---
title: "Dated Futures, Options and ETFs"
book: "Markets III: Commodities, Energy and Crypto"
subject: quant
language: en
chapter: 19
exercises: 8
source: https://one-course.com/books/quant/3/en/chapter/19-dated-futures-options-and-etfs
---

# Chapter 19 — Dated Futures, Options and ETFs

On 10 January 2024 the US Securities and Exchange Commission let spot bitcoin [exchange-traded products](#def-m3-dated-futures-options-and-etfs-etp) list, after a court had found that it had not adequately explained its refusal of one of them. The next day their shares began trading on US exchanges. By September 2026 the largest held about USD 67 billion of bitcoin for its shareholders, and a trader could hold bitcoin in a brokerage account, lend it, finance it, and sell a regulated future against it. The crypto market’s derivatives now come in two families: the [coin-margined contracts](#def-m3-dated-futures-options-and-etfs-dated) of the crypto-native venues, with their own conventions, and the dollar-margined contracts and funds of the regulated markets of One Quant Book 1. This chapter covers [dated futures](#def-m3-dated-futures-options-and-etfs-dated) on both, the basis trade between them, the options of the dominant crypto options venue with their premium paid in coin, the shape of the crypto volatility surface, and the [exchange-traded products](#def-m3-dated-futures-options-and-etfs-etp) and how their shares are created.

## 19.1 Dated futures on crypto venues and on regulated exchanges

**Definition 19.1 (Dated future, coin-margined contract).**

A *dated future* on a crypto asset is a futures contract with a fixed expiry, settled in cash against an index or a reference rate at expiry, as distinct from a [perpetual future](https://one-course.com/books/quant/3/en/chapter/17-perpetual-futures#def-m3-perpetual-futures-perp). A *coin-margined contract* is a futures or options contract whose margin, P&L and settlement are in the underlying coin rather than in dollars or a [stablecoin](https://one-course.com/books/quant/3/en/chapter/14-blockchains-for-traders#def-m3-blockchains-for-traders-stable).

The crypto-native venues list [dated futures](#def-m3-dated-futures-options-and-etfs-dated) as [inverse contracts](https://one-course.com/books/quant/3/en/chapter/17-perpetual-futures#def-m3-perpetual-futures-types) ([Chapter 17](https://one-course.com/books/quant/3/en/chapter/17-perpetual-futures#ch-m3-perpetual-futures)): a dollar notional, margin and settlement in coin, and expiries weekly, monthly and quarterly, all at the same hour. The regulated exchanges list dollar-settled contracts on the model of any other cash-settled index future (One Quant Book 1, chapter 18), settled to a benchmark computed from spot trades.

**Definition 19.2 (Crypto reference rate).**

A *crypto reference rate* is a benchmark price of a crypto asset computed by an administrator from trades on a set of constituent spot venues over a stated window, with rules (partitions, medians, venue criteria) that make it costly to move with a few trades; it is used to settle futures and to value funds.

**As of September 2026 — A reference rate and its uses.**

The CME CF Bitcoin Reference Rate is a once-a-day benchmark aggregating trades from bitcoin–dollar markets on constituent exchanges and is the settlement index for bitcoin futures listed by CME Group, which self-certified them on 1 December 2017 for a first trade date of 18 December. Its New York variant, used to value the largest spot bitcoin fund, takes every spot trade on its constituent platforms (listed in the fund’s 2025 annual report as Bitstamp, Coinbase, itBit, Kraken, Gemini, LMAX Digital, Crypto.com and Bullish) between 3:00 and 4:00 p.m. New York time, splits them into twelve five-minute partitions, takes each partition’s volume-weighted median price, and averages the twelve medians with equal weights.

The construction is chosen against manipulation: a trader who prints one large trade at an off-market price moves one partition’s median little, and must move the median of all constituent venues for a whole hour to move the rate much. The build of this chapter implements it.

