V7 Derivatives Errata: Forward Pricing, Parity, and Binomial Valuation

1. Module 1 — The SIXV Index Option Is Cash Settled, Not a Purchase Right

Curriculum location: Derivative Underlyings, Investor Scenarios — Scenario 1: Hightest Capital, p. 11.

"The contract is a contingent claim, which grants Hightest the right to purchase SIXV"

SIXV is the underlying index, not the option contract or a deliverable asset. Cboe's specifications identify options on its Select Sector Indexes, including options on the SIXV index, as European-style and cash settled. Exercise therefore produces a cash settlement determined from the index settlement value and the strike; it does not give the holder a right to purchase or receive the index.

Correct reading: Hightest holds a European-style, cash-settled call option on SIXV. At expiration, the contract may produce a cash payoff based on the difference between the index settlement value and the strike, rather than a purchase or delivery of SIXV.

This correction prevents candidates from carrying a physical-delivery model into index-option payoff and settlement questions.

2. Module 1 — The Clearinghouse, Not the Exchange, Provides the Guarantee

Curriculum location: Derivative Markets, Exchange-Traded Derivative (ETD) Markets, p. 15.

"This deposit is paid by each counterparty via a financial intermediary to the exchange, which then provides a guarantee against counterparty default."

The paragraph assigns the collateral-receipt and performance-guarantee roles to the trading exchange. Those are clearinghouse or central counterparty functions. A trading exchange standardizes contracts and provides the venue or system for trading; as the Bank of England explains, a clearinghouse interposes itself between clearing members and manages the financial safeguards supporting performance. Affiliated exchange and clearing entities may sit in the same corporate group, but their market functions remain distinct.

Correct reading: Customers post required margin to their financial intermediaries, while clearing members post required margin to the clearinghouse or central counterparty. The clearinghouse clears the trade, becomes the counterparty to each clearing member, and supports contract performance against participant default.

This distinction is answer-critical whenever a question asks whether an exchange or a clearinghouse stands between the parties and guarantees performance.

3. Module 2 — The Forward Seller's Settlement Direction Is Reversed

Curriculum location: Forwards, Futures, and Swaps, Forwards Question Set item 3 solution, p. 29.

"A forward seller pays $\left[F_0(T)-S_T\right]$ to the forward contract buyer at maturity"

The curriculum's own payoff table defines the seller's maturity payoff as the negative of the buyer's payoff. Its worked gold-forward example likewise has the losing buyer pay the seller. A positive value of $F_0(T)-S_T$ is therefore received by the seller; it is not paid by the seller to the buyer.

Correct reading: A forward seller receives a payoff of $F_0(T)-S_T$ at maturity. When this amount is positive, the buyer pays the seller, so the seller benefits as $S_T$ declines relative to $F_0(T)$.

This correction prevents a candidate from reversing the cash-settlement direction when moving between buyer and seller payoff formulas.

4. Module 2 — The Exercise Price Is Called a Future Spot Price

Curriculum location: Options, option definition paragraph, p. 39.

"the exercise price, a pre-agreed future spot price"

The same page uses $X$ for the exercise price and $S_T$ for the future underlying spot price. These are separate quantities: $X$ is fixed by the option contract, whereas $S_T$ is the market price observed at expiration.

Correct reading: The exercise price, or strike price, is a pre-agreed contract price. At expiration, it is compared with the then-current spot price to determine whether exercise has value.

This correction preserves the distinction needed to calculate call and put payoffs and to identify moneyness correctly.

5. Module 2 — The Practice Solution Reverses the Loss-Comparison Inequality

Curriculum location: Forward Commitments vs. Contingent Claims, Practice Problem 3 solution, p. 52.

"If $\left[F_0(T)-S_T\right]>-p_0$, then VFO's loss would be greater under the firm commitment than under the contingent claim."

The solution defines the short-forward profit as $F_0(T)-S_T$. When the put expires worthless, its profit is $-p_0$. The strategy with the greater loss must have the lower signed profit, so the printed greater-than sign supports the opposite of the sentence's conclusion.

