Contracts with Contingent Cash Flows

Distinguishing the long from the short and the bid from the ask.

This post is an extract from my forthcoming monograph Pricing Multi-Period Insurance Risk. It describes Contracts with Contingent Cash Flows (CCF contract) and represents an attempt to bring order to the notions of a security, asset, derivative, and insurance contract. I also dig into the exact meaning of long and short (and describe their fascinating history dating back to medieval times), and bid and ask.

Current practice and financial ingenuity stretch ancient terminology, and we are often left with “Guidelines rather than rules.” Getting these fundamentals straight turns out to be surprisingly difficult. There’s a whole academic industry around market micro-structure!

TL;DR

• Cash flow is a vector: It is defined by a magnitude and a direction. The magnitude is called the amount and is always positive (think: speed). The direction goes from the payer to the recipient. A flow of \(-1\) from Party B to Party A means a flow of \(+1\) from Party A to Party B.

• The “Long” and “Short” contract participant labels are relative: While contracts are often drafted between a “Party A” and “Party B,” these roles are mapped to “Long” and “Short” based on the chosen perspective and market conventions (guidelines!).

• Sign conventions are the coordinate system: Interpreting a random variable as a cash flow \(X\) requires fixing both the position it applies to (Long vs. Short) and the sign convention (Loss vs. Payoff). Under the Payoff convention, positive is a receipt; under the Loss convention, positive is a payment made.

• Bid and Ask quotes contain a spread: The party who accepts a quote pays the spread for immediate execution. Typically, the ask amount paid to enter the contract as the long position and the bid the amount received to enter as the short.

• In quoted markets the market maker faces uncertainty about which side the customer will take but there is typically no information uncertainty (transacting a commodity). In a negotiated market each side knows its role but there is often considerable information uncertainty (transacting a second-hand car or insurance policy).

• The contract’s purpose is independent of its accounting placement: A CCF contract can have distinct economic purposes (operating, investment, financing, deposit, insurance, or hedging). However, its placement as an asset or liability is a separate accounting result determined by whether the present value of rights exceeds obligations.

• Transformation and Intermediation: Instruments like Catastrophe Bonds prove that the same risk can be morphed between an insurance security and an investment security by shifting the perspective and sign convention through an intermediary like an SPV.

---

1 Contracts with Contingent Cash Flows

contract template · cash flow vector · sign convention (loss/payoff) · position (long/short) · market structure and role · bid and ask prices · placement (asset/liability) · function · information · cat bonds

1.1 Introduction

A contract with contingent cash flows (a CCF contract) is a formal agreement defining the transfer of value between two parties—traditionally labeled the Long and the Short—based on future events. A CCF contract has cash flows that depend on future states of the world, but it does not presume tradability, regulatory treatment, balance-sheet placement, or market micro-structure. This terminology keeps the focus on economics rather than institutional classification and allows insurance, reinsurance, and financial contracts to be analyzed within a single, consistent framework.

Terminology varies across markets. I reuse familiar words (Long, Short, bid, ask, dealer, broker) in a deliberately abstract way to unify notation across settings; when a market uses these terms more narrowly, treat the mapping as approximate and follow the definitions given here.

Remark 1 (Why “CCF contract” instead of “security” or “asset”). We prefer CCF contract to security because security is heavily overloaded. In legal and regulatory contexts it has a precise meaning defined by bodies such as the Securities and Exchange Commission, while in market practice it often connotes tradable financial instruments governed by securities law. That meaning is subtly but importantly different from commodity-style contracts regulated by exchanges such as the Chicago Mercantile Exchange, and different again from insurance contracts, which sit outside both regimes. Using security as a generic label therefore risks importing unintended legal, regulatory, or market connotations. Another alternative is asset, but the same CCF contract can be an asset or a liability. To avoid these ambiguities, we adopt the neutral term contract with contingent cash flows.

Remark 2 (Primary and derivative contracts). Traditional accounting distinguishes between “primary” securities and “derivatives,” but a rigorous contingent-claims view reveals that almost all financial instruments are contingent claims. As Robert Merton demonstrated in 1974, even the capital structure of a firm fits this lens: equity resembles a long call option on the firm’s assets, while a corporate bond resembles a long position in a risk-free asset combined with a short put option granted to shareholders. From this perspective, the distinction between a stock, a bond, and a credit default swap is not one of kind, but of the specific triggers and topologies of the underlying contingencies.

