The Pricing of Uncertainty

Preface

This essay is an exploration of an idea still in development.

Its purpose is not to present a finished theory, but to introduce a framework for thinking about uncertainty, information, and the formation of prices. As the ideas mature, they will be refined, challenged, and, where necessary, replaced. I hope that this essay will eventually evolve into a formal working paper with a more rigorous mathematical treatment.

The questions explored here were inspired by Grant Stenger’s Trillions of Markets. While his essay asks how markets come into existence as the cost of market creation approaches zero, this essay asks a different question: how should a rational agent value uncertainty before a market has even discovered its price? The two ideas are complementary, but they begin from different first principles.

Although I have tried to make this essay as accessible as possible, readers interested in the broader context may find it worthwhile to read Trillions of Markets alongside this work. I hope that, taken together, the two pieces encourage deeper thinking about markets, not merely as mechanisms for discovering prices, but as systems for transferring, measuring, and reasoning about uncertainty.

I. What We’ve Been Pricing All Along

“We do not trade certainty. We trade our willingness to own uncertainty.”

Economics tells a remarkably consistent story.

People possess goods they value less than other goods. Markets exist so that the goods may be exchanged. Price is the model through which supply meets demand, and equilibrium is the point at which both sides agree.

It is an elegant story; it’s also incomplete.

At its most fundamental state, markets exist so risks can be shared or transferred. You take away the legal wrappers, accounting rules, and physical objects, you know, the regular financial stuff, and you start to notice a pattern. A seller owns an exposure whose uncertainty is more valuable to transfer than to remain exposed to; markets exist to broker this trade for a price.

The baker sells the uncertainty that unsold bread will go bad before nightfall; a farmer sells grain because tomorrow’s harvest, weather, and storage conditions remain unknown; an entrepreneur raises capital because she wishes to transfer part of the uncertainty surrounding a business that does not yet exist.

On the other hand, buyers bet that the future state they expect justifies the uncertainty they accept today. The bread bought this morning is not valuable because it is bread, it is valuable because the buyer believes he will need it for nourishment before it becomes stale; a share of stock is not valuable because it is a certificate, it is valuable because someone believes the future cash flows attached to it will exceed the price paid today; insurance is not purchased because people relish paying premiums, it is purchased because they cannot bear the uncertainty of future costs. This observation appears almost trivial at first, but it rearranges much of an economist's framing. Markets are not fundamentally systems for exchanging goods; they are systems for redistributing uncertainty.

The financial markets, when viewed through this lens, remain objectively the same: a startup unsure of a future state without funding needs a venture fund to purchase the uncertainty surrounding its technological progress, a currency trader purchases uncertainty regarding the future purchasing power of nations, and the stock market is full of companies sharing future states with investors who are willing to bet on this uncertainty. Regardless of form or size, the key framing remains ‘uncertainty transfer’.

If uncertainty is the true object of exchange, a new argument emerges that prices cannot be primitive; they must themselves be consequences. For centuries, prices were treated as the main focal point that markets aim to discover, but markets never observe price directly; they observe information, information changes beliefs, beliefs create confidence, confidence brews the willingness to trade, and trade produces prices. The causal chain is counterintuitive to the consensus. Information does not emerge from prices; prices emerge from information.

A quick thought exercise: Imagine walking through a local market, and you purchase peppers for one dollar, and on your way home, you run into a friend who tells you he bought the same quantity for ninety-five cents. Same market, same stall; Instantly your opinion changes. The peppers themselves have not changed, your need for them did not change, one thing changed: Information. Without consciously performing any arithmetic, you update your internal estimate of what those peppers should cost. The next day, another friend tells you heavy rains have destroyed nearby farms; now your estimate rises again. Later that afternoon, traders arriving from another region report an unusually abundant harvest; once more, your estimate changes. This process feels so natural that we rarely notice ourselves performing it, yet it is among the most sophisticated computations humans conduct. Every day, billions of people continuously revise beliefs in response to new information long before any formal market announces a new equilibrium.

Markets simply aggregate these revisions; they do not invent them.