Correct reading: The short-forward loss is greater only when $F_0(T)-S_T<-p_0$, equivalently when $S_T-F_0(T)>p_0$. The keyed answer C is unaffected because the values needed to rank the two strategies are not provided.

This correction reinforces a reusable comparison rule: compare signed profits first, and identify the greater loss as the lower profit.

6. Module 3 — Example 3 Labels a Per-Barrel WTI Price as USD per Contract

Curriculum location: Derivative Benefits, Example 3 chart, p. 59.

The chart banner states:

"NYMEX Oil Futures Price (USD per contract), January–June 2020"

The embedded chart title repeats the same unit:

"NYMEX Oil futures price (US$ per contract), January–June 2020"

Both labels assign the plotted market price to an entire contract. The same example states that one WTI futures contract represents 1,000 barrels, while the CME contract specification quotes standard WTI futures in USD per barrel. A whole-contract notional scale therefore applies the 1,000-barrel contract multiplier to the quoted price.

Correct reading: The chart's vertical price scale is USD per barrel, not USD per contract. One standard WTI futures contract represents 1,000 barrels, so a whole-contract notional scale is the per-barrel quote multiplied by 1,000.

The wrong unit can make a candidate misread the price, contract notional, or profit-and-loss sensitivity by a factor of 1,000.

7. Module 3 — The Hedge-Accounting Paragraph Assigns Mark-to-Market Changes to OCI

Curriculum location: Issuer Use of Derivatives, hedge accounting treatment paragraph, p. 69.

The curriculum states:

"Derivative mark-to-market changes are held within an equity account (Other Comprehensive Income)"

This unqualified statement follows a table covering cash flow, fair value, and net investment hedges, but those designations do not all use the same presentation. Under IFRS 9, gains and losses on a hedging instrument in a fair value hedge are generally recognized in profit or loss together with the offsetting hedged-item adjustment. For cash flow and net investment hedges, the effective portion is generally recognized in other comprehensive income, while hedge ineffectiveness is generally recognized in profit or loss.

Correct reading: Under IFRS 9, other comprehensive income is not the universal destination for derivative mark-to-market changes in hedge accounting. Fair value hedge gains and losses are generally recognized in profit or loss with the offsetting hedged-item change. The effective portions of qualifying cash flow and net investment hedges are generally recognized in other comprehensive income, while hedge ineffectiveness is generally recognized in profit or loss.

Treating other comprehensive income as the universal destination can cause candidates to misclassify the accounting effects of a fair value hedge.

8. Module 3 — The Gold Forward-or-Futures Summary Claims No Initial Cash Outlay

Curriculum location: Investor Use of Derivatives, Forward Commitments, p. 71.

The summary refers to an investor that:

"purchased a three-month gold forward or futures contract."

It then says the position increased exposure:

"with no initial cash outlay"

Yet the same Module's earlier gold-futures example on p. 61 states:

"Procam borrows the USD4,950 initial margin"

The summary incorrectly collapses forwards and futures into one funding statement. A forward commonly requires no payment at initiation, but an exchange-traded futures position requires the trader to post initial margin. That margin is collateral or a performance bond rather than a purchase-price down payment, but it remains an upfront funding and liquidity requirement. Neither instrument requires paying the full spot purchase price at inception.

Correct reading: A gold forward commonly requires no payment at initiation. A gold futures position requires an initial margin deposit, although that collateral is much smaller than the full cash-market purchase price. Neither contract requires immediate delivery of the physical asset at initiation.

The distinction matters when candidates compare upfront funding, leverage, and liquidity requirements across forward commitments.

9. Module 4 — Example 7 Reverses the Domestic and Foreign Rate Labels

Curriculum location: Cost of Carry, Example 7, p. 93.

In the euro investment leg, the text says Montau:

"invests this for 75 days at a continuously compounded $r_f=-0.25\%$:"

The South Korean won investment leg then uses the opposite label:

"South Korean won risk-free rate ($r_d=0.75\%$) for 75 days"

The example defines KRW/EUR as South Korean won per euro. Under its own notation, the won is the price/foreign currency and the euro is the base/domestic currency. The immediately preceding formula uses $F_{0,f/d}(T)=S_{0,f/d}{e}^{(r_f-r_d)T}$, so the two subscripts printed in the quoted replication legs are reversed. The prompt's $r_d=-0.25\%$ label for the euro rate is already correct. The named-currency rates, investment amounts, and displayed forward result nevertheless use the correct numerical inputs.