1.2 The Contract as a Template

A CCF contract starts as a template with blank spaces for the parties’ names, a schedule of contingencies, and an up-front transaction cash flow (the price paid by one side to enter the contract). The contingencies define state-contingent cash-flow magnitudes and directions: “If event \(i\) occurs, the Short pays the Long amount \(A_i>0\),” or the reverse. In this framework, each payment has a positive magnitude (the amount \(A_i\)) and a direction (Long to Short, or Short to Long). Which party experiences which cash flows depends on which role they occupy.

A CCF contract normally includes several standard clauses.

1. The named Parties to the transaction. CCFs are usually bilateral.
2. Effective and expiration Dates, important to specify the contract boundary.
3. The Trigger Event: the stochastic state variable (e.g., total losses from insured events, a hurricane’s landfall intensity, or a stock’s closing price).
4. The Payoff Function: the mathematical rule determining the cash-flow amount from the state variable.
5. The Settlement Method: whether the contract is settled via physical delivery or cash.
6. The Calculation Agent: the “oracle” responsible for determining the terminal value.
7. Any Cash Due at Inception, representing the “price” or “premium”.

As the contract is negotiated each of these is gradually filled in. For exchange traded contracts the clauses are very standard. In negotiated markets such as reinsurance the wording of the contract is itself subject to negotiation.

1.3 Cash Flow Vectors and Loss vs. Payoff Sign Conventions

In a CCF contract, we treat a cash flow as a vector, or directed quantity, not a signed scalar. Like velocity, it has a non-negative magnitude, called its amount, and a direction: either “Long to Short” or “Short to Long.” (Amount is analogous to speed, and direction to bearing.)

When we collapse a CCF cash-flow vector to a signed scalar quantity we need a sign convention.

Definition 1 (Cash flow scalar sign conventions.)  

• The loss sign convention models payments made as positive
• The payoff sign convention models payments received as positive

Under the loss convention, the right tail is bad: higher values mean larger outflows. It is used for insurance losses. We usually use \(X\) for variables using the loss convention. Under the payoff, the left tail is bad: lower values mean greater amounts owed. We usually use \(Y\) for variables using the payoff convention.

The sign convention is a modeling choice and not part of the contract. The contract specifies the cash-flow vector explicitly; the sign convention enters only when the cash-flow vector is mapped into a signed random variable \(X\) representing one participant’s perspective. To specify \(X\), we must specify the perspective (Long’s or Short’s) and the sign convention.

1. For a fixed sign convention, negating \(X\) switches perspective: if \(X\) is defined from Long’s perspective, then \(-X\) is defined from Short’s perspective, and vice versa.
2. For a fixed perspective, negating switches sign conventions: Long-payoff \(X\) becomes Long-loss \(-X\), and Short-payoff \(X\) becomes Short-loss \(-X\).
3. Combining bullets 1 and 2, the same value of \(X\) can be read as Long-payoff and Short-loss, or as Long-loss and Short-payoff.

Table 1 shows the signed cash flow corresponding to the cash flow vector “Short pays Long \(1\)” under each perspective and sign convention.

Table 1: The same cash flow by sign-convention and perspective.

Item	Long's perspective	Short's perspective
Payoff sign-convention	+1	-1
Loss sign-convention	-1	+1

Insurance cash flows are commonly modeled with the payoff convention from the insured’s (Long) perspective and the loss convention from the insurer’s (Short) perspective. The Long/payoff and Short/loss views coincide because of the double negative \((-1)(-1)=1\).

Remark 3 (Vector space interpretation of cash flows). Cash flows are a vector in a one-dimensional real vector space. We can pick as basis \(\mathbf{1}_{A\rightarrow B}\) or \(\mathbf{1}_{B\rightarrow A}\) denoting, respectively, a payment of amount \(1\) from \(A\) to \(B\) or \(B\) to \(A\). Then, the table shows the slight ambiguity: the four expressions \[ -\mathbf{1}_{A\rightarrow B} =(-1)\mathbf{1}_{A\rightarrow B} =(+1)\mathbf{1}_{B\rightarrow A} =\mathbf{1}_{B\rightarrow A} \] all represent the same cash flow, c.f., Table 1. Both are equal and also equal to $$. Picking the basis corresponds to selecting the sign convention. The scalar in a vector space can be positive or negative, whereas we consider the magnitude of a cash flow to be positive. Requiring positive cash flows in this way allow contracts to be written unambiguously without specifying a basis.