This essay begins from a simple proposition: Perhaps economics has spent centuries studying the shadow rather than the object.

Price is the shadow.  Uncertainty is the object casting it.

To understand markets more completely, we must first understand how uncertainty itself becomes measurable, comparable, and ultimately tradable because in a world full of trillions of new markets, the question is no longer, “What is this asset worth?” The more fundamental question becomes, “How should a rational agent value an uncertain future before the market has decided its price?” Everything that follows is an attempt to answer that question.

II. Information Before Price

"Every market price is simply millions of private beliefs made public"

The previous chapter argued that markets are better understood as systems for transferring uncertainty than simply exchanging goods. If that proposition is true, it immediately raises a more fundamental question; What exactly is uncertainty?

For centuries, uncertainty has often been treated as something intangible: a feeling of doubt, a lack of knowledge, or simply the opposite of certainty. While these descriptions are intuitively correct, they are too vague to build a useful theory upon. If uncertainty is to become something that can be measured, priced, and traded, it must first be defined more precisely.

Throughout this essay, uncertainty refers to the incomplete knowledge of future states of the world at the moment a decision must be made.

This definition is important because uncertainty is not the same as randomness. A coin toss may appear random to the person flipping it, yet to an observer with perfect knowledge of every force acting upon the coin, its outcome is already determined. What makes the event uncertain is not necessarily the world itself, but the information available to the decision maker. In other words, uncertainty is not a property of reality alone. It is a property of the relationship between reality and the observer. This naturally leads to the next concept: if uncertainty represents incomplete knowledge, then information is whatever reduces that incompleteness.

We define Information as any observation, signal, or piece of evidence capable of changing an agent’s understanding of future states.

The source of that information is irrelevant. It may come from financial statements, weather forecasts, satellite imagery, scientific research, market prices, news reports, personal experience, conversations, or even a passing remark overheard in a local market. Each contributes, to varying degrees, toward reducing uncertainty. Not all information, however, deserves equal treatment. Imagine reading a hundred newspaper articles predicting that a recession is imminent. At first glance, this appears to be overwhelming evidence, yet suppose every article simply republishes the same report from a single news agency; despite there being hundreds of articles, only one genuinely independent observation has been made.

Now let's imagine a different scenario: A central bank unexpectedly raises interest rates; commodity prices begin falling; shipping volumes decline; small businesses report weakening demand; consumer confidence surveys deteriorate. Each of these observations originates from a different source. Individually, they are only fragments of the picture, but together, they tell a much stronger story because they provide independent evidence pointing toward the same conclusion.

This distinction is fundamental as the quantity of information is not the same as the quality of information, nor is it the same as the independence of information; a hundred identical observations should not persuade us as much as ten genuinely independent ones; humans understand this instinctively.

Considering our earlier stated scenario; suppose you buy peppers for a dollar, and on your way home, a neighbour tells you he paid ninety-five cents for the same quantity. Immediately, your opinion changes. Not because the peppers themselves changed, but because your information changed. Now imagine another neighbour repeats the same story, your belief changes very little, and a third person repeats it, still very little changes. The information is new only in appearance; in reality, it is merely another copy of the same observation. Contrast this with hearing that heavy rains have destroyed nearby farms, that transport routes into the city have been flooded, and that merchants from another region expect shortages next week. Although none of these observations directly mentions the price of peppers, each provides new information about the future supply of peppers. Your understanding changes far more because each observation explains the market from a different direction.

This is how humans reason every day: we rarely calculate explicit probabilities before making decisions. Instead, we continuously collect, discard, compare, and reinterpret information as new evidence arrives. Long before markets announce a new equilibrium price, individuals have already begun updating their own internal estimates of what the future may hold.

Markets do not perform this reasoning for us; they aggregate the reasoning already taking place inside millions of independent minds.

This observation suggests a different way of thinking about prices; prices are not the first quantities markets discover; information is.