Futures on the two families of venues differ in more than margin. A coin-margined future’s P&L in dollars is the coin P&L times the coin’s price, so a dollar-based trader who is long the future with coin margin is long twice, as with inverse perpetuals. The regulated future is margined in dollars through a clearing member, in the waterfall of One Quant Book 1, chapter 5, not the venue-level waterfall of [Chapter 18](https://one-course.com/books/quant/3/en/chapter/18-margin-liquidation-and-loss-allocation#ch-m3-margin-liquidation-and-loss-allocation).

## 19.2 The regulated-futures basis trade

A [dated future](#def-m3-dated-futures-options-and-etfs-dated) trades at a basis to spot. With $F$ the future, $S$ the spot index and $\tau$ the days to expiry, the annualised basis is $(F/S - 1)\times 365/\tau$ (or $\ln(F/S)\times 365/\tau$ continuously compounded). The [cash-and-carry trade](https://one-course.com/books/quant/3/en/chapter/10-forward-curves-storage-and-convenience-yield#def-m3-forward-curves-storage-and-convenience-yield-carry) (One Quant Book 1, chapter 21) buys spot, sells the future, and earns the basis if it holds to expiry.

**As of September 2026 — A crypto futures curve.**

On 24 September 2026, Deribit’s bitcoin index was 83 499.12 and its quarterly futures were marked at 84 533.98 (December 2026), 85 668.78 (March 2027), 86 833.65 (June 2027) and 87 948.30 (September 2027): annualised basis of 4.9%, 5.2%, 5.3% and 5.3%. Its futures and options expire at 08:00 UTC.

**Proposition 19.3 (The carry of a fund–future basis trade).**

Buy a spot [exchange-traded product](#def-m3-dated-futures-options-and-etfs-etp) with financing at rate $r_{\mathrm{fin}}$, pay its annual fee $\phi_{\mathrm{ETF}}$, and sell a regulated future at an annualised basis $b$, with futures costs $c$ a year (fees and rolls). If the fund tracks spot and the position is held to the future’s expiry, the carry per unit of notional is $b - r_{\mathrm{fin}} - \phi_{\mathrm{ETF}} - c$ a year, and its return on the capital tied up (the future’s margin $m$ plus the haircut $h$ on the financed fund) is that carry divided by $m + h$.

**Proof.** At expiry the future converges to the reference rate and the fund’s shares, by creation and redemption, to its net asset value, which tracks the same spot price; the price legs cancel and what remains is the basis earned less the costs of holding the fund. The capital is what the financier and the clearing house hold back. ∎

The trade is only as good as the basis net of financing. [Table 19.1](#tab-m3-dated-futures-options-and-etfs-carry) compares a rich basis of 10% a year, the average level of crypto carry that researchers at the BIS measured ([Chapter 17](https://one-course.com/books/quant/3/en/chapter/17-perpetual-futures#ch-m3-perpetual-futures)), with the 4.9% of the snapshot above, at an illustrative financing rate of 4.5%. At a rich basis the trade earns about 5% a year on notional and 14% on capital; at the snapshot’s basis it loses money. The trade’s risks are those of a leveraged carry trade: the basis can widen against the short future before expiry, requiring margin; financing can be withdrawn; and the fund can trade at a discount to its net asset value when creations and redemptions are impaired.

| per year, % of notional | rich basis | snapshot basis |
| --- | --- | --- |
| Basis earned by the short future | 10.00 | 4.92 |
| Financing of the fund | $-4.50$ | $-4.50$ |
| Fund’s fee | $-0.25$ | $-0.25$ |
| Futures costs | $-0.30$ | $-0.30$ |
| Carry | 4.95 | $-0.13$ |
| Return on capital (25% margin + 10% haircut) | 14.14 | $-0.38$ |

***Table 19.1.** The carry of long spot fund, short regulated future ([Proposition 19.3](#prop-m3-dated-futures-options-and-etfs-carry)). The rich basis is the BIS average for crypto carry; the snapshot is the December 2026 future of [Box 19.2](#dat-m3-dated-futures-options-and-etfs-curve); financing, costs, margin and haircut are illustrative; the fee is the largest fund’s.*

## 19.3 The dominant options venue’s conventions: inverse options

On the crypto-native venues, options follow the conventions of Deribit, described below; regulated exchanges list dollar-settled options on futures, and options on the spot funds trade on securities exchanges, the first approved by the SEC on 20 September 2024 for the iShares Bitcoin Trust.