1.4 Contingent Cash Flows

Definition 2 A contingent cash flow is a stochastic process specifying nominal monetary cash flows, in a specified unit of account, at future times, contingent on future states of the world. A single-payment contingent cash flow is a random variable giving the cash flow at a single future time.

The definition is deliberately broad. In some academic settings there is a single consumption good used as the unit of account; here the unit of account is the contract’s currency, but the same abstraction applies.

Example 1 (CCF Contracts.) Here are standard examples of contracts and their underlying contingent cash flows.

1. A stock; cash flows: dividend payments and any residual (liquidation) value.
2. A bond; cash flows: coupon payments and return of principal.
3. A stock or index forward (or future, which is an exchange-traded forward with daily settlement); cash flow at maturity (ignoring interim margining): \(S_T - F_0\) per share (or per contract share multiplier), where \(S_T\) is the stock or index price at \(T\), and \(F_0\) is the delivery price set at inception.
4. A stock option. European call: payoff at maturity: \(\max(S_T - K, 0)\) per share (or contract multiplier). European put: payoff at maturity: \(\max(K - S_T, 0)\) per share (or contract multiplier). American options allow exercise at any time before expiration.
5. A weather derivative; payoff: a function of the number of heating or cooling degree days, or the cumulative number of degree days the temperature is above or below a strike over the contract period.
6. A property insurance policy; payoff: a function of the individual and aggregate loss after applying occurrence and aggregate limits and deductibles.
7. An aggregate excess of loss reinsurance contract; payoff: aggregate losses from an underlying book subject to a retention and aggregate limit.

1.5 Position: Long or Short

Any contract has two sides, and we must specify which side the model represents in order to determine actual cash flows. For historical reasons the two sides are called the Long and the Short. Broadly, the long party tends to:

• benefit from an increase in the value of the underlying,
• own the claim,
• pay when the contract is entered into (in many, but not all, settings), and
• take delivery or receive the asset (when settlement is physical).

The short party has the opposite characteristics: they owe or write the claim, often receive cash at inception, and deliver the asset (or make the payment) under the contract’s triggers. A cash flow for the short position is always the vector negative (opposite direction) of that for the long.

Example 2 (Long and short sides of standard contracts.)  

• For an insurance contract, the insured takes the long position, giving them the right to indemnity payments contingent on loss. The insurer takes the short position, writing the contract. The loss is the underlying; it may be transformed by policy limits and deductibles.
• For a reinsurance contract, the insurer takes the long position and the reinsurer the short.
• For an option, the long position buys the option, giving them the right, but not the obligation, to transact at a specified strike. The short position sells (writes) the option and must perform if exercised. (For a put, the long benefits from a decrease in the underlying, not an increase.)
• For a future or forward, the long position agrees to buy the underlying asset on a specified future date for a specified price, and the short position agrees to deliver. There is typically no initial transaction when these contracts are entered into. In this case, both parties have obligations at expiration so neither strictly “owns the claim.”

Remark 4 (Parties, positions, and the language of “owning”). It is useful to distinguish parties to a contract from the colloquial ideas of owning, buying, or selling a contract. Strictly speaking, contracts are not owned; they are entered into. A contract is a legal relationship between counterparties that specifies reciprocal rights and obligations, and those rights and obligations exist only by virtue of the parties’ participation. The language of ownership arises once contracts become sufficiently standardized and transferable that the economic exposure can be separated from the original counterparty relationship. Exchange-traded futures and options are the canonical example. For bespoke insurance and reinsurance contracts, by contrast, “ownership” is misleading: the contract exists only between named parties, cannot be freely transferred, and is better described in terms of who is bound by it.

Remark 5 (The Origin of Long and Short). This terminology originates from the use of tally sticks in medieval Europe, particularly in the English Exchequer. When two parties entered an agreement—such as a loan or a contract to deliver goods—they would record the details on a hazel wood stick.

• The Long Side (the Stock): The stick was split down the middle, but not perfectly. One piece was kept longer than the other. The longer piece, called the “stock” (hence the term “owning stock”), was given to the party who had the claim or was “owed” the asset. This person was “long.”
• The Short Side (the Foil): The shorter piece, called the “foil,” was given to the party who had the obligation to deliver the asset or repay the debt. This person was “short.”