Correct reading: The euro investment earns $r_d=-0.25\%$, and the South Korean won investment earns $r_f=0.75\%$. The displayed 75-day investment values and $F_0(T)=1,302.67$ remain unchanged.

This distinction is exam-relevant because carrying the reversed labels into another FX quote can invert the interest-rate differential and misprice the forward.

10. Module 5 — Equation 9 Omits the Base-Currency Discount Factor

Curriculum location: Pricing and Valuation of Forward Contracts, Equation 9, p. 114.

$$V_t(T)=S_{t,f/d}-F_{0,f/d}(T)e^{-(r_f-r_d)(T-t)}$$

Curriculum location: Pricing and Valuation of Forward Contracts, Example 5 worked result, p. 115.

$$=\mathrm{USD}1,192,000-\mathrm{USD}1,201,000e^{-(0.0075+0.0025)}=\mathrm{USD}2,950.15\text{ MTM gain}$$

Let $\tau =T-t$. Applying the module's own Equation 8 at time $t$ gives $F_t(T)=S_t{e}^{(r_f-r_d)\tau }$. A long forward's current value is the replacement-forward difference discounted at the price-currency rate:

$$V_t(T)=[F_t(T)-F_0(T)]e^{-r_f\tau }=S_t{e}^{-r_d\tau }-F_0(T)e^{-r_f\tau }.$$

Equation 9 is therefore the correct current price-currency value multiplied by $e^{r_d\tau }$, not the current MTM itself. Example 5 carries that scaling error into the dollar result. The IMF's valuation guidance independently corroborates the two-leg present-value interpretation.

Correct reading: For a long forward on one unit of the base currency, quoted as price currency $f$ per base currency $d$, the price-currency value is

$$V_t(T)=S_{t,f/d}{e}^{-r_d(T-t)}-F_{0,f/d}(T)e^{-r_f(T-t)}=e^{-r_d(T-t)}\left[S_{t,f/d}-F_{0,f/d}(T)e^{-(r_f-r_d)(T-t)}\right].$$

In Example 5, $V_0(T)=1.192e^{0.0025}-1.201e^{-0.0075}=0.002957534$ USD/EUR, or USD2,957.53 for EUR1,000,000.

Using the printed expression in another FX forward can systematically misstate the mark-to-market amount whenever the base-currency rate and remaining maturity are nonzero.

11. Module 5 — Question Set Item 5 Reports a Positive Value as Rook Point's Loss

Curriculum location: Pricing and Valuation of Forward Contracts, Question Set item 5 solution, p. 117.

The solution defines the displayed MTM "from Rook Point's perspective" and then reports:

$$\begin{array}{rl}{V}_t(T)& =17.2506e^{-(0.035--0.005)\times (0.5)}-16.5\\ & =16.909-16.5\\ & =0.4090\end{array}$$

The qualitative loss conclusion is correct, but a positive signed $V_t$ defined from Rook Point's own perspective cannot represent that loss. The separate phrase "seller of ZAR/EUR" can reasonably be read as a currency-name role label, so it is not the hard-error basis. Rook Point sells ZAR and buys base-currency EUR; applying the two-leg FX forward valuation above makes its signed value negative.

Correct reading: From Rook Point's perspective, $V_t(T)=16.5e^{0.0025}-17.2506e^{-0.0175}=-0.410039$ ZAR/EUR, approximately $-0.4100$ ZAR/EUR. This is an MTM loss.

The correction prevents candidates from confusing an unsigned loss magnitude with signed MTM value or reversing the valuation formula for a long-base-currency position.

12. Module 5 — FRA Definition and Item 4 Incorrectly Fix MRR at Inception

Curriculum location: Pricing and Valuation of Interest Rate Forward Contracts, Forward Rate Agreements, p. 124.

