Kspectra See the unseen

Pricing the risk that will not diversify.

AI compute became a traded financial asset — cleared GPU-rental futures, exchange-listed reservations, and roughly a trillion dollars of circular vendor financing — faster than anyone built the tools to price it. This is how we value a whole portfolio of compute-capacity contracts, built up in five steps from a single contract to the bound on the risk that neither spreading your bets nor a commodity hedge can remove.

1 — A single contract: commodity + credit
2 — A portfolio: five priced dynamics
3 — Technology: obsolescence & competition
4 — Financial shock: contagion
5 — The result: a good-deal bound


The gap

A contract that is neither a commodity nor a bond

A compute-capacity contract is a promise to deliver rented GPU time in the future — say, a block of H100 hours next quarter — from a named issuer who has to survive to deliver it. That one sentence breaks both standard playbooks. It is not a clean commodity, because the value that changes hands depends entirely on which issuer and whether they are still standing. And it is not debt, because the risk is not an unpaid loan — it is a prepaid good that never gets delivered. Worse, the good melts: each new chip generation marks down everything already deployed.

So the market is incomplete — nothing you can trade replicates the claim, and no textbook arbitrage pins its price. That is the regime where a model has to earn its keep. We build it in five steps.

Step 1 / A single contract

Commodity value, times the odds the issuer delivers

Price one contract as a defaultable claim on a commodity forward. It splits into two branches that most models keep in different departments:

  • a commodity branch — what the delivered compute is worth as it obsolesces; and
  • a credit branch — the chance the issuer survives to deliver, plus what is recovered if they fail.

Put together, the fair value is the survival-weighted delivery value plus a recovery term. Call it F — the whole single-issuer contract in one line, and the building block the portfolio in Step 2 sums over:

F = S · Gg + (1−S) · R operating loss

S = survival probability  ·  Gg = the obsolescing compute forward  ·  R = recovery on default

The move that makes compute an asset class of its own is what happens between the branches. A single hardware-obsolescence lifecycle ζ drives both at once — the same cadence that depreciates the good also raises the issuer's default risk, and, through the bankruptcy estate's option to keep or reject the contract, sets the recovery. One clock, three effects:

value melts:   ηg = ηlife(ζ)

default rises:   λ = λ0 + βlife·D(ζ)

The same lifecycle ζ appears in both lines — fixed in advance from the roadmap, not fit as a free knob. That is why compute credit is wrong-way: when compute prices fall, the issuers who sell it get riskier at the very same moment.

One hardware-lifecycle clock  ζ frontier rate ≈ 23% / yr · pinned to each maker's roadmap Commodity branch what the compute is worth value melts as the next generation ships Credit branch will the issuer deliver? survival S — recovery R if it fails The contract’s fair value
The single-issuer engine. Both branches hang off one lifecycle clock; the coupling is what makes compute credit wrong-way. Reality check: calibrated only to the H100→B200 transition, the obsolescence curve predicted the older A100's cross-generational forward to within one percentage point in the annualized rate — out of sample, no A100 data in the fit. The headline 23%/yr is the frontier rate; an older grade like the A100 melts a little slower as it commoditizes — one calibrated curve captures both.
Step 2 / A portfolio

The book is a sum — but its risk is not

The object a desk actually manages is not one contract but a book across many issuers — a weighted sum of single-name values:

Π(t,T) =i wi Fi(t,T)

One portfolio, priced by one closed-form engine — but carrying five distinct dynamics the single-name model treats in isolation or not at all.

Each dynamic enters a different term of the price and pushes in a different direction, so it is the joint distribution — not the marginals — that governs the book. The five:

  • Obsolescence — the deployed fleet ages as each new generation ships, lowering both value and survival.
  • Competition — a rival architecture can displace the incumbent: a rare tip on locked-in workloads, a steady share-walk on the rest.
  • Continuous factors — shared macro and supply moves; the one channel a basket index genuinely hedges.
  • Common shocks — a single event (an outage, a ruling, a shared supplier) defaults a whole tied group at once.
  • Self-exciting cascade — each failure tightens financing on the others, raising the odds of the next.

Two are on the technology side, three on the credit side. Four push value down and, unspanned by any tradeable hedge, land in the unhedgeable residual; only continuous market co-movement is hedgeable by a basket index.