**Definition 19.4 (Inverse option).**

An *inverse option* is a European option on the dollar price of a coin whose premium is quoted and paid in the coin and whose payoff is settled in the coin: a call pays $(F_T - K)^+/F_T$ coins at expiry, where $F_T$ is the settlement price and $K$ the strike in dollars.

**As of September 2026 — Option conventions at the largest crypto options venue.**

Deribit’s instrument data on 24 September 2026 describe its bitcoin options as European, one bitcoin per contract, quoted and settled in bitcoin, with strikes in dollars and expiries at 08:00 UTC, daily, weekly, monthly and quarterly. On that day the December 2026 options, with the underlying future at 84 538.67, were marked at implied volatilities of 47.1% (strike 60 000), 40.8% (70 000), 38.2% (80 000), 37.5% (90 000), 38.1% (100 000), 39.6% (110 000) and 42.2% (120 000). Coinbase, which acquired Deribit on 14 August 2025 for about USD 4.3 billion, calls it in its 2025 annual report the global leader in crypto options trading by volume and open interest.

**Proposition 19.5 (Inverse option prices and deltas).**

Let $V$ be the Black price in dollars of an option on the future $F$ (One Quant Book 1, chapter 25), with zero discounting. The [inverse option](#def-m3-dated-futures-options-and-etfs-inverse)’s premium in coin is $V/F$; put–call parity in coin reads $C/F - P/F = 1 - K/F$. The option’s delta in coin, for a holder who paid the premium in coin, is the dollar delta $\partial V/\partial F$ less the coin premium $V/F$: the premium-adjusted delta. At expiry a call’s value in coin, $(F_T - K)^+/F_T$, is less than one coin however high $F_T$ goes, and a put’s, $(K - F_T)^+/F_T$, grows without bound as $F_T \to 0$.

**Proof.** The dollar value $V$ is worth $V/F$ coins at the current price; dividing Black’s parity $C - P = F - K$ by $F$ gives the coin form. A holder whose account is in coin and who bought the option with $V/F$ coins has a dollar exposure of $\partial V/\partial F$ from the option and $-V/F$ from the coins spent; its hedge in coin is their sum. The bounds follow from $(F_T - K)/F_T = 1 - K/F_T < 1$ and $K/F_T - 1 \to \infty$. ∎

The convention is that of the premium-adjusted delta of currency options (One Quant Book 2, chapter 19): the premium is paid in the asset whose price the option is on. Deribit’s own marks confirm the pricing: the December 90 000 call’s mark of 0.0492 bitcoin is Black’s dollar price at 37.46% divided by the future.

![Value in bitcoin at expiry of inverse options struck at 90 000 (): the call’s coin value approaches but never reaches one bitcoin; the put’s grows without bound as the price falls. In dollars both are the ordinary payoffs. Data: the chapter’s tutorial.](https://one-course.com/images/onecourse/chapters/quant-3/m3-dated-futures-options-and-etfs/fig-78ade6b670e5.svg)

***Figure 19.1.** Value in bitcoin at expiry of [inverse options](#def-m3-dated-futures-options-and-etfs-inverse) struck at 90 000 ([Proposition 19.5](#prop-m3-dated-futures-options-and-etfs-inverse)): the call’s coin value approaches but never reaches one bitcoin; the put’s grows without bound as the price falls. In dollars both are the ordinary payoffs. Data: the chapter’s tutorial.*

![Deltas of December 2026 inverse calls across strikes, at the venue’s marked volatilities of . Deep in the money the premium-adjusted delta falls: the premium, paid in bitcoin, is itself a large bitcoin exposure, and the 60 000 call’s adjusted delta (0.645) is below the 70 000 call’s (0.658). Data: the chapter’s tutorial.](https://one-course.com/images/onecourse/chapters/quant-3/m3-dated-futures-options-and-etfs/fig-6be5ac3d1a35.svg)

