Trading in US listed equity options is a large and important financial market for institutional and retail investors.
Below are some facts and fictions about the trading and markets of these securities.
TL,DR
- Market makers (MMs) fill a very large portion of investor US listed equity options trades (instead of investors trading with each other) and therefore their role is central to the economics of options prices and options markets
- MMs hedge investor trades with a portfolio (which includes underlying stock) that has a gain/loss independent of the investor equity gain/loss, a property called delta-neutral
- The MM hedging portfolio is called a replicating portfolio, it is a financing transaction that transmits the return/risk of the underlying stock to the investor’s option position
- The economics of an individual trade between a MM (having a replicating portfolio) and an option investor is in general not zero sum and the aggregate market of such trades is in general not zero sum
While a post on this board cannot provide an exhaustive explanation of options markets, it can provide a basic foundation of understanding:
- how options are priced,
- how option pricing depends on the underlying asset,
- how option pricing enables financial firms (MMs) to have a viable business model in options trading (and hence enable option trading by investors), and
- how the above determines the economics of individual trades, financial firms’ trading businesses, and entire markets
Fact:
Option Definition
Call/put options grant the buyer the right to buy/sell stock (or ETF) - the underlying - at a set price (strike), before a certain date (expiry, American style).
Fact:
Meaning of Derivative
Options derive their value from the value of the underlying stock, hence the name derivative.
Fact:
Riskless Replicating Portfolio
The theory of asset pricing provides a method to replicate the economics of an option with a portfolio that is riskless (value doesn’t change) with respect to changes in the price of the underlying (all else equal). The change in portfolio value with respect to changes in value of a reference security (such as the underlying stock) is called delta (delta is a mathematical derivative). A replicating portfolio has delta near zero, is called delta-neutral and therefore has little directional equity risk. The theory of asset pricing explains well known options models like Black-Scholes, which is a canonical model in options pricing and trading.
Fact:
Replicating Portfolio Business
The replicating portfolio provides a well-defined and established trading strategy that serves as a foundation for financial firms, including market makers (MMs), to run a sustainably profitable business while minimizing directional equity risk. The business of the MM, in arrangements with options exchanges, is to provide bid-ask quotes and take the opposite position of investors’ options trades: their business of being available to take trades is called providing liquidity.
Fact:
Replicating Portfolios Are Financing Transactions
The replicating portfolio for a long call/put is to borrow dollars/stock and buy/sell the number of shares that makes the portfolio delta-neutral while also selling the call/put to the investor. The borrowing of dollars/stock is the financing portion of the portfolio and the long/short stock position hedges the delta of the short call/put trade facing the investor. In effect, this is a financing transaction. The MM is providing the capital, subject to the MM’s cost of funds, to finance the long/short shares that produce the equity return/risk of the investor-facing call/put. The MM is financing the transfer of equity return/risk - return/risk that derives from the underlying’s stock market - to the investor. It’s only natural that investment banks have a role in this business: banks are in the financing business!!! (The same kind of financing transaction applies to other derivatives, such as equity futures and swaps. These are also trades that finance the transfer of return/risk from the underlying asset to a derivative investor.) Options are said to be leveraged trades - this financing mechanism is how the leverage originates. Very interesting!
Fact:
The Market Maker’s Business and Economics are Explicitly and Necessarily Linked to the Market of the Underlying
The MM’s replicating portfolio is long/short the underlying stock and transfers equity return/risk from the underlying stock to the investor’s call/put position. Thus the MMs’ trading books and the options market as a whole, for each underlying, are directly linked to the market and economics of the underlying stock.
Fact:
Replicating Portfolio Rate of Return
Using a replicating portfolio, a MM can take the opposite side of any investor option trade (buy/sell any option the investor wants to sell/buy in the market) and then also go long the replicating portfolio of the investor’s option position. In financial mathematics, because the trade is riskless, a standard representation is that the replicating portfolio earns the risk-free rate (eg, the Treasury rate). In practice, MMs finance their business at some cost of funds specific to their enterprise and also endeavor to earn a profit above their cost of funds. So, as a reasonable foundation, we can expect the MM to earn its cost of funds plus a spread on its capital used to finance its market making. In practice, there are more risk factors (interest rate risk, dividend risk, etc) that affect returns, but the rate of return that equals cost of funds plus a spread provides the foundation.
Fact:
Replicating Portfolio Returns, For a Given Trade, Do Not Depend on Investor Returns
From above, we know, by using the replicating portfolio when taking investor trades, a MM earns its cost of funds plus a spread. The investor could be trading any number of strategies: a hedge against its portfolio, a speculative strategy, a strategy that mimics a long position in a major index like S&P 500, an option in combination with some other position, etc. In any particular trade with a MM, the investor could have any magnitude gain or loss. However, regardless of the investor’s return, the MM receives the return on the replicating portfolio (cost of funds plus a spread). Interestingly, the MM’s return (from the replicating portfolio) is independent of the investor’s gain/loss.
Fiction:
An Investor’s Gain/Loss is the Market Maker’s Loss/Gain (Each Trade is Zero Sum)
One will see written many places, that options trades are zero sum. This would mean that the MM’s gain/loss is the equal and opposite of the investor’s gain/loss. But this is false as the preceding fact shows. Individual options trades (investor trade with MM, as defined above) are not, in general, zero sum.
Speculation:
Further, because options are explicitly linked to their underlying stock markets and options transfer equity return/risk from the stock market to the option trader (via the replicating portfolio), underlying stock markets might need to be zero sum for options markets to be zero sum (if one wants to argue that options trades and markets are zero sum).
Fact:
Market Maker’s Are the Primary Liquidity Providers in Options Markets
Option market making is a big business and MMs trade a very large volume: the mandate and business model of MMs is to trade as much volume as possible. Also, aspects of the market structure such MM’s obligations to the exchanges to take trades, payment for order flow and the mechanics of how orders are brought to the exchange all serve to increase the MMs’ trading volume.
Fiction:
Investors Often Trade with Each Other, Not Market Makers
Because of the dominance of market makers, explained just above, investors’ opening trades are vastly more likely to be filled by market makers than other investors.
Fact:
For a Single Underlying, the Net Aggregate Book Is Not Typically Perfectly Balanced
Even for a single underlying, options trades have a very large number of specific instruments defined by call/put, strike, expiry and quantity. The chance that all investor trades of calls and puts exactly balance out in delta terms to have delta equal to zero for a meaningful amount of time is very small relative to the alternative case of investor positions netting to non-zero delta.
Fiction:
(This one is a doozy!)
The Net Total of All Investor Trades Perfectly Offset Each Other in Delta Terms, Producing a Perfectly Balanced Book of Open Investor Trades
Because of the prior fact, this fiction is obvious.
Fact:
The Aggregate Economic Outcome of an Options Market is Not Zero Sum
As note above, there will typically be an unbalanced book of open investor trades and MMs will have taken a very substantial volume of these open trades. Because, as explained above, individual trades with MMs will not be zero sum, the aggregate economic outcome of these trades will not be zero sum.
Fiction:
The Aggregate Economic Outcome of an Options Market is Zero Sum
Fiction because of the preceding fact.
References
Retail Options Trading with Wholesalers
Wharton Payment for Order Flow
CBOE Retail Option Flow
Risk Citadel MM of Year
SEC Equity Market Structure