"a market reference rate that is fixed at contract inception $(t=0)$."

The same statement reappears in the Question Set:

Curriculum location: Pricing and Valuation of Interest Rate Forward Contracts, Question Set item 4 solution, p. 127.

"at a market reference rate fixed at contract inception $(t=0)$."

The surrounding curriculum contradicts both sentences: Exhibit 9 labels the floating MRR as set at $t=A$, and the text immediately after the first sentence says it is determined on or just before settlement. It is the FRA's fixed contract rate—not the future floating reference rate—that is set at inception.

Correct reading: In the FRA structure used in this module, the fixed rate is agreed at inception $(t=0)$. The floating market reference rate for the underlying period from $A$ to $B$ is observed on or just before the settlement date $t=A$, and the cash settlement reflects the difference between those rates.

This error can make candidates treat the future floating benchmark as known at trade date and misidentify what drives FRA settlement.

13. Module 6 — Example 2 Uses an Incorrect Term in the Storage-Cost Calculation

Curriculum location: Pricing of Futures Contracts at Inception, Example 2 final result, p. 137.

= USD1,780.78 per ounce

Example 2 adds storage and insurance costs to the gold contract in Example 1. That contract has 91 days to maturity and an annual effective risk-free rate of $2\%$. Its year fraction is $91/365\approx 0.24932$, but Example 2 uses $0.24982$ in both the cost discounting and the final compounding step.

The curriculum provides a direct self-check: Example 1's price without storage costs is USD1,778.76 per ounce. Because the additional USD2 is paid at maturity, it adds exactly USD2 to the maturity price. Equation 4 gives the same result: discounting that cost and then compounding it over the same term cancel each other. Rounding the cost's present value to USD1.99 does not explain the printed USD1,780.78.

Correct reading: Use $T=91/365$ consistently. With the storage cost paid at maturity, $f_0(T)=1,770(1.02{)}^{91/365}+2=1,780.76$, or USD1,780.76 per ounce, rounded to cents.

Keeping the stated maturity throughout the cost-of-carry calculation makes the worked answer reproducible and avoids compounding with an unrelated year fraction.

14. Module 6 — Example 3 Omits Minus Signs from Both Forward MTM Results

Curriculum location: MTM Valuation: Forwards versus Futures, Example 3 beginning-of-day 2 result, p. 140.

= USD4.98 per ounce.

Curriculum location: the same example, beginning-of-day 3 result, p. 140.

= USD8.95 per ounce.

Both results follow signed valuation equations for the forward buyer. Recalculating the curriculum's displayed inputs gives

$$1,765.12-1,778.76(1.02{)}^{-0.24657}\approx -4.98,$$ $$1,761.24-1,778.76(1.02{)}^{-0.24384}\approx -\mathrm{8.95.}$$

The adjacent contract tables already show forward losses of USD498 and USD895 on the 100-ounce contract. They confirm the negative signs; they do not make the positive results correct. The equations have neither an absolute-value operator nor a label identifying their outputs as unsigned loss magnitudes.

Correct reading: The forward buyer's MTM values are −USD4.98 and −USD8.95 per ounce. Keep the tables' negative contract MTM values unchanged. These are unrealized forward losses; they are distinct from the daily cash settlement of the futures position.

Retaining the sign prevents a fall in the underlying price from being interpreted as a gain to the forward buyer, while preserving the distinction between forward value and futures cash settlement.

15. Module 7 — Example 1 and Question Set 4 Call the Swap Rate an IRR

Curriculum location: Swaps vs. Forwards, Example 1 interpretation, p. 159.

"the fixed swap rate as an internal rate of return on the implied forward rates"

Curriculum location: Swaps vs. Forwards, Interest Rate Swaps vs. Forward Contracts Question Set, item 4 solution, p. 163.

"False. The fixed swap rate is the internal rate of return on the implied forward rates over the life of an interest rate swap."

