Investment committee memo -- Capped Short Unit (CSU)
Generated 2026-08-20 from results/table3_prices.csv and results/table4_hedging.csv. Methodological study; not investment advice.
The answer
The CSU can be issued in 2 of 4 volatility regimes (2010 Flash Crash, Normal Market): the price is validated, the tail risk is explicitly loaded, and delta hedging keeps the issuer's mean P&L positive in every regime tested. In 2008 Crisis, COVID-19, the knock-out probability makes the listed terms unattractive to the holder; reprice with a wider buffer before issuing.
Three reasons
- The price is right (valuation). The Monte Carlo engine matches the Black-Scholes closed form within 0.5 standard errors once the Broadie-Glasserman-Kou barrier shift is applied, and the Fourier vanilla benchmark agrees to 5e-9. Every quoted price carries a standard error.
- The tail is funded (risk). The quote embeds an Expected Shortfall (99.9%) loading estimated by peaks-over-threshold GPD with bootstrap confidence intervals, so the issuer is compensated for the unhedgeable jump risk rather than exposed to it.
- The book is manageable (operations). Barrier-aware delta hedging with transaction costs produces a positive mean issuer P&L in all four volatility regimes; the suitability layer (MSI/USI, fractional Kelly, dynamic buffer) bounds position sizes ex ante.
Verdict by volatility regime
| Regime | Price (final) | KO prob. | Tail margin / price | Hedged mean P&L | Worst path | Verdict |
|---|---|---|---|---|---|---|
| 2008 Crisis | 0.2383 | 66.2% | 73% | +16.4% | -5.9% | Do not issue at listed terms |
| 2010 Flash Crash | 0.1639 | 48.2% | 70% | +11.6% | -0.6% | Issue at reduced size (alpha = 0.5) |
| COVID-19 | 0.2691 | 68.9% | 73% | +18.0% | -23.9% | Do not issue at listed terms |
| Normal Market | 0.0971 | 13.5% | 74% | +6.9% | +1.9% | Issue at full size |
- 2008 Crisis: Knock-out probability 66% means the certificate mostly expires worthless; widen the buffer or shorten the maturity before listing.
- 2010 Flash Crash: Knock-out probability 48% is elevated; the triage layer caps the allocation factor at 0.5.
- COVID-19: Knock-out probability 69% means the certificate mostly expires worthless; widen the buffer or shorten the maturity before listing.
- Normal Market: Knock-out probability 13% and tail margin 74% of price are both inside issuance limits.
What could change the answer
- Scenario parameters are volatility-regime anchors, not calibrations to live option surfaces; recalibrate before quoting real terms.
- The ES margin is a stress loading, not a market risk premium; a competitor pricing without it will look cheaper until the tail hits.
- The dynamic-barrier rule is a disclosed heuristic (paper Eq. 13), not an optimal policy; treat its output as a floor, not a target.
Email version (< 150 words)
Recommendation: proceed with CSU issuance, sized by regime. Three reasons. (1) The price is trustworthy: the Monte Carlo engine reproduces the closed-form benchmark within statistical error. (2) The tail is paid for: an Expected Shortfall loading is embedded in every quote, so extreme scenarios are funded, not hoped away. (3) The book is hedgeable: barrier-aware delta hedging produced a positive mean issuer P&L in all four regimes tested. Key evidence: knock-out probability ranges from 13% (Normal Market) to 69% (COVID-19); price per unit notional from 0.097 to 0.269. Constraint: in high knock-out regimes, list only with a wider barrier buffer. Full memo attached.
Generated from the open-source engine; methodological study, not investment advice.