Portfolio price Π = Σ wᵢ Fᵢ — one affine engine TECHNOLOGY SIDE 1 · Obsolescence 2 · Competition CREDIT SIDE 3 · Continuous factors 4 · Common shocks 5 · Self-exciting cascade The unhedgeable residual four of five push value down and no index spans them
The five-dynamics map. Two technology dynamics and three credit dynamics feed one closed-form pricing equation. Only continuous factors (3) are hedgeable by a basket index; the other four collect in the residual — and the cross-issuer cluster inside it is the risk this whole framework is built to price. Steps 3 and 4 develop the two sides.
Step 3 / Technology

Obsolescence, and the fight to replace the architecture

Compute value melts for two reasons, and they behave nothing alike. The first is obsolescence: within one architecture, the deployed fleet ages as each successor generation ships, on a one-to-three-year cadence. That is a steady, roadmap-pinned depreciation — the melting is predictable.

The second is competition: the whole architecture — today, NVIDIA and its CUDA moat — can be displaced. The two-part depreciation splits exactly this way:

ηg = ηlife + ηarch

ηlife = within-architecture obsolescence (steady)  ·  ηarch = cross-architecture substitution (regime-dependent)

Obsolescence — the fleet melts on the roadmap value HopperBlackwellnextnext+1 ≈ 23% / yr
Obsolescence (ηlife). Unlike a building or an aircraft — which obsolesce over decades, far beyond any financing tenor — compute's technology cycle runs on the same timescale as the contract, so lifecycle risk is a first-order pricing factor, not a footnote.

Substitution — the ηarch piece — arrives in two regimes, and a single ratio decides which. Write ρ for how strongly an architecture's gains spill to rivals and γ for the strength of lock-in:

ρ < 2γ → lock-in (a rare tip)   |   ρ > 2γ → coexistence (a steady walk)

On the contestable training market — where everyone builds on the incumbent stack — lock-in holds: a challenger must clear a high ridge, so migration is a rare, discrete tip, a tail event. On the overall market — training plus the fast-diversifying inference workloads — there is no ridge; share simply erodes, and that slow walk widens the price band even when nothing dramatic happens.

(a) Contestable — lock-in, ρ < 2γ deep valley + ridge → a switch is a rare tail event incumbent (CUDA moat) challenger rare tip
Competition (ηarch) — (a) contestable. On locked-in training workloads the incumbent sits in a deep basin; a challenger must clear a ridge, so a switch is a rare tail event (a tip).
(b) Overall — coexistence, ρ > 2γ share erodes smoothly → the band widens, no tail needed 1.0 0.5 now +10y 0.87 ~0.57 incumbent value share of the overall accelerator market
Competition (ηarch) — (b) overall. On the overall market, value share slides from ~0.87 toward ~0.57 as inference diversifies — a deterministic walk that widens the valuation band with no dramatic event at all.
Step 4 / Financial shock

How a tied cluster fails together

On the credit side, one dynamic is benign — continuous factors, the shared macro and supply co-movement that a basket index genuinely hedges. The other two are where the cluster risk lives, and they are why it does not diversify: the issuers are bound to one another.

The first is a common shock: one event — a datacenter outage, a regulatory ruling, a shared supplier — strikes a whole tied group at the same instant. Names that looked independent default together because they share a cause.

The second is subtler and more dangerous: a self-exciting cascade. In a circular-financing web, one failure does not just happen — it raises the odds of the next: a shortfall at one node tightens financing on the others, which makes their failure more likely, which tightens financing further. The whole spiral collapses to one number, the branching ratio n — the average count of fresh failures each failure sets off — and that number multiplies the price band:

band multiplier = 1 / (1 − n)

n = knock-on failures per default. In the flagship cluster n ≈ 0.64 already widens the band ×2.8; as buffers erode it climbs, and at n → 1 the band blows up.