The narrative introduces the IRR comparison as an analogy, but the solution on p. 163 repeats it as an unqualified definition. The calculation on p. 159 holds the zero-rate discount factors fixed and solves for the fixed payment rate. It therefore calculates a par coupon, not an internal rate of return. In the annual-payment example, rearranging the displayed three-period equation gives

$$s_3=\frac{D_1{\mathrm{IFR}}_{0,1}+D_2{\mathrm{IFR}}_{1,1}+D_3{\mathrm{IFR}}_{2,1}}{D_1+D_2+D_3},D_i=(1+z_i{)}^{-i}.$$

An IRR instead solves for a single discount rate that equates a specified cash-flow stream with its present value. That is a different calculation from solving for the fixed payment rate with the discount factors held fixed. The printed swap rate of $3.9641\%$ is correct; the error is the IRR interpretation, repeated as the justification in the question-set solution.

Correct reading: The fixed swap rate equates the present values of the fixed and expected floating payments. For the annual-payment example, it is the discount-factor-weighted average of the implied forward rates. Keep the calculated $3.9641\%$. Question Set item 4 remains False, but its justification should describe this weighted-average par rate rather than an IRR of the implied forward rates.

To reproduce a par swap rate, equate the discounted cash-flow legs; entering the forward-rate sequence into an IRR calculation solves a different problem.

16. Module 8 — Exhibit 5 Reverses the Short Put's Payoff Subtraction

Curriculum location: Replication, Exhibit 5, lower-state box, p. 188. The stated condition is $S_T<X$.

$-p_T=(X-S_T)<0$

The condition makes $X-S_T$ positive, so the displayed equality cannot represent a negative short-put payoff. The exhibit itself supplies the correction: its short-put payoff graph is negative below strike, and the adjacent long-forward expression is $S_T-F_0(T)<0$, with $X=F_0(T)$.

For example, with strike $X=100$ and terminal spot $S_T=90$, the put holder receives $10$ and the writer's payoff is $-10$. The printed middle expression instead produces $+10$. This comparison concerns payoff; the premium received is accounted for separately when calculating the writer's profit.

Correct reading: When $S_T<X$, the short put's payoff is $-p_T=-(X-S_T)=S_T-X<0$. It equals the long forward's payoff in this state when $X=F_0(T)$.

This correction prevents reversing the writer's terminal cash flow in payoff and replication calculations.

17. Module 8 — The Exercise-Price Discussion Treats Strike as a Call Payoff Floor

Curriculum location: Factors Affecting Option Value, Exercise Price, p. 191.

"For a call option representing the right to buy the underlying, the exercise price represents a lower bound on the option's exercise value at maturity, leading to a higher option value for a lower exercise price."

Curriculum location: Factors That Affect Option Value, Question Set 1 solution, p. 194.

"For a call option representing the right to buy the underlying, the exercise price represents a lower bound on an option's exercise value at maturity, leading to a higher option value for a lower exercise price."

The next sentence on p. 191 gives the correct call payoff, $\max (0,S_T-X)$, whose lower bound is zero. With $X=100$ and $S_T=105$, the payoff is $5$, well below the strike. If the option expires out of the money, its payoff is zero.

Strike is a threshold for the underlying price at which exercise produces a positive payoff. It is not a minimum amount the call holder receives. The paragraph's conclusion that a lower strike raises call value is correct; the asserted payoff bound is wrong. Question Set 1 reinforces the mistake by asking candidates to supply “lower” for that bound.

Correct reading: A call has a positive payoff when $S_T>X$, and its payoff is $\max (0,S_T-X)$ with a lower bound of zero. A lower strike raises the payoff in exercised states and expands the set of states with a positive payoff. The lower-strike/higher-call-value conclusion remains unchanged; the question's payoff-bound premise must be replaced by this exercise-threshold distinction.

This correction keeps an exercise trigger separate from a guaranteed cash-flow floor when interpreting option bounds or answering the embedded question.

18. Module 9 — The Forward Replication Descriptions Fix the Financing Direction

Curriculum location: Learning Module Overview, p. 202.

"Under put–call forward parity, we may demonstrate that a purchased put option and a sold call option are equivalent to a long risk-free bond and short forward position, and a sold put and purchased call are equivalent to a long forward and short risk-free bond."

