Goldman Sachs // Tech Adventurer NVDA Principal Protected Note
on NVIDIA (NVDA)
Pricing date: April 6, 2026 | Maturity: April 6, 2036
Client Problem, Design Logic, and the Core Answer
Design logic: a principal protected note is an accounting problem before it is an option problem. The investor's $100 must always equal the zero-coupon bond cost, the structuring fee, and the maximum fair option budget.
- Step 1: discount the $100 maturity floor to today.
- Step 2: deduct the 3.00% structuring fee.
- Step 3: spend the remaining budget on NVDA upside.
- Step 4: compare option cost and budget on the same per-$100 note basis.
Locked Inputs and Term Sheet Discipline
Locked market inputs
Why the lock matters: every number in the deck uses the same input set, so the zero-coupon bond, Black-Scholes call, Monte Carlo diagnostics, and alternatives all move together.
Primary term sheet
| Issuer | Goldman Sachs & Co. LLC |
|---|---|
| Client | Tech Adventurer |
| Underlying | NVIDIA Corporation common stock (NVDA) |
| Pricing date | April 6, 2026 |
| Maturity date | April 6, 2036 |
| Protection level | 100% principal protection at maturity |
| Coupon | None |
| Participation | 53.99% on the primary structure |
| Structuring commission | 3.00% of note proceeds |
| Settlement | Cash settlement at maturity |
| Option framework | European-style call exposure valued with Black-Scholes-Merton |
| Ranking | Unsecured senior note of Goldman Sachs |
| Calculation agent | Goldman Sachs or an affiliate |
| Adjustments | Customary market-disruption and corporate-action adjustment provisions apply |
Funding the Guarantee and Stress-Testing the Budget
Primary decomposition per $100 note
Interpretation: the option budget is not a modeling output. It is a hard constraint that falls directly out of discounting and fees.
Interactive assumption lab
Default settings match the locked paper inputs. Move rate and volatility to see how the bond cost, option cost, and fair participation change. This is a sensitivity tool, not a re-underwriting of the note.
Option Pricing, Basis Conversion, and the Fair Participation Rate
The basis-conversion control point
Why this matters: the option budget is denominated per $100 note, while Black-Scholes first prices one call on one share. Without the conversion, the participation rate would be materially wrong.
Black-Scholes inputs and outputs
| Measure | Value | Why it matters |
|---|---|---|
| d₁ | 0.986779 | Captures forward moneyness plus volatility carry. |
| d₂ | -0.331259 | Drives the risk-neutral in-the-money probability. |
| N(d₁) | 0.838124 | Appears in the discounted stock term. |
| N(d₂) | 0.370225 | Corresponds to the theoretical risk-neutral P(ST > K). |
The investor receives 53.99% of NVDA upside above the initial reference level and still redeems at par if the stock finishes flat or lower at maturity.
- Why less than 100%? High volatility and long maturity make a 10-year NVDA call expensive relative to the available budget.
- Why this is fair: the participation rate is a ratio, not a managerial choice. It is implied by the funding identity and the call premium.
- What would raise it? Higher rates, lower volatility, or a lower fee.
Proposal A: Cap Calibration
Calibration equation
Interpretation: this is not a guessed cap. It is the unique strike that makes the long-call cost minus the short-call value exactly exhaust the same budget used in the primary proposal.
- Monotone pricing function: the call price falls as strike rises, so the root-finding problem is well posed.
- Same model on both legs: the long and short calls are both priced with the same locked-input BSM framework.
- Reliable convergence: Brent's method is robust because it combines bracketing discipline with fast interpolation.
- Economic meaning: the cap is the strike where 100% upside below the cap becomes exactly affordable.
How Proposal A compares with the primary note
| Market regime | What happens | Takeaway |
|---|---|---|
| Below S₀ | The capped note still redeems at $100. | Same principal floor as the primary proposal at maturity. |
| Between S₀ and $656.64 | The investor gets dollar-for-dollar upside. | Proposal A outperforms the 53.99% primary note in moderate and strong rallies. |
| Above $656.64 | The payoff stays fixed at $369.65. | The primary note wins in extreme upside because it keeps participating beyond the cap. |
Main tradeoff: Proposal A converts a lower but uncapped slope into a full slope over a wide range, then gives up everything above the cap.
Primary vs. Capped Alternative: Scenario Checkpoints
What changes across price regions
Both structured notes redeem at $100 at maturity, while direct NVDA falls one-for-one with the stock.
The capped structure delivers 100% upside slope until the cap, while the primary note rises more gradually at 53.99% participation.
Proposal A stops at $369.65, while the primary note continues to participate in additional upside above the cap.
| Terminal NVDA price | Direct | Primary | Capped |
|---|
Read it like this: below the initial price the structured notes protect principal at maturity. Between the initial price and the cap, Proposal A has the strongest slope. Above the cap, the capped note flattens while the primary note keeps participating in further upside.
Terminal scenario explorer
Move the terminal NVDA price to compare maturity payoffs across the primary note, the capped note, and direct stock ownership. Proposal B is path-dependent, so it cannot be reduced to a single terminal price.
