Scene 4 — Optionality, numerics, and calibration fights

1) Start from the control problem, not the product label

Lukas: “Storage first.”

He writes:

• State: inventory $I_t$

• Decision: inject / withdraw / hold each period

• Constraints:

  • $0 \le I_t \le I_{\max}$
  • $0 \le \mathrm{inj}_t \le \mathrm{inj}_{\max}(I_t)$
  • $0 \le \mathrm{wd}_t \le \mathrm{wd}_{\max}(I_t)$
  • plus costs: fuel, losses, tariffs

Lukas: “Swing is similar, but the contract wraps the flexibility differently.”

He adds a second list:

• State: cumulative take $Q_t$, plus sometimes a local counter (week / month)

• Decision: daily nomination $q_t$

• Constraints:

  • daily min/max $q_{\min} \le q_t \le q_{\max}$
  • global min/max over life $Q_{\min} \le \sum_t q_t \le Q_{\max}$
  • sometimes penalties for deviating from a profile

Then hydro:

• State: reservoir level $R_t$
• Decision: generate vs store (and spill if forced)
• Dynamics: $R_{t+1} = R_t + \mathrm{inflow}_t - \mathrm{gen}_t - \mathrm{spill}_t$
• Constraints: capacity, turbine limits, environmental flows

Anna looks at the board and smiles once.

Anna: “So not Black-76 then.”

Lukas: “Definitely not.”

He underlines Decision.

Lukas: “These are stochastic control problems. The value comes from choosing well over time. Which means two things you care about: the policy can change abruptly, and the exposures can be regime-dependent.”

Anna points.

Anna: “That’s the thing the risk pack never admits. It prints a delta as if it’s a bond.”

2) Numerics: why the method matters and where it breaks

Lukas draws a triangle and labels the corners:

Accuracy — Speed — Stability

Lukas: “You asked whether trees, PDE, or Monte Carlo choice matters to you. It matters because it determines which corner you sacrifice.”

He writes three short rows:

• Trees/lattices: good intuition, early exercise OK, but state space blows up
• PDE: accurate in low dimension, but impractical with many factors and constraints
• Monte Carlo + regression (LSMC): handles many factors and constraints, but Greeks can be noisy

Anna interrupts with the desk question.

Anna: “Give me the failure modes in plain language.”

Lukas nods. He writes four headings.

3) The calibration fight: what is being calibrated, and to what?

Anna crosses her arms.

Anna: “Now calibration. This is where I lose patience. You calibrate something Friday night, and Monday morning my marks move. Explain your philosophy.”

Lukas does not defend the current setup. He frames the contract between desk and quant.

Lukas: “Calibration is a promise. It says: given this market snapshot, this model reproduces these reference instruments. If we don’t agree on the reference set and stability rules, calibration becomes a source of PnL.”

He draws two layers:

Layer 1 — Vanilla calibration (market-traded anchors) Layer 2 — Structured valuation (policy-driven instruments)

Lukas: “Layer 1: we calibrate to instruments the market actually trades and quotes in a consistent way. Vanilla options on forwards, sometimes spread options where we have robust quotes. Objective is: fit market implied vols with weights, enforce no-arbitrage, keep parameters stable.”

Anna: “So vanillas anchor the dynamics.”

Lukas: “Yes. Layer 2: we feed that into the structured engine to value storage, swing, hydro. But here is the uncomfortable truth: structured deals often have no unique calibration. Two models can fit vanillas equally well and give you different storage values.”

Anna’s eyes narrow.

Anna: “So which one is right?”

Lukas answers like someone who has sat through model risk committees.

Lukas: “Neither is right. We choose a model class and then control it with governance: stability, backtesting on realised optionality, and consistency with desk marks on a fixed reference pack.”

Anna taps her notebook.

Anna: “That’s what I want in writing: what is fixed, what can move, and how we detect when the engine moved.”

4) What gets versioned, and what gets reported

Lukas writes three IDs on the board:

• Snapshot ID: curves + vols + fixings + build config
• Model ID: code version + parameters + constraints config
• Run ID: trade set + snapshot + model + valuation settings

Lukas: “If you only remember one thing: every number we hand you needs a run ID. Otherwise we cannot explain Monday.”

Anna points at constraints config.

Anna: “That’s important. For storage: injection curves, fuel, losses. For hydro: inflow scenario set. Those are inputs, not model. But they move the mark.”

Lukas: “Exactly. That’s why we treat them as artefacts. And we log them.”

He adds, without embellishment:

• calibration fit metrics (RMSE, weighted errors)
• parameter time series monitors
• regression diagnostics for LSMC (exercise frequency stability, out-of-sample checks)
• numerical settings (time grid, paths, seed, basis)

Anna looks at him.

Anna: “And you show me what changed.”

Lukas: “Yes. A diff.”

5) The desk acceptance criteria: when do you trust the numbers?

Anna writes her own list on the board.

Anna: “My acceptance criteria are simple.”

1. Marks do not jump day-to-day without a market reason or a clearly stated model reason.
2. Greeks are directionally sane and stable enough to hedge.
3. Explain residual is explainable: data vs model vs mapping vs lifecycle.
4. I know the limits: when linear explain and VaR break, and which scenario ladder to use instead.

Lukas nods.

Lukas: “Agreed. And we can formalise this into two outputs you get daily.”

He writes:

• Stability card: what changed (snapshot/model/run diffs, expected impact)
• Trust signals: how reliable are today’s Greeks (noise indicators, boundary proximity, calibration drift)

Anna looks at the clock. 15:45.

Anna: “Good. Now connect this to what risk asked Friday: why VaR missed it.”

Lukas answers without hedging.

Lukas: “Because their VaR and explain assumed local linearity. Your book is policy-driven and non-linear. When the optimal policy regime shifts, the PnL distribution has jumps. A percentile based on linear shocks will miss regime change risk.”

Anna nods.

Anna: “That is the truth. Now we need it to be acceptable.”

Lukas picks up the marker again.

Lukas: “Then Scene 5 is: how we present risk for optionality books. Not just VaR. A scenario ladder, regime shifts, and a stress narrative that maps to hedgeable actions.”

Anna caps the meeting.

Anna: “Do that. And also: no more silent releases.”

Lukas does not argue.

Lukas: “Agreed. We’ll put a pre-release impact run against your reference pack. If it moves your mark by more than a tolerance, it gets flagged before it hits production.”

Anna stands up.

Anna: “That’s what I needed to hear.”