Investment XYZ

Sunday, July 16, 2006

How the Derivative Market Works

[Keywords] Liquidity; Fungibility; Quasi-Fungibility

Investment starts and ends with the buy and sell of assets. The buy/sell can take place in private or public market; the products to trade can be actual assets or contracts. In this article we will look at one special type of market: public derivative market.


Derivatives are security products derived from other products (the underlying securities). For example, equity options are derivatives derived from equities (stocks); currency options derive from currency. Etymologically, you can derives something from another and call it derivative and the loop can go on forever so there is no clear way to separate derivatives and underliers. In reality, it is easy to draw a clear line between "underlying securities" and "derivatives". I will just call stocks, currency, index futures, commodity futures, bonds, interest rates as underliers, and all the options, vanilla or exotic, would be called derivatives. Certain derivatives may not have the exact tradable underliers. For example, some index options are defined by index values, which are not tradable (index values are simply calculated from the prices of components), while index futures (a tradable product) or ETF replicating an index (also tradable) are not the exact underlier of these index options. Actually these futures and ETF may have their own options. Interestingly, CBOE VIX futures is an underlying product based on VIX index -- the index representing the weighted average implied volatilities of SP500 (SPX) options; while SP500 options are derivatives. In February 2006, CBOE also came up with VIX options which are derivatives on VIX index (not VIX futures).

Public Market Characteristics

All public exchange markets for financial instruments (stocks, commodities, currencies, derivatives, etc.) have these common characteristics:

1. Basic function: Exchanges are where buyers/sellers meet and buy/sell orders are matched automatically;

2. Public prices: the pricing information for the traded securities are public. Typically these prices are the traded prices; bid prices and ask (offer) prices;

2. Price discovery mechanism: Double auction system and Request for Quotes (RFQ) system;

3. Market players: 1) Brokers; 2) Market Makers; 3) Dealers; 4) Customers/Investors.

The Players

Investors/Customers: the players who have speculations or opinions of certain financial instruments and initiate orders, either long or sell or short. This type of players includes individual investors, institutional investors, hedge funds, etc. The customers are the party who is willing to take risks and make profit if the speculations turn out to be correct.

Brokers: Brokers connect the buyers with sellers and take no risks in the transaction, earn on commissions (fees) only;

Dealers: dealers are the party who would provide and commit to a quote if customers request, or have to take opposite side of customer orders if the order is executed. For example, if a broker has a buy order from a customer, but there is no exact sell order from another customer to match, the broker has to find a dealer to take the other side to sell and complete the trade. Dealers have to use its own capitals to take risks (take positions) and provide liquidity (namely, taking the other side of customer/investor orders).

Market Makers (MM): a special kind of dealers. MM have the obligation to post two-side market (bid prices for sell side, ask prices for buy side) for the product they cover and commit capitals to those prices -- that means if a customer wants to buy at the ask price the MM posts (within the size the MM willing to take), the MM has to take the order, no matter whether he can find a seller on the other side or not. If he cannot find a seller immediately, he has to commit his capital to take the position (which is opposite to the buying customer, i.e., short in this example).

In an ideal world, a public market should be just a matching engine that match willing buyers and seller on both sides, so that both sides have opposite opinions and both willing to take risk for their views. In reality, such perfect matches can only fulfill part of orders. Large part of orders require a temporarily "bag holders" -- the dealers and market makers -- to hold the other sides of customer trades, otherwise the liquidity would be thin or dried up. When the media or the public yelling "Everyone is selling! The market is crashing!" it only means all the initiated trades are on the sell side, or "hitting the bids", while obviously there are equal number of buyers at the same time to take the other side of the sell orders.

Let's look at how a trade is made from the liquidity angle: When customers initiate orders, the liquidity provided by the dealers/MM are taken by the orders. For this reason, the initiators trade at the worse end of the prices -- buy on ask (higher) prices and sell on bid (lower) prices, while the passive sides get to trade at the better end of the prices. Customers are called "liquidity takers", and market makers and dealers are called "liquidity providers".