(a) Common shock one cause fires → a group defaults at once shared cause issuer Aissuer Bissuer Cissuer D
Contagion — (a) common shock. One event (an outage, a ruling, a shared supplier) defaults a whole tied group at the same instant — the piece that survives name-diversification.
(b) Self-exciting cascade each failure raises the odds of the next 1st 2nd 3rd… band multiplier 1 / (1 − n) 0 n→1 0.64 ×2.8
Contagion — (b) self-exciting cascade. Each default lifts the hazard on the survivors; the branching ratio n collapses the whole spiral into a single band multiplier 1/(1−n) — n≈0.64 already means ×2.8.
Step 5 / The result

You cannot hedge it away — but you can bound it

Stack the five dynamics and one channel is left with no hedge: the cross-issuer cluster. When the only tradeables are the commodity index and continuous factors, that channel is wholly unhedgeable, and there is no unique price — only a band. The headline result bounds that band. Its half-width is the leftover cluster risk, priced at a maximum reasonable reward-for-risk h (a “good-deal” ceiling — no strategy should earn more than that per unit of risk):

band half-width = h · σcluster · (1 − spanned)

h = the good-deal reward-for-risk ceiling  ·  σcluster = the unhedgeable cluster volatility  ·  spanned = the fraction of it that credit instruments cover

Add credit instruments — single-name CDS, a CDS index, GPU-loan ABS tranches — and the spanned fraction rises, contracting the residual to an explicit cluster-basis floor. We show the bound is sharp — attained, not loose — and that it closes to zero only in the limit where those instruments fully span the cluster and architectures are diversified. Short of that limit, the correlation is redistributed across tranches, never removed.

The price band closes as credit instruments span the cluster price base (MMM) price commodityhedge only + single-nameCDS + CDSindex + tranches(fully spanned) wholly unhedgeable sharp floor
The good-deal bound. The width of the no-arbitrage band is the price of the unhedgeable cluster risk. Each credit instrument you add spans a little more of the cluster and tightens the band toward a sharp cluster-basis floor — which vanishes only in the fully-spanned, architecture-diversified limit. Read backward, the bound is a design brief: it names the instruments a market would need to actually transfer this risk.

Seen on one deal / The 2025–26 loop

The whole machine, on the deal everyone is arguing about

NVIDIA takes an equity stake in OpenAI; OpenAI commits to buy compute from Oracle; Oracle buys NVIDIA GPUs to build it. Cash flows chipmaker → lab → cloud → and back. Commentators call it round-tripping. The model calls it a cluster, and prices it — technology, contagion, and the bound, all at once.

$100B equity (letter of intent) ~$300B compute · ~$60B/yr GPU purchases funding cascade NVIDIA GPU supplier OpenAI compute buyer Oracle compute producer counterparty · a single payer (OpenAI) funding · self-referential demand architecture · one hardware family (NVIDIA)
The marquee loop. The arrows trace the funding cycle; the dashed core is the funding-cascade shock that strikes all three names at once. The loop concentrates the backlog three ways — one payer, one self-referential demand source, one hardware family — so the apparent chipmaker / lab / cloud diversification collapses into a single exposure.

Here is the counter-intuitive read. NVIDIA's $100B into OpenAI looks like de-risking — fresh capital should make the payer safer. The model says the opposite: that same capital binds the three names into one self-exciting cascade. Vendor financing does not remove risk; it trades idiosyncratic risk (one firm stumbles) for systematic risk (all three fall together) — and only the systematic kind survives diversification. So the priced value of Oracle's backlog is worth materially less than its face, and the discount deepens as the loop tightens.

~$275B → $105B
present value of the backlog as the cascade goes from quiescent to fully armed
±$31B → ±$61B
the good-deal band widens as cluster risk dominates
n ≈ 0.64
funding-cascade branching ratio — already a ×2.8 band multiplier

vendor financing : trades idiosyncratic risk systematic risk

Name-diversification inside the loop buys nothing: the guarantor fails in the same state as the names it guarantees.

The takeaway

What the bound tells a holder to do

Read forward, the good-deal bound is a price. Read backward, it is a playbook — because it names exactly which risk you can shed and which you must hold.

A

Lay off the commodity leg

Compute-price exposure is the one channel a cleared index genuinely hedges. Use it.

B

Diversify across independent clusters

Not across names inside one loop — that buys nothing. Across separately-financed clusters and hardware families.

C

Distrust single-name protection

A guarantor tied into the same loop defaults in the same state. Price it as correlated, not as insurance.

D

Capital-hold the residual

The irreducible cluster-and-architecture risk is real and priced into the spread. Hold capital against it.

Compute is the asset class that makes all of this concrete and timely — but nothing in the machinery is specific to it. The same construction prices any basket of defaultable claims exposed to common shocks that no traded index spans. It is a framework for a market that arrived before its own tools.