The term “short” has roots in common English usage dating back to the mid-19th century (and likely earlier in merchant circles). To be “short” simply means to be “lacking” or “in deficit” of something (e.g., “I am short of cash”). In a futures or forward contract, the seller is “short” the commodity because they have committed to delivering something they may not yet physically possess. They are in a state of deficiency relative to their contractual obligation.

The beauty of the tally system is its biometric security: because hazel wood grain is unique and the split follows the natural fibers, the “Short” piece (Foil) would only fit perfectly back into the “Long” piece (Stock) if they were the original pair. This made the “Short” side’s obligation and the “Long” side’s claim verifiable and tamper-proof.

1.6 Market Structure and Market Roles

Transactions involving CCF contracts occur within three primary market structures:

1. Quote-driven (dealer) markets: intermediaries (market makers) provide continuous liquidity by standing ready to take either side of the contract.
2. Order-driven (auction) markets: a centralized system matches buyers and sellers directly based on price and time priority.
3. Brokered (negotiated) markets: brokers facilitate bespoke matches between specific parties who often have predetermined roles.

Participants in a market have different roles and it is useful to distinguish three:

1. Solicitor (searcher): initiates contact and begins counterparty search.
2. Quoting party (maker, liquidity provider or supplier): names a firm, executable price for a specified oriented contract.
3. Accepting party (taker, liquidity demander): accepts a firm quote and executes immediately at the maker’s terms.

Solicitation and quote-taking are independent. A party can solicit and still end up quoting, or solicit and end up taking, depending on who supplies terms and who accepts them.

A quote is firm in the limited but essential sense used here: conditional on any stated assumptions, it is a price at which the quoter stands ready to trade immediately if the other party accepts. (Indicative quotes do not define bid/ask until converted into firm terms.)

1.7 Bid and Ask Prices

In the benchmark model of asset pricing, markets are competitive and trading is unconstrained. Prices are then well described by a single linear pricing rule: a functional that assigns a unique price to each cash-flow process and respects additivity and scaling. In that setting, no-arbitrage is powerful, and—together with replication in a complete market—it implies exact equalities such as the Black–Scholes option pricing formula.

In the classic frictionless market, trading is costless (no transaction costs), assets are perfectly divisible, and no agent has market power. Prices satisfy the law of one price: two securities with the same future cash flows have the same current price. This produces a single pricing functional \(p(\cdot)\) that is linear:

• \(p(X+Y)=p(X)+p(Y)\),
• \(p(kX)=kp(X)\) for all \(k\) (not just \(k>0\)),
• \(p(c)=c\) for sure cash \(c\) (or \(p(c)=\beta c\) if you separate discounting),

The risk-neutral measure representation that actuaries meet in finance texts is one convenient way to express this linear functional, but linearity is the key point for what follows.

Real markets depart from that textbook benchmark. Trading can be costly, constrained, or capital intensive. Common frictions include transaction costs, inventory and funding costs, margin and collateral requirements, information asymmetry, position limits, short-sale constraints, and costly capital. Once these frictions matter, it is natural to model two prices, the bid and ask defined as follows.

Definition 3 (Bid and Ask Prices) For a given contract, which fixes the obligations of the long and short sides:

• The ask is the amount paid at inception when the long side is the taker (it accepts the short side’s quote).
• The bid is the amount paid at inception when the long side is the maker (its quote is accepted by the short side).

Typically, the ask is paid by the long and the bid by the short, and the ask exceeds bid. The bid-ask spread or simply spread is the ask minus the bid. The spread is borne by the liquidity demander: the demander receives a less favorable price than it would receive if it were supplying liquidity. The spread is not an arbitrage by itself, because round-tripping is no longer free. The actual direction of cash flow depends on the specifics of the contract because amounts are always positive!

The bid-ask spread is the cost of immediate execution. Its determinants include order-processing and operating costs, inventory and funding costs borne by the liquidity supplier, and adverse-selection costs arising from asymmetric information.

Spreads are ubiquitous. Results from [1] imply that SRMs add a non-zero spread to all non-constant risks. If there is a single non-constant risk with no spread then the SRM is just a multiple of the mean, or it “collapses to the mean”.