***Figure 19.2.** Deltas of December 2026 inverse calls across strikes, at the venue’s marked volatilities of [Box 19.3](#dat-m3-dated-futures-options-and-etfs-deribit). Deep in the money the premium-adjusted delta falls: the premium, paid in bitcoin, is itself a large bitcoin exposure, and the 60 000 call’s adjusted delta (0.645) is below the 70 000 call’s (0.658). Data: the chapter’s tutorial.*

## 19.4 The crypto volatility surface

The snapshot of [Box 19.3](#dat-m3-dated-futures-options-and-etfs-deribit) has the shape the crypto surface usually has: high levels (bitcoin’s at-the-money implied volatility near 37% on a quiet day), a smile with both wings bid, and a skew whose sign can change with the market’s mood. In the snapshot the wing 30% below the future carries about 10 points more volatility than the wing 40% above it: a put skew. At times of speculative rallies the call wing can become the richer one, as buyers pay for upside; the equity-index surface of One Quant Book 1, chapter 25, has a put skew almost always. The market trades around the clock, weekends included, so there is no overnight or weekend close and time to expiry is naturally measured in calendar time. Tools for the surface (smile parameterisations, the arbitrage-free interpolation of One Quant Book 5) apply unchanged once premiums are converted to dollars with [Proposition 19.5](#prop-m3-dated-futures-options-and-etfs-inverse).

## 19.5 Spot ETFs: creation and redemption

**Definition 19.6 (Exchange-traded product, grantor trust).**

An *exchange-traded product* is an exchange-listed security whose shares track an asset or index and are created and redeemed by authorised participants, whether or not it is registered as an investment fund; in the United States the spot bitcoin products are trusts that hold bitcoin and are not registered investment companies. A *grantor trust* is a trust whose owners are treated for US federal income tax as owning its assets directly, so that the trust itself is not taxed.

**Definition 19.7 (Cash creation).**

*Cash creation* is the creation of an [exchange-traded product](#def-m3-dated-futures-options-and-etfs-etp)’s shares against cash delivered by an authorised participant, with the fund buying the underlying asset itself; cash redemption is the reverse. They contrast with in-kind creation and redemption, in which the participant delivers or receives the asset.

The mechanism is the exchange-traded fund’s of One Quant Book 1, chapter 14: authorised participants create baskets of shares when the shares trade at a premium to net asset value and redeem them at a discount. For a bitcoin trust the asset is a coin held with a custodian, and the question of who touches it decides how well the arbitrage works. With [cash creation](#def-m3-dated-futures-options-and-etfs-cash) the participant never holds bitcoin; the trust buys it, at the reference rate or through an execution agent, and the participant’s arbitrage is between the share price and a cash amount fixed later, which is harder to hedge. With in-kind creation the participant delivers bitcoin, can source it where it is cheapest, and hedges exactly.

**As of September 2026 — The largest spot bitcoin fund.**

The iShares Bitcoin Trust’s 2025 annual report states that its registration statement became effective on 10 January 2024, that its shares were listed on Nasdaq on 11 January 2024, that it creates and redeems in baskets of 40 000 shares through authorised participants, that its bitcoin is held by Coinbase Custody Trust Company, that it values its bitcoin at the New York variant of the CME CF Bitcoin Reference Rate, and that on 29 July 2025 the SEC issued orders permitting in-kind creations and redemptions for the trust; its sponsor’s fee was 0.25% a year, and the report assumes it is a [grantor trust](#def-m3-dated-futures-options-and-etfs-etp) for US tax. The fund’s website gave net assets of USD 67.08 billion on 23 September 2026 and a premium to net asset value of $-0.21\%$ on 22 September.