Read after the cap-derivation slide: once the cap is calibrated at $656.64, Proposal A dominates between S₀ and the cap, then flattens at $369.65.
Proposal B: Asian Averaging and Directional Pricing
Directional pricing logic
- State variable change: replace the single terminal stock price with the arithmetic average of the final 24 monthly closes.
- Why that matters: averaging dampens extreme last-day outcomes, so the embedded option is cheaper than a terminal-value call.
- Economics intuition: even with higher bespoke issuance economics in live market terms, the lower option cost can still support participation around 58.8%.
Rubric fit: this is the required additional proposal—client-relevant, directionally priced, and intentionally not fully component-costed, which is consistent with the assignment.
Why this structure fits this client
The client worries about an AI bubble that lifts NVDA for a long stretch and then reverses late. An Asian design targets that timing risk because the payoff depends on where the stock spends time, not only where it lands on one day.
| Client scenario | Effect on Proposal B |
|---|---|
| Bubble then late correction | The average can stay elevated even if the final print weakens, which is where this proposal is strongest. |
| Smooth steady rally | The structure still participates, but without the same simplicity as the primary note. |
| Sharp last-minute upside jump | The average lags the terminal stock price, so Proposal B can underperform the primary or capped note. |
- Pro: less dependence on one terminal trading day.
- Pro: better fit for the client's bubble-and-reversal narrative.
- Con: path dependence makes valuation, hedging, and early-redemption marks more model sensitive.
- Con: Goldman Sachs must manage realized fixing history, not just spot and volatility.
Simulation Viewer: What the Paths Show
| Time | 25% | Median | Mean | 75% | 90% |
|---|
Interpretation: this slide is about mechanics and visualization: the stock paths are simulated first, then the call and embedded-note values are derived from those same paths.
What the Paths Mean for the Client
Terminal distributions from the paper
| Series | 25% | Median | Mean | 75% | 90% |
|---|---|---|---|---|---|
| Terminal NVDA stock price | 49.61 | 118.24 | 373.51 | 299.24 | 639.07 |
| Terminal full-call payoff | 0.00 | 0.00 | 261.18 | 121.60 | 461.43 |
| Terminal embedded option payoff | 0.00 | 0.00 | 79.38 | 36.96 | 140.24 |
| Terminal total note payoff | 100.00 | 100.00 | 179.38 | 136.96 | 240.24 |
- The stock paths spread out over time because volatility compounds uncertainty over a long horizon.
- The mean rises above the median because GBM produces a right-skewed lognormal terminal distribution.
- The option and note payoffs are even more skewed because downside is floored at zero for the option and at par for the note, while upside stays open.
- For the client, the key message is economic: many paths redeem at $100, while a smaller set of favorable outcomes generates the upside tail.
- This slide is descriptive, not a pricing proof: it translates the saved 120-path sample into client-facing payoff intuition.
Validation Checks: Scaling, Consistency, and Convergence
Three-layer validation
- The 200,000-path run is a separate high-path Monte Carlo control, not the chart sample. It focuses on terminal payoff convergence rather than path visualization.
- It verifies that discounted Monte Carlo pricing converges to the analytic Black-Scholes-Merton full-call value under the same locked inputs.
- It also verifies that the note-basis scaling is correct: the simulated embedded option starts at the same $32.2092 budget implied by the analytic setup.
Bottom line: slide 10 explains the outcome distribution, while slide 11 shows that the simulation engine and the analytic pricing framework agree.
Investor Risks and Liquidity
Bottom line: the PPN removes direct downside below par at maturity, but it does not remove issuer credit risk, mark-to-market risk, or the cost of giving up yield and some upside.
Will Goldman allow early redemption?
How Goldman Hedges the Note
Primary proposal advantage: it is the most hedgeable structure because the bank manages a plain bond leg plus a standard terminal-value call exposure.
| Structure | Main hedge challenge | Implication |
|---|---|---|
| Primary note | Standard terminal-value option plus rates hedge | Cleanest day-to-day hedge and easiest risk reporting. |
| Proposal A | Short call above the cap adds tail sensitivity | Cheaper structure, but more attention to upside tail risk. |
| Proposal B | Running-average state variable changes through time | Highest model, hedge, and operational complexity. |
Why this matters for the recommendation
- More hedge complexity usually means wider live economics and more model reserve.
- The client does not need that complexity to solve the core objective of principal protection plus meaningful NVDA upside.
- That is why the primary note remains the recommended structure even though the alternatives are useful comparison points.
Final Recommendation and Why the Primary Note Still Wins
The note preserves principal at maturity, keeps the payoff transparent, and maintains meaningful NVDA upside without forcing the client into the model and hedge complexity of a bespoke path-dependent structure.
Closing sentence
The final recommendation is coherent because the client diagnosis, the pricing, the alternatives, the simulation logic, and the risk discussion all point to the same answer: use the standard principal protected note as the main proposal, then show the capped and Asian structures as targeted alternatives rather than replacements.