TL;DR: When you accept a firm quote, you pay the spread.

The bid–ask spread is not just a detail of quoting. It signals a change in market structure. With frictions, prices become nonlinear and “no-arbitrage” becomes a family of conditions. Pricing functionals are typically monotone and cash-invariant, but not linear. Under nonlinear pricing, there are several non-equivalent “no-arbitrage” concepts depending on the transactions needed to create potential arbitrages. One approach is to demand the absence of buy and sell arbitrage opportunities, see [2] and [3].

In a quote-driven market, the market maker faces directional uncertainty. When a customer approaches, the dealer does not know whether the customer intends to be the long or the short. To manage this, the dealer provides a two-sided quote on the up-front transaction price. The customer pays the ask to enter as long and receives the bid to enter as short. The spread compensates the dealer for inventory risk, funding and operating costs, and uncertainty about which side the customer will take, including adverse-selection risk.

In brokered (negotiated) markets—such as the reinsurance “Firm Order Terms” or “Best and Final Quotes” process—identities and roles are typically fixed from the outset. A seller knows they are selling, and a buyer knows they are buying. Negotiation proceeds through iterative, one-sided quotes toward a single agreed price. In the last instance, one party accepts the other’s final firm terms. Relative to a fixed oriented contract, either (i) the long side accepts the short side’s final quote (execution at the ask), or (ii) the short side accepts the long side’s final quote (execution at the bid).

In reinsurance, the long side’s final firm quote is often called a firm order term. In a hard market, the firm order term commonly matches the reinsurer’s quoted terms, so execution occurs at the reinsurer’s ask for \(X\). In a soft market, the firm order term can lie below the reinsurer’s most recent quote; if the reinsurer accepts it, execution occurs at the bid for \(X\).

Small commercial and personal lines insurance behaves like a quoted market in the present sense that insurers commonly supply terms and insureds commonly accept them. Large commercial insurance and reinsurance behave like negotiated markets: solicitation and bargaining are central, and executable terms emerge only after an exchange of quotes and counterquotes.

Remark 6 (Valuation acquire/dispose interpretation of bid and ask prices). Definition 3 defines bid and ask using the maker/taker, market micro-structure perspective. In terms of cost to acquire or dispose of a position in a contract, this is phrased as:

• The ask is the amount required to acquire the long position in the contract.
• The bid is the amount received to dispose of the long position in the contract.

The two definitions are consistent as they describe the same economic cash flows for a participant seeking or holding a long position.

Table 2: sdaf

Term	Taker/Maker Perspective	Cash Flow Perspective	Logical Link
Ask	Long side is the taker. They pay the price set by the seller.	Amount required to acquire the long position \(X\).	To acquire a position as a taker, one pays the higher price (the Ask).
Bid	Long side is the maker. Their quote is accepted by the short side.	Amount received to dispose of the long position \(X\).	To dispose of a position, one receives the price the market is willing to pay (the Bid).

There is an important relationship between bid and ask prices.

If a single dealer (or a single internally consistent pricing rule) quotes prices for both \(X\) and \(-X\), then “acquiring \(X\)” is the reverse trade of “disposing of \(-X\).” When those two descriptions refer to the same economic trade against the same quotes, the prices must match up to sign. That assumption enforces an important relationship between bid and ask prices.

Proposition 1 (Bid-Ask Pricing Relationship) Assume bid and ask quotes come from a single internally consistent quoting rule applied to both \(X\) and \(-X\), with no counterparty credit risk. Then \[ \mathrm{ask}(X)=-\mathrm{bid}(-X). \tag{1}\]

Proof. Buying the security with long position \(X\) requires an upfront outflow of \(\mathrm{ask}(X)\) and produces the future cash flow \(X\). Selling (disposing of) the security with long position \(-X\) produces an upfront inflow of \(\mathrm{bid}(-X)\) and leaves the seller obligated to pay \(-X\) in the future, which is the same as receiving \(X\).

Thus, buying \(X\) and selling \(-X\) create the same future cash flow \(X\) against the same quoting rule. With no counterparty credit risk, internal consistency requires their upfront cash flows to match up to sign: \[ -\mathrm{ask}(X)+\mathrm{bid}(-X)=0, \] which implies \(\mathrm{ask}(X)=-\mathrm{bid}(-X)\).