Repeated in Put–Call Forward Parity, paragraph preceding Equation 5, p. 212.

"If we rearrange these terms, we can demonstrate that a long put and a short call are equivalent to a long risk-free bond and short forward position:"

Equation 5 correctly states $p_0-c_0=[X-F_0(T)](1+r{)}^{-T}$. Exhibit 7 gives a long forward's terminal payoff as $S_T-F_0(T)$; reversing that position gives $F_0(T)-S_T$ for a short forward, so matching the option payoff $X-S_T$ requires an additional cash payoff of $X-F_0(T)$. That amount need not be positive. In the immediately following Example 4, $X=265$ and the displayed forward price is $300.84$: the cash leg requires repayment of $35.84$, hence borrowing. The displayed pricing equation and the example's calculation using its rounded forward price remain valid.

Correct reading: A long put and a short call equal a short forward plus a cash position paying $X-F_0(T)$ at expiration. Lend when this amount is positive, borrow when it is negative, and omit the cash leg when it is zero. Equation 5 and Example 4's calculation using its rounded forward price remain unchanged. Reversing both option positions gives a long forward plus a cash position paying $F_0(T)-X$; this is not necessarily borrowing.

The sign of the financing position matters when converting the pricing equation into an executable portfolio.

19. Module 9 — Exhibit 3 Uses Covered-Call Payoffs to Illustrate a Protective Put

Curriculum location: Put–Call Parity, Exhibit 3 and its preceding paragraph, p. 205.

The September 2026 official errata notice directs candidates to swap the labels of Exhibits 1 and 3 on pp. 204–205. In the printed version reviewed here, the figure labeled Exhibit 3 is the figure described below.

"The payoff for Portfolio 2 at time $T$ is shown in Exhibit 3."

Exhibit 4 on p. 206 gives the protective put a payoff of $X$ below the strike and $S_T$ above it. Exhibit 3 instead shows a sold call plus the underlying, and a sold put plus a bond: both are covered-call constructions, paying $\min (S_T,X)$. Their upside is capped and their downside is exposed. They cannot illustrate the protective put described in the preceding paragraph or establish the claimed equivalence with the fiduciary call.

Correct reading: A protective put holds the underlying and buys a put, producing $S_T+\max (X-S_T,0)=\max (S_T,X)$. Its payoff is $X$ below the strike and $S_T$ above the strike.

Using the printed diagram as a protective-put template reverses which side of the payoff is protected.

20. Module 9 — The Shareholder Replication Omits Repayment of Debt

Curriculum location: Firm Value as a Put–Call Parity Application, Shareholder replication, p. 215.

"Note that the shareholder's combination of a purchased put option and a long position in the firm's assets is equivalent to a call option on the firm's assets."

The curriculum correctly gives shareholder payoff as $\max (0,V_T-D)$ on p. 214. But the two positions named here pay $V_T+\max (D-V_T,0)=\max (V_T,D)$, exceeding equity payoff by $D$ in every state. The debt repayment must be included. Equation 6 on p. 215 confirms the same missing leg when rearranged as $c_0=V_0+p_0-\mathrm{PV}(D)$. The preceding discussion of residual equity explains the intended result but does not make the explicit two-position equivalence true.

Correct reading: Equity is replicated by long firm assets, a long put with exercise price $D$, and a short risk-free bond paying $D$ at maturity: $V_T+\max (D-V_T,0)-D=\max (V_T-D,0)$.

Keeping the debt repayment prevents confusing insured gross assets with the shareholders' residual claim.

21. Module 9 — Question Set 2 Omits the Funding Bond from Match 2–C

Curriculum location: Firm Value as a Put–Call Parity Application, Put–Call Forward Parity and Option Applications, Question Set 2, match 2–C, p. 216.

"2. C is correct. A long risk-free bond position is equivalent to a long forward purchase, a short call option, and a long put option."

The question explicitly identifies position 2 as a bond worth $X(1+r{)}^{-T}$, paying $X$ at maturity. Using Exhibit 7's standard forward payoff, portfolio C instead pays $[S_T-F_0(T)]-\max (S_T-X,0)+\max (X-S_T,0)=X-F_0(T)$. Its payoff is short by $F_0(T)$. Treating the forward as already funded conflicts with Exhibit 7, which lists the zero-cost forward and its funding bond separately.

