is not necessarily the same asset. If a buyer in one location dis- covered that it is possible to buy the asset more cheaply in another location, the buyer would still have to incur the cost of moving the asset to the buyer’s location. Transportation costs could offset any such price differences.
We have just had a taste of not only the powerful forces of arbitrage but also a pricing model for one derivative, the forward contract. In this simple example, according to the pricing model, the forward price should be the spot price increased by the interest rate. Although there is a lot more to derivative pricing than shown here, the basic principle remains the same regardless of the type of instrument or the complexity of the setting: Prices are set to eliminate the opportunity to profit at no risk with no commitment of one’s own funds.
There are no opportunities for arbitrage profits.
Lest we be too naive, however, we must acknowledge that there is a large industry of arbitrageurs. So how can such an industry exist if there are no opportunities for riskless profit? One explanation is that most of the arbitrage transactions are more complex than this simple example and involve estimating information, which can result in differing opinions. Arbitrage involving options, for example, usually requires estimates of a stock’s volatility. Different participants have different opinions about this volatility. It is quite possible that two counterparties trading with each other can believe that each is arbitraging against the other.
But more importantly, the absence of arbitrage opportunities is upheld, ironically, only if participants believe that arbitrage opportunities do exist. If market traders believe that no opportunities exist to earn arbitrage profits, then they will not follow market prices and compare these prices with what they ought to be, as in the forward contract example given above. Without participants watching closely, prices would surely get out of line and offer arbitrage opportunities. Thus, eliminating arbitrage opportunities requires that participants be vigilant to arbitrage opportunities. In other words, strange as it may sound, disbelief and skepticism concerning the absence of arbitrage opportunities are required in order that it hold as a legitimate principle.
Markets in which arbitrage opportunities are either nonexistent or are quickly eliminated are relatively efficient markets. Recall from your study of portfolio theory and investment analysis that efficient markets are those in which it is not possible, except by chance, to earn returns in excess of those that would be fair compensation for the risk assumed. Although abnormal returns can be earned in a variety of ways, arbitrage profits are definitely examples of abnormal returns, relatively obvious to identify and easy to capture. Thus, they are the most egregious violations of the principle of market efficiency. A market in which arbitrage profits do not exist is one in which the most obvious violations of market efficiency have been eliminated.
Throughout this blog, we shall study derivatives by using the principle of arbitrage as a guide. We will assume that arbitrage opportunities cannot exist for any significant length of time. Thus, prices must conform to models that assume no arbitrage. On the other hand, we do not want to take the absence of arbitrage opportunities so seriously that we give up and believe that arbitrage opportunities never exist. Otherwise, they will arise, and someone else will take them from us.

Posted in DERIVATIVE MARKETS | Comments Off

CRITICISMS OF DERIVATIVE MARKETS

Derivatives have been highly controversial for a number of reasons. For one, they are very complex. Much of the criticism has stemmed from a failure to understand derivatives. When derivatives fail to do their job, it is often the derivatives themselves, rather than the users of derivatives, that take the blame. Yet, in many cases, the critics of derivatives simply do not understand them well enough. As described in former posts, when homeowners take out mortgages, they usually receive a valuable option: the right to prepay their mortgages. When interest rates fall, homeowners often pay off their mortgages, refinancing them at lower rates. The holders of these mortgages usually sell them to other parties, which can include small organizations and individuals. Thus, we often find unsophisticated investors holding securities based on the payments from mortgages. When homeowners refinance, they capture huge interest savings. Where does this money come from? It comes from the pockets of the holders of mortgage securities. When these unsophisticated investors lose a lot of money, derivatives usually get the blame. Yet these losses went into the pockets of homeowners in the form of interest savings. Who is to blame? Probably the brokers, who sold the securities to investors who did not know what they were buying-which leads us to the next common criticism of derivatives.
The complexity of derivatives means that sometimes the parties that use them do not understand them well. As a result, they are often used improperly, leading to potentially large losses. Such an argument can, however, be used to describe fire, electricity, and chemicals. Used improperly, perhaps in the hands of a child or someone who does not know how to use them, all of these can be extremely dangerous. Yet, we know that sufficient knowledge of fire, electricity, and chemicals to use them properly is not very difficult to obtain. The same is true for derivatives; treat them with respect and healthy doses of knowledge.
Derivatives are also mistakenly characterized as a form of legalized gambling. Although gambling is certainly legal in many parts of the world, derivatives are often viewed as a government’s sanction of gambling via the financial markets. But there is an important distinction between gambling and derivatives: The benefits of derivatives extend much further across society. By providing a means of managing risk along with the other benefits discussed above, derivatives make financial markets work better. The organized gambling industry affects the participants, the owners of casinos, and perhaps some citizens who benefit from state lotteries. Organized gambling does not, however, make society function better, and it arguably incurs social costs.
We have taken a look at what derivatives are, where they come from, where they are now, why we have them, and what people think of them. Understanding derivatives, however, requires a basic understanding of the market forces that govern derivative prices. Although we shall cover derivative pricing in more detail in later posts, here we take a brief look at the process of pricing derivatives by examining some important fundamental principles.

Posted in DERIVATIVE MARKETS | Comments Off

« Previous Entries
Next Entries »