This proposition does not depend on a loss vs payoff sign convention. It follows from reversing the position.

Example 3 The framework applies to the securitization of insurance losses. Let the random variable \(X\) represent losses on an insurance policy with a maximum loss \(a\). When an insurer writes the policy \(X\) backed by assets \(a\), they become short \(X\) and the insured is long. The insured pays \(\mathrm{ask}(X)\) to initiate their long position. At this point, the insurer is long the residual payoff \(Y := a - X\). It can exit its position for \(\mathsf{bid}(a-X)\), leaving it obligated to pay \(a\) in every state. The investor becomes long \(a-X\). By no arbitrage, \[ \mathrm{ask}(X)+\mathrm{bid}(a-X)=a. \] But, \(\mathrm{bid}(a-X)=a+\mathrm{bid}(-X)\) and so \(\mathrm{ask}(X)=-\mathrm{bid}(-X)\). \(\quad\square\)

Frictionless markets, with linear pricing rules, do not have a spread because the bid equals the ask: \(-p(-X)=--p(X)=p(X)\). Notice that if \(p\) is just positive homogeneous this doesn’t work: it relies on applying homogeneity with constant \(-1\).

The literature suggests many reasons why a market might include a spread: information asymmetry, inventory risk, operating costs, and funding and margin costs. For insurance and reinsurance, two additional forces matter repeatedly.

1. Costly capital and limited risk-bearing capacity. Holding risk consumes scarce capital, and capital has a required return. This creates wedges between expected value and transaction price, and it becomes more severe for concentrated, illiquid, or tail-heavy risks. Froot develops this idea for insurers and reinsurers, building on Froot and Stein’s capital allocation framework [4, 5].

2. Default or performance aversion. Many insurance customers care about the insurer’s ability to perform in bad states. That preference makes “risk transfer” different from a pure expected value trade, and it supports nonlinearity and spreads even when the nominal contract looks simple [4].

In catastrophe reinsurance and other opaque, nonstandard risks, intermediation itself becomes part of the product: intermediaries specialize in bearing and managing these risks, but they do so at a cost that shows up as a spread over “fair” value [6].

Remark 7 (Related literature). The connection between limited loss and residual \[ a = (X\wedge a) + (a - X)^+ \] is reminiscent of put-call parity. Put-call parity has two subtly different formulations. Writing \[ X - a = (X-a)^+ - (a-X)^+ \] leads to a Put-Call Partity (PCP) condition for a translation invariant pricing functional \(f\) that requires \[ f(X) - a = f(X-a)^+ + f(-(a-X)^+). \] We can also write \[ (a-X)^+ = (X-a)^+ - X + a \] leading to a Call-Put Partity (CPP) condition \[ f((a-X)^+) = f(X-a)^+ +f(-X) + a. \] The fact that \((X-a)^+\) and \(-(a-X)^+\) are comonotonic, whereas \((X-a)^+\) and \(-X\) are not is an important difference between these formulations. [7] shows that \(f\) satisfies PCP, translation invariance and monotonicity if and only it it is a Choquet pricing rule. A SRM is a subadditive Choquet rule. Notice this implies law invariance and comonotonic additivity. [3] shows that if \(f\) is monotone then is satisfies CPP if and only if it has a formulation as a Choquet-Šipoš pricing rule—a slightly different formulation of the Choquet integral that treats upside and downside symmetrically. See also [2]. \(\quad\square\)

To conclude: bid–ask spreads are not a defect of the model. They are the model’s way of admitting that trading risk is costly, capital is scarce, and different agents face different constraints. Under mild regularity, imposing law invariance together with too much linearity forces a pricing functional to reduce to (an affine transform of) expectation, so non-trivial pricing requires genuine nonlinearity [8].

1.8 Placement: Asset or Liability

The same CCF contract can be an asset or a liability, reported on the left or right of the balance sheet. A CCF is held as an asset when the present value of its expected rights to receive cash exceeds the present value of its expected obligations to pay, and otherwise it is held as a liability. A contract’s name does not determine placement; expected rights and obligations determine placement.

A security can be issued as a liability but later become an asset. For example, consider a very profitable, low-risk insurance policy. If the premium is paid in advance it is a liability (only loss payments remain). If premium is deferred it can be an asset because the insurer has a premium receivable that dominates expected loss payments.