Before any trade can occur, before any bid meets any offer, before supply intersects demand, participants must first interpret the information available to them. Only then can they form beliefs about an uncertain future. Information therefore occupies a more fundamental position than price itself. I dare say it is the raw material from which every market is ultimately constructed, and the question that naturally follows is, if information changes our understanding of uncertainty, how do those countless pieces of information become a single willingness to act?

III. Confidence

“Information may explain the world; confidence determines whether we are willing to act within it.”

If information reduces uncertainty, then a more difficult question immediately follows. Why do people, having observed the same information, still make different decisions?

Classical economics often avoids this question by assuming rational agents eventually converge toward the same valuation as information becomes widely available, but reality looks very different. Every day, millions of people see the same earnings report, watch the same press conference, read the same research paper, or hear the same weather forecast, yet some still buy. In contrast, some sell, some wait, and some do nothing at all.

The difference cannot simply be information because the information is shared. Something else sits between information and action, and I believe that the missing variable is confidence.

Throughout this essay, I'll refer to confidence as the degree to which an agent trusts that their current understanding of the future is sufficient to justify a decision.

Confidence is not the same thing as certainty. Certainty implies that uncertainty has disappeared. Confidence assumes the opposite. It exists precisely because uncertainty remains, and every meaningful decision is made before the future reveals itself, never after. Confidence, therefore, is not the absence of uncertainty but a willingness to act despite it.

The distinction is almost obvious, yet it subtly explains an enormous amount of human behaviour: Imagine two farmers reading the same weather forecast predicting an 80% chance of drought; both understand the forecast, both trust the meteorological model, and both recognize the consequences. One immediately purchases irrigation equipment, the other waits another week; the information is identical, and their interpretation may even be identical, only their confidence differs. The same pattern is everywhere: an entrepreneur delays launching a company despite months of favourable customer interviews; an investor watches an opportunity pass while another deploys capital immediately; a doctor orders another diagnostic test before recommending surgery. In each case, information has already arrived, but the decision depends on whether the individual believes that information is now sufficient.

Confidence, therefore, should not be viewed as an emotion or personality. It is an internal threshold governing when observation becomes action. Humans perform this calculation almost unconsciously; we collect information, compare it against what we already know, discard some of it, and trust other parts more heavily. We're continuously revising our understanding of the future until, at some point, acting becomes more reasonable than waiting. The noteworthy thing is that this threshold differs across individuals; some require overwhelming evidence before committing, but others act after only a handful of observations; neither behaviour is universally rational nor irrational. The appropriate threshold depends on incentives, experience, consequences, and the cost of being wrong.

This is where markets become interesting. Every trade is evidence that two confidence thresholds have crossed in opposite directions; the buyer believes the available information justifies accepting the uncertainty attached to an asset, and the seller believes the opposite. Markets therefore do not aggregate information directly; they aggregate the millions of different actions, and action is a subset of confidence.

This interprets what a market price represents; a price is not simply an estimate of value, nor a measure of certainty. It is the temporary equilibrium reached after millions of individuals, each possessing different information, experiences, and confidence thresholds, decide whether the future is worth acting upon; if information is the fundamental framework from which markets are built, confidence is what turns that information into decisions.

The question is whether this process itself can be formalized; can confidence be measured? Can different pieces of information contribute differently to it? Can we model the point at which confidence becomes sufficient for action?

If so, we move beyond describing uncertainty.

We begin to price it.

IV. The Pricing of Uncertainty

“Markets discover prices. Rational agents discover confidence.”

Up to this point, the argument has remained deliberately qualitative. We have argued that markets are systems for transferring uncertainty, that information reduces uncertainty, and that confidence determines an individual's willingness to act. These ideas are intuitive, but intuition alone is difficult to test; if the framework is to become useful beyond philosophy, it must eventually become quantitative.

The objective of this essay is therefore not to predict the future with perfect accuracy, as such a goal is nearly impossible. Instead, it's to provide a structured way of reasoning about uncertain futures before markets have fully priced them.

Most valuation models begin with price and attempt to explain why the market arrived there. The framework proposed here begins much earlier. Before there is a price, there is information; before there is information, there is uncertainty. The problem is therefore not one of valuation, but of transforming information into a rational willingness to act.

