Game theory and option trading
As we learned in class, game theory is ubiquitous game theory and option trading our lives. We can use game theory to guide our daily strategic decisions.
So why not use game theory to generate positive returns on the game theory and option trading market as well? Well, we should use game theory to maximize our financial success.
The article states the stock market decisions everyday investors or speculators make in terms of different investment strategies and different players investors in game theory format.
The central thesis Hunt made is that traders should successfully predict the investing decisions of other players and then, based on those decisions, choose profit maximizing strategies for themselves. This game theory discussion is rather complex because of the large amount of players and different types of players investors, Federal Reserve, governments, corporations as well as the sheer amount of strategies buy, short, hedge, limit orders, stocks, bonds, real estate in the stock market.
In class, we discussed the concept of dominant strategies and strictly dominant strategies. However, those are rather difficult to decipher since other players in the stock market have so many options. In turn, it is unlikely that one option or strategy consistently leads to the highest payoff definition of a dominant strategy.
In response, I believe game theory only helps investors at certain times. At other times, it can complicate the process or not even be able to suggest a best response or Nash equilibrium. To elaborate on this idea, I have created a simple possible stock market scenario below.
I have attached the table. The scenario is as follows. TSLA with a holding period of 6 months you are a short-term investor. If you decide to go long and the majority of other investors in terms of investment capital and investor population go long as well, you both will profit. If you agree with overall market sentiment, you will profit in the short-term as you can see by the table. However, if you disagree, you will lose in the short-term. Even in this simple scenario, there is no pure strategy Nash Equilibrium or dominant strategy.
Your game theory and option trading depend on how well you can predict the investment decisions of the majority of other investors but of course, the stock market and its investors are hard to predict. It very much makes sense that there is often never a Nash equilibrium in the stock market, and that is why the stock market is so volatile and fast-paced.
After all, the stock market is a place people go for profit and not equilibrium. Indeed, following this model gives us insight into why the stock market is highly unpredictable. Game theory can however, in some situations, can make game theory and option trading easier to interpret and understand. For instance, there is a mixed strategy equilibrium in this situation. Let us assume q is the probability that majority of investors will go long and 1-q is the probability they will go short.
Then, let us assume p is the probability you will go long and 1-p is the probability you will go short. Solving out this scenario, we can figure out that the mixed strategy equilibrium is that you go game theory and option trading half the time and the majority of investors go long half the game theory and option trading.
Even though, this situation and Nash Equilibrium is not particularly telling, other situations could be of use to help you profit in the stock market. September 13, category: Mail will not be published required. Notify me of followup comments via e-mail.
Shall we make some profits? Game Theory and the Stock Market As we learned in class, game theory is ubiquitous in our lives. Some definitions to consider: Skip to toolbar Log In Search.
He received his doctorate in finance from Mississippi State University. In the book Flash Boys: This has since sparked a debate in the media and in financial circles regarding the usefulness of high frequency trading HFT.
For clarification, throughout this manuscript, high frequency traders are referred to as HFTs while the practice of high frequency trading is referenced as HFT. Proponents of high frequency trading tout the technique as being important in providing enhanced liquidity and efficiency to financial markets. Opponents regard HFTs as an unnecessary tax on an already efficient market where they tack on the expense associated with an extra layer of middlemen.
In his book, Lewis highlighted some unethical practices in the HFT industry that result from HFTs collusion with some stock exchanges and dark pools that grant these HFTs preferential access to their order books. Some exchanges have special order types that allow traders to remain on top of the order queue at all times.
Others may flash their order flows to HFTs a few microseconds Lewis noted that the blink of an eye reportedly takes milliseconds ormicroseconds before making it available to other traders. HFTs do not bear the responsibility of making the markets, and as a result, they are able to post and cancel orders thousands of times in a given day. HFT provides the infrastructure for trading at speeds unimaginable only a decade ago. However, the problem is not in the speed.
The real advantages are built on relationships. HFT does represent an evolution in the marketplace. Given the competitive advantages it provides compared to traditional trading, HFT is likely here to stay.
The larger issue at debate is whether it is useful in making markets more efficient and liquid. Lewis explained that front-running of large institutional orders by HFTs was made possible as an unintended consequence of Reg NMS.
Instead, NBBOs have simply become less stable. Hence, it is possible that the appearance of enhanced liquidity in the marketplace is illusionary. Cartea and Penalvap.
In a recent study sponsored by the U. Commodities and Futures Trading Commission, Raman, Robe, and Yadav observed that in futures markets, the anonymity provided by electronic trading to HFTs makes them behave much like fair weather friends only. They tend to withdraw from market making activities during times of high volatility, high order imbalances, and high bid-ask spreads.
This tends to reduce market liquidity when it is much needed. Hendershott, Jones, and Menkveld attributed HFT with making markets more informationally efficient with narrower spreads and improved liquidity.
Cumming, Zhan, and Aitken attributed HFT with demonstrably lower end-of-day price dislocation deviation from fundamentalsespecially on days when it is more likely to occur due to manipulation, such as on options expiration dates. The perceived usefulness of HFT is not uncontested, however.
The HFT infrastructure also has the potential to be misused. Some HFTs engage in questionable practices, often assisted by preferred access granted to them by some public and private exchanges.
This leaves the retail investor at a disadvantage, often bearing higher trading costs by not obtaining the best price execution. The following is a list of what many would agree are questionable practices:. Some HFTs place and cancel thousands of small orders a day to tease information about order flows from public and private exchanges.
Then they use this information to profit by front-running larger orders Lewis This is possible because a large institutional order— broken into smaller lots and routed to several stock exchanges—reach different exchanges at different times, if only a few milliseconds apart.