Under IFRS 17, groups of insurance contracts issued and reinsurance contracts held each present as either an insurance contract asset or liability depending on net fulfilment cash flows at the reporting date. An insurance CCF corresponds to contracts typically issued as a liability, but that can net to an insurance contract asset when rights to cash exceed obligations (e.g., front-loaded premiums or the insurance acquisition cash flow asset that IFRS 17 carries and then recoups from future premiums). A reinsurance contract held is usually a liability when issued, because it contains a positive margin for the reinsurer, but it may become an asset depending on covered losses. The IFRS 17 treatment depends on the prior grouping of contracts into onerous and non-onerous.

1.9 Function: What the Contract Does

Actuaries are expected to be familiar with insurers’ financial statements, which are atypical because insurance contracts dominate the right-hand side of the balance sheet. To gain a broader understanding, it helps to compare financials for a manufacturer, a bank, and an insurer.

A manufacturer’s balance sheet centers on operations. Its key contracts support producing and selling goods: trade credit, customer advances, leases, and occasional borrowing. The operating cycle converts cash to inventory to receivables back to cash, servicing these claims and creating profit. Financial instruments appear, but production assets and working capital dominate. Hedging instruments may be used to reduce cost volatility for important inputs.

Banks and insurers look different because their businesses are financial intermediation and risk transfer. Their assets are mostly financial (loans and securities for banks; bond-heavy portfolios and reinsurance recoverables for insurers). Each issues a distinctive kind of CCF contract. Banks accept deposits—claims designed to function as money and liquidity. Insurers issue insurance contracts—contingent claims designed to transfer risk and fund uncertain, often long-dated obligations. A bank earns the spread between its funding costs and the yield on its assets, plus fees. An insurer earns underwriting margin and investment income while transforming premium funding into claim payments over time. In both, the core business is managing risk, timing, and spread.

CCF contracts have six functions by economic purpose, independent of whether they appear as assets or liabilities:

1. Operating. Arising from producing and delivering goods and services: trade credit (receivables/payables), accrued expenses, customer advances, deferred revenue, warranty obligations, taxes payable, leases tied to operations, and similar working-capital and operating-cycle claims.
2. Investment. Held primarily for income, capital appreciation, or liquidity: cash, government and corporate bonds, loans, equities, mutual funds and ETFs, repos, securitizations, and collateral arrangements.
3. Financing. Raise capital or funding and include equity and debt issues.
4. Deposit. Claims designed to provide transaction and liquidity services: bank deposits (and close substitutes), typically redeemable at par on demand or short notice. Deposits are concentrated in banks, though some non-banks issue limited deposit-like claims (e.g., gift cards or store credit).
5. Insurance. Contingent claims that transfer non-financial risk: insurance policies and reinsurance contracts. Insurance uses its own terminology: these contracts are usually called policies or contracts and they are written or issued rather than sold. Insurance-like liabilities outside insurance exist (notably warranties), but insurance contracts are concentrated overwhelmingly in insurers and reinsurers.
6. Hedging. Contingent claims used to offset or mitigate existing economic and financial exposures: derivatives, swaps, and other specialized contracts. While many CCFs can serve a hedging function, one is specifically a hedge when its primary purpose is to reduce the volatility of an existing portfolio. Hedging is often characterized by an “initiator’s premium,” where a party accepts a less favorable price to achieve immediate and certain risk reduction.

Insurance and reinsurance can be analyzed using financing concepts because they embed funding and timing transformation, but we classify them as insurance contracts because risk transfer is their primary economic purpose.

1.10 Asymmetric Information, Model Transformation Risk, and Structural Frictions

The complexity of CCF contracts is compounded by the nature of their contingencies. In many exchange-traded markets—stocks, rates, and widely traded commodities—the object being traded is standardized, prices are public, and value is disciplined by continuous trading and rapid feedback. Private information still exists, but it is diluted by disclosure rules, deep liquidity, and fast price discovery.

Insurance markets sit closer to the canonical “second-hand car” problem. The contract’s cash flows are tightly linked to characteristics that are privately observed (or costly to verify) and to actions taken after the contract is written. As a result, a CCF contract can embed two distinct uncertainties: type uncertainty (hidden risk or quality at inception) and action uncertainty (hidden behavior after inception). When cash flows depend on private information or behavior, the market faces asymmetric-information risks:

• Adverse selection: high-risk parties are more likely to seek the contract (the lemons problem).
• Moral hazard: possession of the contract alters behavior, increasing the probability or severity of a payout.
• Signaling: the better-informed party takes a costly action to credibly convey information.
• Screening: the less-informed party offers a menu of choices to induce self-selection (e.g., high-deductible vs low-deductible options).