The central proposition of this essay can be stated simply: A rational agent should purchase uncertainty only when the confidence generated by available information exceeds the confidence required to justify accepting that uncertainty.

Expressed formally,

where,

• (C) Represents the agent’s confidence generated from available information.
• (C*) represents the minimum confidence required before action becomes a rational trade.

This inequality plays the same role in this framework that expected utility plays in classical decision theory, or that surplus exceeding transaction costs plays in Grant Stenger’s theory of market formation; it does not determine what the future will be. It determines whether the available information is sufficient to justify acting despite not knowing the future.

Our immediate question becomes: how should confidence itself be measured? Throughout this essay, confidence is treated as an emergent quantity rather than a primitive one. It is not assumed. It is constructed.

Every observation contributes a certain amount toward an agent’s understanding of the future, but not every observation contributes equally. Some information is highly reliable; some is weak; some merely repeats information already known; others provide genuinely independent evidence capable of changing beliefs. Confidence therefore emerges from the aggregation of information rather than from any single observation.

Conceptually,

where $(I)$ represents the total body of information available to the agent.

Information $I$; may be viewed as an accumulation of many individual observations,

Where:

• $w_i \in [0,1]$ : Reliability weight of information source $i$.
• $d_i \in [0,1]$ : Independence factor of observation $i$, representing the amount of novel information it contributes beyond previously observed evidence.

The final term is particularly significant; suppose a hundred newspapers report that inflation is rising because they all copied the same central bank announcement, although the quantity of information appears large, its independence is extremely small; by contrast, if bond markets, shipping rates, commodity prices, wage growth, and consumer surveys all begin pointing toward higher inflation independently, confidence should increase substantially because each observation contributes new evidence rather than repeating existing evidence, this distinction allows confidence to grow through diversity of information rather than volume alone.

The framework therefore suggests that rational agents should not ask, “How much information do I have?” Instead, they should ask two questions.

How reliable is the information?

How much of it is genuinely new?

Only after answering these questions does confidence begin to emerge. The model presented here is intentionally simple; its purpose is not to claim that human reasoning can be perfectly reduced to an equation, rather, it provides a framework through which different forms of evidence can be compared, weighted, challenged, and updated as new information arrives. In this sense, confidence is not a fixed quantity. It is a continuously evolving estimate of how well an agent understands an uncertain future. As new information arrives, confidence changes; as confidence changes, rational decisions change. When millions of individuals update simultaneously, markets change.

The remaining challenge is perhaps the most interesting of all. Information rarely arrives in isolation; markets observe one another; people observe other people, and beliefs spread through networks. The question should no longer be how one agent prices uncertainty.

It is how uncertainty is priced collectively.

V. Price Formation

“Markets do not average opinions. They reveal the outcome of millions of independent decisions made under uncertainty.”

Up to this point, uncertainty has been treated from the perspective of a single decision maker. An individual observes information, forms beliefs about future states, builds confidence, and decides whether that confidence is sufficient to justify the uncertainty. While this describes how one rational agent reaches a decision, markets are not built from one decision. They are built from millions. The immediate question, therefore, is how countless private judgments become a single public price.

A common interpretation is that markets simply aggregate beliefs, while this captures part of the story; it is not entirely accurate. Beliefs remain private, confidence remains private, and even the information upon which those beliefs are formed is often private. The market never observes any of these quantities directly. What the market observes are actions; every participant arrives with a different history, different information, different experiences, and a different confidence threshold. Long before any trade occurs, each individual has already performed an internal process of reasoning. The market never sees that reasoning; it only observes the decision that emerges from it. It's, however, important to note that confidence alone does not determine prices. Confidence determines whether an individual is willing to participate in the market at all. Individuals whose confidence remains below their required threshold do not trade, regardless of how informed they may be; their beliefs never become part of price formation because they were never expressed through action. Markets therefore aggregate only the judgments of those willing to participate.

Participation alone does not determine prices; entering a market answers only one question: whether an individual is willing to accept uncertainty. A second question should be: how much uncertainty should one own?