The current arrangement allows some proprietary HFTs to pursue market manipulating strategies that were traditionally prohibited, as well as some new questionable strategies made possible by the HFT infrastructure, according to a Mayer Brown Legal Update De Simone, Roche, and Rossi Some of the more common forms of market manipulation strategies described by De Simone et al. This is a form of market manipulation usually designed to trick market participants and compromise informed decisions on their part.
This results in the disappearance of volume from an exchange after the execution of one trade. Given current incentives, many exchanges find it profitable to provide preferred access to HFTs.
Some HFTs are glad to pay for their preferred access, and in fact, demand such access because it allows them to generate enormous profits.
Lewis reported that in the CEO of one HFT firm told some university students that his firm had gone four years without a single day of trading losses. The opacity of the relationship arrangements between HFTs and stock exchanges both public and private results in high profits for exchanges that provide preferential access to HFTs conforming stock exchange.
Non-conforming exchanges see less business. The resulting equilibrium results in higher trading costs for investors, as they do not get their trades executed at the best price.
Table 1 shows the short-run Nash equilibrium yellow shaded box given the current arrangements in the stock markets. In game theory, a Nash equilibrium refers to a solution where two or more players, with full knowledge of equilibrium strategies of other players, see no benefit to switching their strategy.
Here, HFTs and conforming stock exchanges gain, while investors, lacking other options, are stuck bearing higher trading costs. Game theory literature asserts that opportunistic behavior has limited rewards in the long term over iterated games Hill This is because reputation has economic value.
Crawford introduced an adaptive learning model where sophisticated players may take adaptive actions in a dynamic setting. While equilibrium in a single stage of a game may be dominated by opportunistic behavior, it may not be consistent with the equilibrium in a repeated set of identical games. In the present context, the opportunistic behavior and the collusion between some exchanges and some HFTs could start to yield lower economic value over repeated iterations as informed investors take adaptive actions.
With reputation at stake, the pressure on exchanges and HFTs has been mounting. Commodities and Futures Trading Commission, suggested that exchanges and regulators should consider requiring some market-making obligations from HFTs. Some conforming exchanges are already under legal scrutiny. Several class action lawsuits are currently underway filed by private plaintiffs against HFT firms as well as against stock and commodities exchanges De Simone et al.
Regulators have also stepped up their scrutiny of HFT practices. Co-location services are primarily used by HFTs. The firm had been accused of using high frequency algorithms for price manipulation in its favor. It is important to note that current SEC regulations do not prevent exchanges from offering co-location and direct data feed services. Reg NMS, however, prohibits exchanges from independently transmitting their own data to anyone sooner than they transmit it to a data processor for inclusion in the consolidated tape.
This may give HFTs a legal argument that market information based on co-location and direct data feeds is public information. However, various forms of market manipulation by HFTs and other forms of collusion with exchanges still remain under legal scrutiny by several regulatory bodies.
However, these rules are largely intended to minimize the impact of systems failure on securities markets. At this time, it appears that the SEC does not intend to enact separate laws to address the improprieties involving HFT.
The SEC intends to conduct a holistic review of problems in broader securities markets and, sometime next year, it hopes to introduce rules intended to protect investors from predatory trading practices VerHage and Gasparino As Dick asserted, it is not trading at high speeds but rather trading with special relationships between HFTs and exchanges that poses a threat to retail investors.
Lewis chronicled the evolution of IEX, which has devised a system that does not grant special access to any trader. IEX is able to route orders to multiple exchanges simultaneously in order to avoid front-running in a fragmented marketplace. IEX was established by a group of people led by Brad Katsuyama, who, while working with the equities trading group at Royal Bank of Canada, was concerned that a large number of his orders went unfilled at posted prices.
His team discovered how some HFTs were using their high-speed infrastructure and privileged access to exchanges to front-run client orders. For orders routed through IEX, HFTs can still trade at high speeds and anticipate price movements, but they are unable to glean order flows before other traders.
Nor are they able to glean information from quotes at one exchange a few microseconds before that quote appears on another exchange. Rather than allowing HFTs to dictate the terms of the arrangements, the exchange moves first in denying them preferred access. This changes the outcome of the dynamic game.
Reputation can prove potent in trust-based institutions and financial markets. Over the long term, other exchanges may need to emulate the non-conforming with HFTs attitude adopted by IEX or lose business. Table 2 demonstrates this long-run outcome in the yellow shaded box. The current dysfunction in financial markets should not affect financial planning for most individual client situations.
However, high net worth and institutional clients could lose much to rents extracted by HFTs if they are not vigilant. The following guidelines can assist financial planners in preserving the wealth of their clients: Even so, small orders should only be placed using a limit order at the posted bid and ask quotes.
Most share orders do get filled at posted quotes. Even as HFTs scour various exchanges to detect large order flows, they do end up filling some small orders as they stay ahead of the queue.
Clients interested in small company stocks should exercise just as much caution by only using limit orders at posted quotes. This is because even relatively small orders can cause significant order imbalances in order flows. Individual and institutional clients placing large orders should ask their brokers to route their trades through IEX.
IEX maintains a list of retail and institutional brokers connected to their trading platform on its website www. In due course, more exchanges are likely to adopt non-conforming standards, giving all retail investors and their advisers more options.
Conforming exchanges will lose revenue as more orders are routed to non-conforming exchanges. Over time, as suggested by Raman et al. De Simone, Joseph, Jerome J. Roche, and Matthew Rossi. Hendershott, Terrence, Charles M. Jones, and Albert J. Implications for Transaction Cost Theory. A Wall Street Revolt. Raman, Vikas, Michel A. Robe, and Pradeep K.