A critical asymmetry arises from model transformation risk: the risk created when a qualitative written description is collapsed into a quantitative pricing model. In insurance, the insured “owns” the underlying risk and often has a more intuitive, if not statistical, understanding of it. The insurer bears the primary burden of parameter risk—the danger that the model used to represent the contract’s contingencies is miscalibrated or misspecified. While the insured evaluates the premium’s utility, the insurer faces the existential risk that the contract’s “if-then” logic triggers cash flows at a frequency or severity the model fails to predict.

Finally, these contracts are subject to three structural frictions:

• Basis risk: the gap between the actual loss suffered and the payout triggered by the contract’s language.
• Credit (counterparty) risk: the risk that promised payments are defaulted. In organized exchanges this is mitigated by clearinghouses and margin; in negotiated markets it remains a central pricing factor.
• Liquidity (exit) risk: the ease with which a party can exit their role in the contract. In fungible, quote-driven markets, a position can often be offset quickly; in negotiated, bespoke contracts, exit may require novation or commutation, and a party may be effectively locked in for the duration.

1.11 Capstone Example: Catastrophe Bonds

This example illustrates how a catastrophe bond transforms a (re)insurance liability into an investment security.

A catastrophe bond is a securitized instrument that bridges the insurance and capital markets using a special purpose vehicle (SPV). The structure functions through two simultaneous transactions:

1. The reinsurance leg: the SPV acts as the provider (short side) of a reinsurance contract to a sponsor insurer (long side). The sponsor pays premiums to the SPV to cover losses from a specific peril.
2. The investment leg: to collateralize its reinsurance promise, the SPV issues (short side) bonds to investors. The reinsurance premium is passed to investors as coupon payments.

The SPV passes the residual value of the bond back to the investor. If no catastrophe occurs, the investor receives the full principal; if a catastrophe occurs, the investor’s principal is reduced by the loss payment made to the sponsor. The principal usually acts as the aggregate limit of the bond so the sponsor bears no credit risk.

By passing the insurance premium to investors as a coupon spread above the risk-free rate, the SPV converts an insurance-protection position into an investment return stream. The investor becomes the ultimate provider of the insurance contingency, incentivized by a yield that compensates them for providing protection to the sponsor.

References

1.

Bellini, F., Koch-Medina, P., Munari, C., Svindland, G.: Law-invariant functionals beyond bounded positions. arxiv. 1–20 (2020)

2.

Chateauneuf, A., Cornet, B.: The risk-neutral non-additive probability with market frictions. Economic Theory Bulletin. 10, 13–25 (2022). https://doi.org/10.1007/s40505-022-00216-4

3.

Bastianello, L., Chateauneuf, A., Cornet, B.: Put–Call Parities, absence of arbitrage opportunities, and nonlinear pricing rules. Mathematical Finance. 2021, 1–21 (2024). https://doi.org/10.1111/mafi.12433

4.

Froot, K.A.: Risk management, capital budgeting, and capital structure policy for insurers and reinsurers. Journal of Risk and Insurance. 74, 273–299 (2007)

5.

Froot, K.A., Stein, J.C.: Risk management, capital budgeting, and capital structure policy for financial institutions: An integrated approach. Journal of Financial Economics. 47, 55–82 (1998). https://doi.org/10.1016/S0304-405X(97)00037-8

6.

Froot, K.A., O’Connell, P.G.J.: On the pricing of intermediated risks: Theory and application to catastrophe reinsurance. Journal of Banking and Finance. 32, 69–85 (2008). https://doi.org/10.1016/j.jbankfin.2007.09.008

7.

Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M.: Put-Call Parity and market frictions. Journal of Economic Theory. 157, 730–762 (2015). https://doi.org/10.1016/j.jet.2014.12.011

8.

Bellini, F., Koch-Medina, P., Munari, C., Svindland, G.: Law-invariant functionals that collapse to the mean. Insurance: Mathematics and Economics. 98, 83–91 (2021). https://doi.org/10.1016/j.insmatheco.2021.03.002