![Creation of shares in a spot bitcoin trust. In kind, the authorised participant delivers bitcoin, which goes to the custodian; in cash, it delivers dollars and the trust buys the bitcoin through an execution agent. Redemption reverses the arrows. Schematic.](https://one-course.com/images/onecourse/chapters/quant-3/m3-dated-futures-options-and-etfs/fig-092368b691af.svg)

***Figure 19.3.** Creation of shares in a spot bitcoin trust. In kind, the authorised participant delivers bitcoin, which goes to the custodian; in cash, it delivers dollars and the trust buys the bitcoin through an execution agent. Redemption reverses the arrows. Schematic.*

The funds changed the market’s plumbing. Bitcoin held for their shareholders sits with a few custodians; creations and redemptions move coins in large blocks at New York’s close; and the basis trade of [Proposition 19.3](#prop-m3-dated-futures-options-and-etfs-carry) joined the regulated future to the fund, so that a rich basis draws creations and a collapsing one draws redemptions. A listed trust that cannot redeem its shares for its assets lets the share price drift from their value: from May 2015 to December 2022 Grayscale’s bitcoin trust traded between a premium of 142% and a discount of 49% to its bitcoin per share, and ended 2022 at a discount of 45%. The court decision that preceded the 2024 approvals concerned its application to convert into an [exchange-traded product](#def-m3-dated-futures-options-and-etfs-etp).

## 19.6 Tutorial: premiums, deltas and the basis

**Goal.** Convert [inverse option](#def-m3-dated-futures-options-and-etfs-inverse) premiums between coin and dollars, compute the delta that includes the premium currency, annualise the basis of [dated futures](#def-m3-dated-futures-options-and-etfs-dated) and cost the fund–future trade. **End state:** Figures [19.1](#fig-m3-dated-futures-options-and-etfs-expiry) and [19.2](#fig-m3-dated-futures-options-and-etfs-deltas) and [Table 19.1](#tab-m3-dated-futures-options-and-etfs-carry).

1. **Premiums and deltas.** Black’s price on the future, divided by the future. `def coin_premium (forward: float , strike: float , years: float , vol: float , right: str , rate: float = 0.0 ) -> float : """Premium in coin of an inverse option (the dollar price divided by the future).""" return price(forward, strike, years, rate, vol, right) / forward def usd_premium (coin_prem: float , forward: float ) -> float : return coin_prem * forward def forward_delta (forward: float , strike: float , years: float , vol: float , right: str ) -> float : """Dollar-price delta to the future: N(d1) for a call, N(d1) - 1 for a put.""" s = vol * math.sqrt(years) d1 = math.log(forward / strike) / s + 0.5 * s return _phi(d1) if right == " C " else _phi(d1) - 1.0 def premium_adjusted_delta (forward: float , strike: float , years: float , vol: float , right: str ) -> float : """Delta, in coin per option, of an option whose premium is paid in the coin: the dollar delta less the coin premium (a buyer who paid the premium in coin is already short that much coin's dollar value).""" return forward_delta(forward, strike, years, vol, right) - coin_premium(forward, strike, years, vol, right)` **Listing 19.1.** Inverse option premium in coin, and the dollar and premium-adjusted deltas. code/firm/cryptoopt/firm_cryptoopt.py
2. **The reference rate.** Twelve partitions, a volume-weighted median in each, and their average. `def reference_rate (trades: list [tuple [float , float , float ]], start: float , end: float , parts: int = 12 ) -> float : """Benchmark in the style of a published bitcoin reference rate: trades (time, price, size) inside [start, end) are split into equal time partitions; the rate is the equally weighted average of the partitions' volume-weighted medians (empty partitions are skipped).""" width = (end - start) / parts meds = [] for i in range (parts): lo, hi = start + i * width, start + (i + 1 ) * width part = [(p, s) for t, p, s in trades if lo <= t < hi] if part: meds.append(weighted_median(part)) if not meds: raise ValueError(" no trades in the window " ) return sum (meds) / len (meds)` **Listing 19.2.** A reference rate in the style of a published bitcoin benchmark. code/firm/cryptoopt/firm_cryptoopt.py
3. **The basis and the carry.** `basis_table()` and `scenarios()` ; `fig_etf.py` writes the chart data.

**What to change next.** Recompute the deltas with the smile’s slope (the “smile delta”); price a put spread in coin and in dollars and compare their hedges; test how many one-minute trades an attacker must print to move the reference rate by 1%.