Double Auction System

The modern public financial markets ("the exchanges") operate mostly as a "double auction" system, which is similar to the common auction except it allows competition on both buy and sell sides. Some areas of the exchanges use the Request-for-Quotes -- RFQ -- system for large orders, which is typical for OTC market. With the market becoming more and more electronic (where all electronic exchange all using the double auction system), it seems safe to assume double auction is the prevailing system.

In typical auctions (like on the farmer's market), bidding only happens on the buy side and the competition causes the price to only go up from the starting bid. Ebay's Dutch auction system works in the same way. In the double auction system, the competitions happen on both the buy side and the sell side. In addition, there is no auctioneer to control the settlement point of an auction -- transaction occurs when the highest buy price meets or exceed the lowest sell price. The auction process in the exchange marketplace happens continuously: the buy sides and sell sides are both pools of dynamic participants -- either the participants constantly updating their buy/sell prices, or players constantly coming in and out of the pools. Transactions occurs when the buy and sell currents intersect. It is worth noting that such intersection happens only within one exchange. It is possible at some moment the highest bid in one exchange may be higher than the lowest ask in another exchange on the same product. That is the opportunity for inter-exchange arbitrageurs to bring the prices inline.

So who are in the auction?

Investment public may believe only the professionals battle it out in the auction, while the investors would just stand on the sideline and watch, and trade only on the "official" prices emerged. In fact, it is important to understand that both the customers and dealers take part in auction and the price discovery directly. Any customer orders takes part in the auction just as the market making commitments from the dealers. There is nobody setting prices for any equities. The dealers/MM constantly stay in the market providing bid and ask prices, but when their prices are in the market, they are as equal as any orders coming from individuals or from funds. There are no priority difference except for the best bid/offer (the highest bid and lowest ask), where, by SEC rules, customer orders should have higher priority than dealers' orders if all conditions are the same. The commonly quoted bid/ask prices for any security at any moment are just the highest of all the bids and the lowest of all the asks in the entire auction system. The bid/ask prices posted by market makers and dealers are basically limit orders just like those from coming from the customers. Market is just a mixing pot of buy/sell orders and posted prices.

How the underlying market works

One of the most liquid and diverse underlying markets is the stock market. Stock market behaves like a farm market that constantly moves inventory. The market makers (called "specialists" on NYSE and AmEx) ideally just match liquidity on buy/sell sides and only take in profits in instantaneous bid/ask spreads. When the buy/sell order flows are out of balance, the market makers have to hold the bag (meaning temporarily holding positions sold to him by sellers, while looking for buyers on the other side, and vise versa). Holding bags can lead to profit or loss overwhelming the consistent profits from the bid/ask spreads. Nevertheless, the stock market in the US has huge liquidity, meaning at any moment there are always buyers and sellers readily available, so that statistically market makers can even out the buy/sell imbalance risk and eventually win out on the bid/ask spreads in the long run. That's the idealized principle. In reality, market makers may intentionally take advantage of the information in liquidity bias and lean on one side or the other to profit through the carrying positions, rather than just passively matching buy/sell orders or carrying opposite positions for customers. Of course that entails risk, the same risk as investors are carrying when holding positions.

How the derivative market works

In principle, shouldn't the derivative market work in the same way as the stock market? The market makers should just match orders on both sides and profit from the bid/ask spreads? After all, the derivative market in the world is growing rapidly and there is huge liquidity in it.

However, the liquidity is still much worse in the derivative markets comparing with the underlying markets (like the stock market and commodity market), and it is because the intrinsic nature of derivatives, not because of the any immaturity of the markets.

The products traded in the derivative markets are contracts based on the underlying securities. Take a look at equity options, for one underlying stock, in principle there are unlimited number of ways to create contracts as derivative products. The exchange traded option market has standardized the option products, but still for the public traded equity options, for each underlying stock there are about 70 options products due to variation in strikes, expiries and settlement types. Even when overall liquidity for all options products are high, when spreading out over all these individual options, the liquidity on each one becomes relatively thin especially when comparing with underlying stocks. Furthermore, liquidity is not spread out evenly over all these products. Typically the far out-of-money or deep-in-the-money options have much smaller liquidity than the near-the-money ones.