Correct reading: To replicate the specified bond paying $X$, add a long risk-free bond paying $F_0(T)$ to portfolio C. The completed portfolio is long forward, long funding bond, short call, and long put.

A constant payoff is not enough to establish equivalence: its amount must match the bond being replicated.

22. Module 9 — Question Set 3 Specifies the Wrong Bond Amount

Curriculum location: Firm Value as a Put–Call Parity Application, Put–Call Forward Parity and Option Applications, Question Set 3 solution, p. 216.

"A synthetic protective put is the combination of a synthetic underlying position (using a forward purchase and a long risk-free bond position equal to the exercise price) and a purchased put."

The subsequent solution correctly says that the bond pays $F_0(T)$ and that the forward pays $S_T-F_0(T)$. This matches Exhibits 7–8. A bond paying the option exercise price $X$, as specified in the opening sentence, would instead produce total portfolio payoff $\max (S_T,X)+X-F_0(T)$. The setup is wrong; the later cash-flow equations and their protective-put payoffs are correct.

Correct reading: The funding bond must pay the forward delivery price $F_0(T)$ at expiration. Retain the subsequent solution: the synthetic protective put pays $X$ when the put is exercised and $S_T$ otherwise.

Following the corrected setup lets a candidate construct the portfolio that actually produces the printed solution.

23. Module 10 — Equation 8's Worked Check Substitutes 50% for 5%

Curriculum location: Pricing a European Call Option, numerical confirmation following Equation 8, p. 230.

$V_1$ = €12 = €11.43 (1 + 0.5)

The same page states a risk-free rate of $5\%$ and correctly uses $1.05$ to obtain the initial hedged-portfolio value. The confirmation then substitutes $0.5$, or $50\%$: its right-hand side equals €17.145, not €12. This is an error in the worked check; the preceding call price of €4.57 remains correct.

Correct reading: Use $0.05$ for the stated $5\%$ rate, which gives $V_1=11.43\times 1.05\approx 12.00$ in euros. Using the unrounded initial portfolio value makes the equality exact. The call price remains €4.57.

The correction lets candidates reproduce the risk-free return check with the same rate used to price the option.

24. Module 10 — Question 5 Switches the Sign of Its Defined Put Hedge Ratio

Curriculum location: Pricing a European Call Option, Binomial Valuation of Options, Question 5(b), p. 233.

$$V_1=V_1^u=h^{\ast }{S}_1^u+p_1^u=0.75\times \pounds 22+\pounds 0=\pounds 16.50.$$

Curriculum location: the same Question 5(b), p. 234.

$$V_1=V_1^d=h^{\ast }{S}_1^d+p_1^d=0.75\times \pounds 18+\pounds 3.00=\pounds 16.50.$$

Curriculum location: the same Question 5(c), p. 234.

$$p_0=V_0-h^{\ast }{S}_0-=\pounds 16.18-0.75\times \pounds 20=\pounds 16.18-\pounds 15=\pounds 1.18.$$

Part (a) explicitly calculates $h^{\ast }=-0.75$. The quoted formulas then substitute $+0.75$ for that same symbol. Literal substitution of the defined negative value into the two terminal portfolio formulas gives $-\pounds 16.50$ and $-\pounds 10.50$, which are unequal. The text's instruction to buy the put and $0.75$ shares is correct, as are its numerical portfolio values and final put price. The stock holding that offsets a long put is $-h^{\ast }$, rather than the signed option hedge ratio itself.

Correct reading: Retain $h^{\ast }=-0.75$ and hold $-h^{\ast }=0.75$ shares with one long put. Then $V_1^u=-h^{\ast }{S}_1^u+p_1^u=\pounds 16.50$ and $V_1^d=-h^{\ast }{S}_1^d+p_1^d=\pounds 16.50$. At inception, $p_0=V_0+h^{\ast }{S}_0\approx \pounds 16.18-\pounds 15=\pounds 1.18$. The numerical answer remains unchanged.