## 19.7 Build: inverse options and the basis

**Purpose.** The miniature firm quotes and hedges options on crypto venues whose premiums are in coin, and runs basis trades across crypto and regulated venues; it needs premiums, deltas and basis in one consistent set of conventions.

**Interface.** `coin_premium(forward, strike, years, vol, right)`, `usd_premium`, `forward_delta`, `premium_adjusted_delta`; `annualised_basis(future, spot, days, compounding)`; `etf_basis_carry`, `return_on_margin`; `weighted_median`, `reference_rate(trades, start, end, parts)`. Prices from `firm.parity`.

**Rules.** Coin premiums are dollar prices divided by the underlying future, never by the index; deltas state their currency; basis states its compounding; reference-rate windows are half-open.

**Acceptance tests.** `code/firm/cryptoopt/tests/`: a coin premium against the venue’s published mark; parity in coin; deltas at the money; basis annualisation; carry arithmetic; the reference rate’s resistance to one large print.

**Stretch.** Smile-consistent deltas; coin-margined futures P&L with margin in coin; options on the spot funds with their dollar conventions side by side.

Sources and further reading

- SEC, “Statement on the Approval of Spot Bitcoin Exchange-Traded Products”, Chair G. Gensler, 10 January 2024.
- iShares Bitcoin Trust ETF, annual report on Form 10-K for 2025 (filed 27 February 2026), and fund web page, September 2026.
- CF Benchmarks, CME CF Bitcoin Reference Rate page, September 2026.
- Deribit, public API (instruments, book summaries and index), 24 September 2026; Coinbase Global, annual report on Form 10-K for 2025.
- CFTC, press release 7654-17, 1 December 2017; CME Group, press release of 1 December 2017; SEC, Release No. 34-101128, 20 September 2024; Grayscale Bitcoin Trust, annual report on Form 10-K for 2022.

## 19.8 Exercises

**Exercise 19.1 ★.**

Spot is 83 499 and the future expiring in 183 days is 85 669. What is the annualised basis, simple and continuous?

**Solution of Exercise 19.1.**

Simple: $(85\,669/83\,499 - 1) \times 365/183 = 5.18\%$. Continuous: $\ln(85\,669/83\,499) \times 365/183 = 5.12\%$.

**Exercise 19.2 ★.**

An inverse call’s mark is 0.0492 bitcoin with the future at 84 539. What is its dollar premium?

**Solution of Exercise 19.2.**

$0.0492 \times 84\,539 \approx \$4\,159$.

**Exercise 19.3 ★.**

Why does a reference rate use medians over partitions rather than the last trade at 4 p.m.?

**Solution of Exercise 19.3.**

A single trade at 4 p.m. can be placed to move the settlement; medians over twelve partitions of an hour, across several venues, require moving most of the volume for most of the hour.

**Exercise 19.4 ★★.**

Check put–call parity in coin for strike 80 000 with the future at 84 539: the call’s mark is 0.1042 and the put’s 0.0505.

**Solution of Exercise 19.4.**

$0.1042 - 0.0505 = 0.0537$ and $1 - 80\,000/84\,539 = 0.0537$: parity holds in coin.

**Exercise 19.5 ★★.**

At what financing rate does the fund–future trade break even with a 10% basis, the 0.25% fee and 0.30% of futures costs?

**Solution of Exercise 19.5.**

$10\% - 0.25\% - 0.30\% = 9.45\%$.

**Exercise 19.6 ★★.**

Why was in-kind creation better for arbitrage than [cash creation](#def-m3-dated-futures-options-and-etfs-cash)?

**Solution of Exercise 19.6.**

In kind, the participant delivers bitcoin it has bought where it chooses and at a known price, hedging the share position exactly; in cash, the trust buys later at a price the participant does not control, so the arbitrage carries execution risk and costs more, which widens the band around net asset value.

**Exercise 19.7 ★★★.**

*Coding.* With `delta_table`, find the strikes at which the premium-adjusted delta is largest, and explain why it is not the deepest in-the-money strike.