Comparing with stock market makers who constantly match buy/sell orders (which these days may be better done through computer system for majority of orders), derivative market making is a high art. Buy/sell order flow matching, if any, is the most ideally way to make market, but there is additional technology needed to make up the lack of liquidity for the derivative market making to be viable.

Can "Fungibility" Help?

By definition, fungibility means interchangeable. In the derivative world, it means two contracts (or instruments) that are identical in terms and specifications can be considered interchangeable. Examples of fungible commodities are gold and petroleum: to fulfill a contract of 1000 oz of gold of certain grade, the delivery can come from any sources, as long as the delivered goods meet the specifications in the contract. On the other hand, diamond and original artworks are non-fungible. Every piece of diamond and artworks is unique, non-interchangeable.

In option market, public listed options are totally fungible, the fungibility is guaranteed and realized through the clearing firms and Options Clearing Corporation (OCC). Option contracts through different parties are netted in the clearing firms, so that counterparty risk is entirely removed. Furthermore, options traded in one option exchange can be easily netted with the same contract traded on another exchange (currently there are 6 public option exchanges).

Pure fungibility, though helpful in liquidity in derivative market, is still far from suffice to enable market makers to stay position free. Due to the prolific derivative products, unlike stocks, it is almost impossible for market makers to perfectly match buyer and seller on the exact same product at the same time. For example, an order to buy 500 contracts of IBM Jan07 strike 80 call is unlikely to meet a sell order of the same call, while in the mean time there may be sell orders of calls on different strikes or expiries. The market makers in the derivative market have to often "hold bag" -- take on positions -- rather than like in the stock market that positions are typically undesirable for market makers and can be avoided. In the above example, after the trade is executed, the customer and the market maker end up in opposite sides of the contract. The market maker is holding a short IBM Jan07 strike 80 call. The customer initiates the trade because he has a certain view (bullish on IBM stock, for example), while the market maker may or may not shares the same view as the customer, he has to hold a position of opposite view. While he is holding the bag looking for another seller that can take his position, the market is constantly moving, and the bag he is holding becomes a big risk, unless some other measure is taken.

Typically that measure is hedging.

The option MM would buy a certain quantity of IBM shares as hedge to the short IBM call position, so that when IBM price goes up or down, one of the leg would make profit, the other one would loss. How can he makes money in the end then? Remember the function of MM is to profit from the bid/ask spread which is the reward for they duty to provide liquidity. The job of MM is not to bet against the customers. However, in this option trade, there is no immediate way to lock in the bid/ask of the profit because there is no immediate sell order to sell the IBM Jan07 80 Call on the bid. The best way the MM can do is to use stock to create a "product" resembling a sell order of the call that the MM can buy to offset his holding position of shorting the call. Obviously, the share he purchases is not the same as the call, not even in the delta (direction) dimension since when the market changes, the delta of the call changes constantly. But that's better than taking naked risk. Furthermore, if the MM regularly adjusts the stock holding according to some model, the created "product" looks more like a real call options. Thus the hedging process of the market makers because of massive mathematical undertaking -- every day they have to recalculate the delta using a certain option pricing model, re-adjust the stock position to create some kind of delta neutral position. A process called "dynamic hedging".

All these are both exact science as well as art. The whole point is for the derivative market makers to create some kind of similar (but far from exact) equivalent compound products to offset the holding positions opposite to customer orders. In this way, such "constructed products" can mitigate the intrinsic problem of lack of liquidity in derivative market.

Since the offsetting is far from exact, the residue risks also open new opportunities for profit and loss, as well as it opens up an art and science of how to create these quasi-offsetting products (you may now get a hint why Wall Street needs so many science PhD).

Hedging and Quasi-Fungibility

If the MM cannot always find perfect interchangable (fungible) products to offset his position, maybe less-than-perfect substitutes can do the trick. I call such process quasi-fungibility. Quasi-Fungibility is to substitute one derivative with another (or a collection of other derivatives and underlying instruments) so that the two have similarity to certain degree on certain dimension.