Distinguishing the signed hedge ratio from the offsetting stock position prevents candidates from constructing a portfolio that retains risk or copying the wrong sign into the put-price formula.

25. Module 10 — The Risk-Neutral Probability Definition Equates Stock Values to an Option Price

Curriculum location: Risk Neutrality, definition immediately before Equation 10, p. 234.

"The risk-neutral probability ($\pi$) is the computed probability used in binomial option pricing by which the discounted weighted sum of expected values of the underlying, $S_1^u=R^u{S}_0$ and $S_1^d=R^d{S}_0$, equal the current option price."

The definition explicitly averages the underlying's terminal prices. Equation 10 implies $\pi R^u+(1-\pi )R^d=1+r$, so discounting that average gives the current underlying price, $S_0$. Equation 9 instead averages the option payoffs to obtain $c_0$. The two calculations price different assets: in the module's example, they give €80 and approximately €4.57, respectively.

Correct reading: Risk-neutral probabilities make the discounted expected terminal value of the underlying equal its current price. To obtain an option price, apply those probabilities to the option's terminal payoffs and discount the resulting expectation at the risk-free rate.

This distinction prevents substituting stock prices for option payoffs in a risk-neutral valuation.

Complete Derivatives Errata Index

Scope: Modules 1–10, pp. 3–242 (printed page numbers).

Reviewed modules. Module 1, pp. 3–22; Module 2, pp. 23–52; Module 3, pp. 53–76; Module 4, pp. 77–102; Module 5, pp. 103–127, excluding the Practice Problems and solutions on pp. 128–132; Module 6, pp. 136–149, excluding the end-of-module Practice Problems and solutions; Module 7, pp. 153–174; Module 8, pp. 175–200; Module 9, pp. 201–221; and Module 10, pp. 225–242, excluding the introductory self-assessment and glossary.

What this review covers. Errors in the printed curriculum that would change a candidate's answer or understanding: wrong numbers, wrong formulas, reversed logic, and statements that contradict the volume's own data. It does not list spelling mistakes, equation-numbering slips, or wording that is loose but defensible. CFA Institute's September 2026 official 2027 Level I errata notice was checked on 5 September 2026; unless a section states otherwise, the issues below were identified independently.

The table lists every high-value, objectively established curriculum error admitted for these modules. Extraction or import-fidelity problems, question errors not printed in the curriculum, disputed readings, and low-value editorial issues are outside the public errata scope.

References

• CFA Institute — 2027 Level I Curriculum Errata Notice, September 2026
• Cboe — Select Sector Index Options Fact Sheet
• U.S. Commodity Futures Trading Commission — The Economic Purpose of Futures Contracts
• Bank of England — The Bank's Approach to Financial Market Infrastructure Supervision
• CFTC and SEC — Further Definition of “Swap” and Related Terms, Forward Rate Agreements
• Investor.gov — An Introduction to Options
• CME Group — Light Sweet Crude Oil (WTI) Futures Fact Card
• IFRS Foundation — IFRS 9 Financial Instruments, paragraphs 6.5.8, 6.5.11, and 6.5.13
• U.S. Commodity Futures Trading Commission — Economic Purpose of Futures Markets and How They Work
• Bank for International Settlements — Covered interest parity lost
• International Monetary Fund — Monetary and Financial Statistics Manual and Compilation Guide
• CFA Institute — Pricing and Valuation of Futures Contracts refresher reading
• Microsoft Support — IRR function and its relationship to net present value
• Options Industry Council — Naked Put (Uncovered Put, Short Put)
• Options Industry Council — Options Pricing
• CME Group — Put-Call Parity
• Aswath Damodaran, NYU Stern — Option Pricing Applications in Equity Valuation
• Durham University, Mathematical Finance — The one-period binomial model, Sections 2.3–2.5

This article is an independent candidate-focused analysis of errors identified in the CFA Level I 2027 Curriculum, Volume 7 Derivatives, Modules 1–10. It is not an official CFA Institute errata notice, and inclusion here must not be read as CFA Institute confirmation, endorsement, or approval.