The answer depends not only on confidence, but also on the amount of capital they are willing, or able, to commit. Two investors may have identical confidence in an asset's future, yet one manages a pension fund while the other invests personal savings. Although their beliefs may be identical, the amount of uncertainty each can purchase differs. This suggests that participation should not be viewed as a binary decision, but as a continuous one.

We may therefore describe an individual’s desired exposure as;

where,

• $X_i$ Represents the desired exposure to uncertainty held by the agent $i$;
• $C_i$ Represents the confidence generated from available information;
• $C_i^*$ Represents the minimum confidence threshold required before the agent, $i$ is willing to participate;
• $W_i$ Represents the risk budget that agent $i,$ Can allocate toward the position.

The intuition is straightforward. As confidence rises above the agent's confidence threshold, an individual becomes willing to accept greater exposure. Likewise, individuals possessing greater capital are capable of expressing stronger convictions than equally confident participants with fewer resources.

Markets never observe confidence itself. They only observe the positions through which confidence is expressed. Once millions of participants independently determine their desired exposures, these individual intentions become aggregated through bids and offers. At any moment, some participants wish to increase their exposure to uncertainty, while others wish to reduce it. The interaction between these competing intentions is what ultimately gives rise to market prices.

Conceptually, price changes emerge from the imbalance between aggregate demand and aggregate supply,

This equation should not be interpreted as a complete pricing model, rather, it captures a simple but important principle: prices adjust because the collective willingness to acquire uncertainty differs from the collective willingness to relinquish it.

Seen through this lens, market prices are neither objective truths nor perfect estimates of intrinsic value. They are temporary equilibria reached after millions of individuals, each possessing different information, different confidence levels, and different capacities to bear risk, express their willingness to own uncertainty, this subtly changes what a market price represents. A price is not merely the value of an asset, it is the equilibrium outcome of competing confidence-adjusted exposures.

The framework developed so far remains incomplete, however. Individuals rarely form beliefs in isolation. Information spreads through conversations, institutions, research, social networks, financial markets, and the actions of other participants. Every new observation has the potential to alter confidence, and every market has the potential to influence another.

VI. Information Networks

“No individual prices uncertainty alone. Every estimate of the future is, to some extent, built upon the observations of others.”

Up to this point, we viewed uncertainty largely from the perspective of a single decision maker. An individual may observe information, update their understanding of an uncertain future, form confidence, and decide whether that confidence is sufficient to justify accepting the uncertainty. While this describes the mechanics of individual decision-making, it omits an important feature of reality.

Information rarely arrives in isolation.

Every observation exists within a much larger network of observations, continuously produced by individuals, institutions, markets, and the physical world itself. Scientific discoveries influence governments, governments influence financial markets, financial markets influence businesses, businesses influence consumers, and consumers generate new information that begins the process once again. Knowledge does not accumulate independently; it propagates through interconnected networks. Human reasoning has evolved to exploit this structure. We rarely construct our understanding of the world entirely from firsthand experience. Instead, we continuously incorporate observations made by others, assigning different degrees of credibility to different sources. A weather forecast may influence a farmer’s expectations. A research paper may change an investor’s outlook. A conversation with a trusted colleague may alter a business decision. In each case, the information itself is not created by the decision maker; it is inherited from elsewhere.

This does not imply that all information deserves equal influence. A hundred articles repeating the same story should not persuade us as much as the original report from which they were copied. Likewise, opinions unsupported by independent evidence contribute little beyond noise. Rational agents therefore benefit not from collecting the most information, but from identifying observations that are both reliable and genuinely independent; consensus emerges naturally from this process. When multiple independent observations point toward the same conclusion, confidence increases not because agreement itself is inherently valuable, but because independent evidence reduces the likelihood that the conclusion is merely coincidental or mistaken. In this sense, consensus should not be viewed as proof; it is itself another observation, one whose informational value depends entirely upon the independence of the reasoning that produced it, and markets uniquely participate in this network.

