Companion demonstrator · open-source pricing engine

CSU Lab — what goes into the price of a Capped Short Unit

É. Lansiaux, Capped Short Units: Pricing, Hedging, and Tail-Risk Loading of Up-and-Out Put Certificates under Stochastic Volatility with Jumps (2026)  ·  Code & manuscript Preprint (SSRN)

Bates SVJ parameters anchored to the realised volatility regime — a stress input, not a market calibration.

Knock-out barrier at K·(1+δ). Monte Carlo grid, linear interpolation in δ.

Margin = ξ · ES99.9% of the issuer's unhedged P&L (POT/GPD estimate). Linear in ξ, so it recomputes exactly in your browser.

2008 crisis · 30-day CSU

Per unit of notional K. Standard error shown where the estimate is Monte Carlo.

Price decomposition — the number a buyer should be shown

0.2383 offered price P₀ = risk-neutral value + tail margin
In stressed regimes the tail margin dominates the risk-neutral value: the offered price is the cost of writing gap risk, and a retail buyer should see both parts.

Knock-out probability

66.2%

Risk-neutral value (SE)

0.0655 (1.5e-4)

Max holder loss

P₀ (premium)

Payoff at maturity versus ST/K (blue), provided the running maximum never touched the barrier (ochre line at 1+δ): touching it anywhere before maturity knocks the certificate out to zero.

How the numbers are produced. Stress-scenario values are precomputed with the open-source engine of the paper: Bates (1996) dynamics simulated by full-truncation Euler with exact compound-Poisson jumps; discrete-barrier bias removed by the Broadie–Glasserman–Kou shift; variance reduced 67–99% by an exact Fourier control variate; the tail margin uses an Expected Shortfall estimated by peaks-over-threshold (generalised Pareto). The closed-form tab evaluates Proposition 2 of the paper exactly in your browser. Every figure is reproducible from the repository (python scripts/run_experiments.py).

Academic demonstrator
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