Delta hedging is one common way of creating quasi-fungibility. There are many more. Besides the delta risk, the market makers have to continue create quasi-fungible products to mitigate position risks on other dimensions. They also have to identify any hidden risks that the quasi-fungible products haven't be able to cover yet. In fact, any quasi-fungible hedging product hedge away some risks, but create new risk on different dimensions. For example,

1) Hedging a call option with stock: even a vanilla call option has many more dimension of risk that quasi-fungible product made of dynamics hedging of stock still cannot remove. The stocks dynamic hedging removing the delta risk, while the implied volatility (vega), time decay (theta), interest rate (rho) and dividend risk are still exposed. Besides, the dynamics hedge with stock actually brings in a new risk: the model risk. To correctly buy/sell stock to hedge the option delta, the hedger needs to use a certain model that tell him whatever the option delta should be. The model itself is certainly not exact science, leaving certain degree of uncertainty in knowing how good the hedge is.

2) Using a near term options plus stock to hedge a far term option. In theory, this quasi-fungible product can hedge away both delta and Vega risk, however, besides the model risk mentioned above that has been brought in, this position is exposed to the volatility term structure risk (the difference in implied volatility for near term and far term options), and additional operation and liquidity risk (the hedger has to keep adding near term options when the old one expires).

The Myth of Hedging

The word "hedge" seems to inject some sophistication and mystery in the air. It is a concept usually misunderstood by the investing public, even worse, the word itself implies some linkage to the often talk about "Hedge Funds" which unfortunately is a misnomer and in fact has nothing to do with hedging. Financial media seems to fan the investment public's imagination by hinting that hedging can create wealth in certain mysterious way, but only the professionals know how to hedge.

The second part of the statement is probably true -- typically only professionals in the market place hedge. But hedge does NOT create wealth.

Hedge is a poor man's way of creating pseudo-balance in buy/sell order flow, creating quasi-fungibility to flat out MM's positions. Hedge is a risk management measure, which is generally a cost, not a revenue (or wealth) generator. The profit cannot come from hedging, but should from other dimensions that are unhedged and intentionally exposed to risks.

In the case of true balance, a position is perfectly closed thus there is no risk remains (perfect hedge). For example, an investor sells all the stock he owns, that is a true balance or perfect hedge without residue risk, he converts a volatile asset (stock) into a stable asset (cash). But typically this closeout trade is not called hedge. "Hedge" typically indicates there is some less-than-perfect balance. For example, if the investor still want to keep the stock but afraid of the stock price going down, he can purchase put options with the amount that offset the directional part of the risk (for example, buying 1 contract of at-the-money put for every 200 shares of stock). This hedges away one dimension of risk ("delta"), but it is a pseudo-balance: 1) when the market moves, the delta can become imbalanced again; 2) the delta can even become imbalance simply as time goes by ("delta decay"); 3) With option in the portfolio, now there is additional dimension of risks (and opportunities) exposed (for example, the implied volatility risk, or "Vega"). In another word, the balance is quite imperfect, thus it is called a hedge.

There are three situations when hedging is used: 1) Hedge as a risk management tool, such as an investor buying puts to protect his stock holding. In such cases, hedge is a typically a cost; 2) Hedge as a liquidity supplement. For example, a corn producer wants to lock in the product price before the harvest by selling corn futures to hedge his crops that are still growing in the field, thus liquidity is created even before the products are available. In these cases, hedge is a cost for the liquidity takers (the farmer), while the liquidity providers (the market makers of the futures contracts) get paid through the bid/ask spread for providing liquidity and take risk of the other side. 3) Some market players speculate on certain dimension of the market (for example, speculating dividend increase for a stock), while there is no direct financial instrument for the dimension, they can construct a compound product to expose the particular dimension, while hedge away all other dimensions. In the example of dividend trade, the trader can buy put, sell call of the same strike, and hedge with stock, so that there are no directional or volatility risks, while the dividend risk is directly exposed (to be exact, the interest rate risk is exposed in the mean time). I will illustrate an example below.