Traditionally, markets are described as mechanisms for discovering prices. While this is certainly true, they also perform another, equally important function: they compress vast quantities of dispersed information into a publicly observable signal. Every trade represents an individual’s attempt to interpret an uncertain future. The resulting market price is therefore more than an exchange ratio between buyers and sellers; it is a continuously evolving summary of countless private judgments; prices consequently become information for other decision makers.

A farmer considering whether to hedge next season’s harvest may observe weather forecasts, satellite imagery, soil conditions, and local rainfall. They may also observe commodity prices, transportation costs, insurance markets, and prediction markets relating to future weather conditions. None of these observations determines the correct price independently, yet together they contribute toward a richer understanding of the uncertainty being evaluated. This process reveals an important property of markets. They are not isolated mechanisms competing for attention. They are interconnected information processors. Every market specializes in interpreting one particular form of uncertainty before transmitting the result, through price, to every other participant capable of learning from it.

As new markets emerge, this interconnectedness becomes increasingly significant. A newly created market may possess little trading history of its own, yet it rarely begins without information. Instead, it inherits observations already produced elsewhere: from related markets, scientific research, economic activity, institutions, and the countless interactions through which societies continuously generate knowledge. Liquidity develops gradually through participation, but understanding begins immediately because information is already flowing through the surrounding network.

Viewed through this lens, price discovery is no longer an isolated event occurring within a single marketplace. It is the product of an economy-wide information network in which every participant, every institution, and every market contributes, however imperfectly, to humanity’s collective attempt to reason about an uncertain future.

VII. Conclusion

“As markets become easier to create, understanding uncertainty becomes more valuable than discovering price.”

I began this essay with a simple question: How should a rational agent value an uncertain future before the market has discovered its price?

The argument developed throughout these chapters has been that prices are not the starting point of markets. They are the consequence of a much deeper process. Individuals observe information, information shapes beliefs, beliefs generate confidence, confidence determines a willingness to accept uncertainty, and the aggregation of those individual decisions produces market prices. Markets do not create understanding; they reveal the temporary equilibrium reached by millions of people attempting to interact with an uncertain future. Viewed through this lens, uncertainty becomes the primitive object of markets, while price becomes its observable consequence. This may seem philosophical today, but I believe it becomes increasingly practical as the cost of market creation approaches zero. The future will almost certainly contain far more markets than exist today. Advances in digital infrastructure, programmable finance, decentralized exchanges, prediction markets, tokenization, and automated market-making are steadily reducing the cost of transforming uncertainty into something tradable. As more aspects of economic and social life become representable as financial claims, markets will no longer be limited to public companies, commodities, or currencies. They may emerge around occupations, weather events, supply chains, intellectual property, scientific discoveries, infrastructure projects, private businesses, local economies, and countless forms of uncertainty that remain unpriced today. The challenge, however, is not merely creating these markets; it is understanding them.

New markets will rarely possess decades of trading history or established valuation frameworks. Many will begin with sparse liquidity, limited participation, and little directly observable price information. Yet they will not emerge into an informational vacuum. Every new market inherits information from the countless networks already surrounding it. Weather markets inform agricultural markets; credit markets inform business formation; commodity markets inform manufacturing; scientific discoveries reshape technological markets. Information flows continuously across markets long before capital does. If this is true, then the problem of the future is no longer simply one of market creation. It is a navigation of uncertainty. The framework introduced throughout this essay is an attempt to provide a language for that navigation. Rather than beginning with price, it begins with information; rather than assuming rationality, it models confidence; rather than treating markets as isolated mechanisms, it views them as interconnected information networks through which uncertainty is continuously interpreted, updated, and transferred.

These ideas remain incomplete. The mathematical treatment can be made substantially more rigorous. Confidence formation can be modeled more formally, and information networks can be represented explicitly as graphs through which beliefs propagate across markets, but these are questions for future work.

For now, the central proposition is deliberately simple.

In a world containing trillions of markets, the scarce resource will no longer be the ability to create markets. It will be the ability to reason about uncertainty before those markets have discovered their prices.

If that world is indeed approaching, then understanding how uncertainty itself should be priced may prove just as important as understanding how markets price assets today.