**Solution of Exercise 19.7.**

At 70 000 (0.658) among the tabulated strikes. Deeper in the money the dollar delta approaches one but the coin premium grows faster, approaching $1 - K/F$, so their difference falls again: the premium paid in bitcoin is itself a large short exposure to bitcoin’s dollar value.

**Exercise 19.8 ★★★.**

*Find the flaw.* “Our book of inverse calls is delta-hedged: we are short futures equal to the sum of the calls’ Black deltas.”

**Solution of Exercise 19.8.**

Black’s delta is the dollar delta. A book whose premiums and P&L are in coin must use the premium-adjusted delta, and deep in-the-money calls then need markedly smaller hedges (0.645 instead of 0.942 at 60 000 in the snapshot); the hedge described overhedges them.

## 19.9 Problem: The ETF Basis Trade

**Problem 19.1.**

Weekend problem — long the fund, short the future

A fund buys USD 200 million of a spot bitcoin ETP financed at 4.5% with a 10% haircut, and sells regulated futures on the same notional with 25% margin. The fund’s fee is 0.25% a year and futures costs are 0.30% a year. Use [Table 19.1](#tab-m3-dated-futures-options-and-etfs-carry).

**Part I — The carry.**

1. With a 10% annualised basis, what does the trade earn in a year, in dollars?
2. What capital does it tie up, and what is its return on capital?
3. At the snapshot basis of 4.92%, what does it earn?
4. At what basis does it break even?
5. Why is the basis on regulated futures a financing rate in disguise?

**Part II — The mechanics.**

6. How do the fund’s shares stay close to their net asset value?
7. At what price is the fund valued each day, and how is that price computed?
8. At what price does the future settle?
9. Why might the two differ at expiry, and what would that do to the trade?
10. What changed on 29 July 2025, and why does it matter for this trade?

**Part III — The risks.**

11. The basis widens from 10% to 20% a month after entry. What happens to the position and its margin?
12. The financier raises the haircut to 25%. What happens to the return on capital?
13. The fund trades at a 1% discount on the day the trade is unwound. What does that cost?
14. What happens to the trade if bitcoin falls 30%?
15. How would the same trade look with a coin-margined crypto future instead of a regulated one?

**Part IV — Judgement.**

16. Who is on the other side of the trade, paying the basis?
17. Why might many funds doing this trade at once make the market fragile?
18. Is this trade an arbitrage?
19. State the *named result* : the trade’s annualised carry and return on capital at a 10% basis, and its carry at the snapshot basis.
20. In one sentence: what did the spot funds add to the crypto market?

**Solution of Problem 19.1.**

**1.** $4.95\% \times 200$ million: USD 9.9 million. **2.** $25\% + 10\%$ of notional: USD 70 million; 14.14%. **3.** About USD 0.26 million lost ($-0.13\%$). **4.** $4.5\% + 0.25\% + 0.30\% = 5.05\%$. **5.** Buying spot and selling the future lends cash against bitcoin until expiry; the basis is the rate earned on that loan, which the trade compares with its own financing rate. **6.** Authorised participants create baskets when shares trade above net asset value and redeem when below. **7.** At the New York variant of the CME CF Bitcoin Reference Rate, computed from 3 to 4 p.m. New York time: twelve five-minute partitions, volume-weighted medians, averaged. **8.** At the CME CF Bitcoin Reference Rate on the expiry day. **9.** If the two benchmarks are computed at different times or from different data, their difference at expiry is left in the trade as unhedged basis. **10.** The SEC permitted in-kind creations and redemptions for the trust: authorised participants can deliver bitcoin, which tightens the link between the share price and bitcoin and makes the trade’s unwind cheaper. **11.** The short future loses about $10\% \times 11/12$ of notional, USD 18.3 million of variation margin to be paid in cash, although the loss reverses if the position is held to expiry: a liquidity risk, not a loss at maturity. **12.** Capital rises to 50% of notional: the return falls to 9.9%. **13.** USD 2 million, 40% of a year’s carry at a 10% basis. **14.** The fund loses USD 60 million and the short future gains about as much, paid in variation margin; but the financier, lending USD 180 million against USD 140 million of collateral at a 10% haircut, asks for USD 54 million back at once: the gains and the calls arrive in different accounts. **15.** Margin and P&L would be in coin: the fund must buy bitcoin to post as collateral, whose dollar value moves with the price, and the trade carries the venue’s credit, liquidation and [auto-deleveraging](https://one-course.com/books/quant/3/en/chapter/18-margin-liquidation-and-loss-allocation#def-m3-margin-liquidation-and-loss-allocation-adl) rules instead of a clearing house’s. **16.** Leveraged longs who prefer futures to spot, and are willing to pay the basis for leverage without financing. **17.** Their exits coincide: when the basis collapses or financing tightens, they all sell the fund and buy back futures together. **18.** Not strictly: it is a funded carry trade with liquidity, financing and [basis risk](https://one-course.com/books/quant/3/en/chapter/1-physical-commodity-markets#def-m3-physical-commodity-markets-basisrisk) before expiry. **19.** *Named result:* 4.95% a year on notional and 14.14% on capital at a 10% basis; $-0.13\%$ at the snapshot basis of 4.92%. **20.** A regulated, financeable, dollar form of bitcoin, and with it a bridge between crypto carry and the ordinary money markets.