In all cases, hedging is a cost, not a wealth creator. However, hedging is the lifeline of derivative market. Through hedging, quasi-fungible products are created, liquidity is expanded, more derivative products can be traded. Market makers can provide liquidity without being forced to take naked risks.

Let's look at a few scenarios how the quasi-fungibility is created to hedge.

1. Option market making

Dynamic delta hedging is the top item on the recipes for option MM, but that's far from the only tool. Ideally, option MM want to hedge away ALL greek risks if possible just to profit from the bid/ask spread. But in reality, only some of the greeks can be flat out at some transient moment, thus the MM have to employ a hierarchy of quasi-fungibility for hedging: 1) Dynamics delta hedging using stocks; 2) Neutrality through call/put parity which is a strong mathematical relationship that to large extend valid or almost valid for various option pricing models; 3) Spreads on the same expiration, which reduce exposure on different volatilities on different time periods; 3) Time spread, which reduce overall volatility exposure; 4) Book level hedge with index options -- for example, buy index put options just to hedge all the residue delta and vega risk of a mixture of equity book. The higher in this hierarchy, the less accurate it is and more subtle risks are exposed. For example, you can construct a time spread that appears to be neutral in delta, vega, but it is actually exposed to risks in pricing models, skew, term structure model, dividend model, interest rate model, etc. Quasi-fungibility is far from risk neutral.

2. OTC option dealers

OTC option trades are usually large contracts between a big investors or a company and a bank (dealers). Warren Buffett's massive short put trade (see my earlier article) is one of such examples. OTC contracts typically are exotic in all kinds of conditions -- such as expiration length of contracts, strike conditions, settlement conditions, etc. How would the dealer hedge their exposure? Dealers, who usually have many OTC deals on the book, would aggregate all the risks in the book level and would first delta hedge, then trying to use some vanilla options that traded on the exchanges to create quasi-fungibility to hedge the exotic parts. That's far from a simple number adding games and require both analytical and simulation techniques to exposure the residue risks. This is the area where PhD's in Wall Street crunching their numbers and models.

As a trickle-down effect, the hedging activities in the OTC options add liquidity in the public option exchanges.

3. Dividend trades

If you speculate that a company is going to increase dividend, how can you trade on such view? Buying stock won't help at all, stock holders won't benefit from dividends at all (see my previous article). Besides, there is no such financial product that represents dividend itself. You can create a synthetic product in this way: buy put, sell call of the same strike, which creates a synthetic short stock position, then hedge with long stock. The exposed risk is equivalent to long dividend and short interest rate, while independent of stock movements. Such a compound structure is a quasi-fungible product for dividend, assuming the interest rate is stable. The inversed position (long call, short put and short stock) is equivalent to short dividend (betting company to cut dividends), or long interest rate.

4. Volatility trades

You can see from the above that for the option market makers, after they use stocks to dynamic hedge away the delta risk, the messy part remains to be tied up is the volatility risk. While market makers try to tuck this in, some proprietary traders explicitly want to expose such volatility risk and trade on the vega dimension. That's the volatility trades. Volatility is a general term that entails many meanings, but in general, the quasi-fungible product volatility traders create to hedge is simply dynamics delta hedging, while expose all other dimensions of volatility risks, including realized volatility risk, implied volatility risk, skew model risk, term structure risk.

Concluding Words

For any market, derivatives or underliers, liquidity is the lifeline and engine that drives its survival and growth, but derivative market is quite a different animal because it needs quasi-fungibility to survive the intrinsic lack of liquidity, and actually it thrives on such less-than-perfect situations. Quasi-fungibility reduces risks in some dimensions, while create new risks on others, to such an extend that derivative market becomes a garden of risks to trade, a fertile ground to create new ideas and test new products. The derivative market grows on the foundation of such imperfect quasi-fungibility and the art and science of hedging and risk management. The richness of the hedging technique and the garden variety of risks associated with the derivatives per se as well as caused by the quasi-fungibility make the derivative market a much complex and lively place.

(The author can be contacted at

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