## 19.10 Interview questions

**Interview question 19.1 ★ trader.**

What is an [inverse option](#def-m3-dated-futures-options-and-etfs-inverse), and how do you convert its premium to dollars?

**Solution of Interview question 19.1.**

A European option on the dollar price whose premium and settlement are in the coin: premium in coin $= V/F$ with $V$ the Black dollar price on the future $F$; multiply by $F$ to convert back.

*What the interviewer is looking for: divide by the future, not the index.*

**Interview question 19.2 ★ researcher.**

How is a bitcoin reference rate constructed, and why that way?

**Solution of Interview question 19.2.**

From spot trades on a set of vetted venues over a window (an hour), split into partitions (twelve of five minutes), with a volume-weighted median per partition and an equal-weighted average of the medians: robust to single prints, representative of volume, and hard to move without trading most of it.

*What the interviewer is looking for: manipulation resistance by construction.*

**Interview question 19.3 ★★ trader.**

Why does the premium-adjusted delta of a deep in-the-money inverse call fall as it goes deeper?

**Solution of Interview question 19.3.**

Its delta in coin is the dollar delta less the coin premium. Deep in the money the dollar delta saturates at one while the coin premium keeps growing towards $1 - K/F$, so the difference falls.

*What the interviewer is looking for: premium currency, and the saturation of the dollar delta.*

**Interview question 19.4 ★★ trader, risk.**

Explain the spot ETF versus regulated-futures basis trade and its risks.

**Solution of Interview question 19.4.**

Long the fund (financed), short the regulated future: earns the basis less financing, fee and costs to expiry. Risks: variation margin if the basis widens, financing withdrawal or higher haircuts, fund discounts at unwind, benchmark mismatch at expiry, and crowded exits.

*What the interviewer is looking for: carry net of financing, and liquidity before expiry.*

**Interview question 19.5 ★★ researcher.**

How does the bitcoin volatility surface differ from an equity index surface?

**Solution of Interview question 19.5.**

Higher levels; both wings bid; a skew that can flip to calls in rallies; continuous trading with no overnight or weekend close; and premiums quoted in coin on the main crypto venue, which must be converted before comparing surfaces.

*What the interviewer is looking for: level, shape, time measure and conventions.*

**Interview question 19.6 ★★★ developer.**

Design a risk system for an options book with [inverse options](#def-m3-dated-futures-options-and-etfs-inverse) on one venue and dollar options on another.

**Solution of Interview question 19.6.**

One internal convention (dollar prices, dollar Greeks) with adapters that convert each venue’s quotes, premiums, P&L and margin; Greeks reported both in dollars and in the currency of each account (premium-adjusted for coin accounts); coin balances marked at market; scenarios that move the coin price and the volatility surface jointly; and margin projections per venue under those scenarios.

*What the interviewer is looking for: normalise conventions, keep currency explicit, and stress collateral with the book.*