Methodology

Pricing intelligence built for a complex instrument.

Taiwan convertible bonds sit at the intersection of fixed income, equity derivatives, and market microstructure. Pricing them for auction participation demands more than a single model — it requires a layered architecture that separates what is mathematically knowable from what must be learned from market behavior.

Why standard models fall short.

A convertible bond is not simply a bond, nor simply an equity option. Its value shifts character continuously — behaving like a fixed-income instrument when the underlying stock is far below the conversion price, and like an equity derivative when it trades above it.

Taiwan's CB market adds further structural complexity: mandatory soft-call triggers, investor put provisions, and concentrated auction dynamics that create systematic behavioral patterns undetectable by purely theoretical models. A model that conflates the mathematics of the instrument with the psychology of the auction will consistently misprice both.

The Moneyness Spectrum

Out-of-Money

Bond floor anchors value. Credit quality and interest rate sensitivity dominate.

At-the-Money

Both components material. Volatility, regime, and behavioral dynamics converge.

In-the-Money

Equity proxy. Conversion premium, dilution, and momentum drive price action.

Bond Floor

Embedded Option

= CB Price

Architecture

Four layers. One price distribution.

Each layer has a distinct role. The output of one becomes the input to the next, progressively refining a raw theoretical value into an actionable confidence interval.

Theoretical Pricing

The Physics

A rigorous mathematical model computes the instrument's fair value from first principles — incorporating the bond's cash flow schedule, the embedded conversion option, and Taiwan-specific structural provisions including soft-call barriers and investor put rights. This layer answers a single question: what should this bond be worth?

Output

P_theoretical

Market Regime Classification

The Context

Auction behavior is not stationary. The same bond issued in a risk-on rally will clear at a materially different premium than in a corrective macro environment. A probabilistic regime model continuously monitors Taiwan equity market signals to classify the current macro state — calibrating how aggressively or conservatively downstream behavioral models should shade their estimates.

Output

Regime
Probabilities

Behavioral Ensemble

The Behavior

The core ML layer. Rather than predicting absolute price — which would require learning both the instrument mathematics and market psychology simultaneously — the ensemble is trained exclusively on the residual: the systematic gap between theoretical value and where auctions actually clear. Multiple model architectures contribute complementary signal, with each trained using quantile loss to produce calibrated probability bounds rather than a single point estimate.

Output

Δ Residual
P10 / P50 / P90

Meta-Consensus

The Output

A final integration layer learns the optimal weighting of signals from all upstream models, minimizing out-of-sample prediction error. It combines the theoretical base price with the ensemble's behavioral residual predictions to produce the final actionable output: a calibrated three-point distribution.

Output

P10 · P50 · P90

Output: Price Distribution

P10

Bargain Floor — statistically unlikely to clear below this level

P50

Fair Value Target — model's best estimate of the market-clearing price

P90

Walk-Away Ceiling — bids above this level carry elevated overpayment risk

Confidence bounds, not false precision.

Expressing auction price predictions as a single number is epistemically dishonest. Taiwan CB auctions are influenced by factors that no model can fully observe — undisclosed institutional order flow, intraday sentiment shifts, and idiosyncratic issuer relationships.

The ConvexMarkets engine outputs a calibrated three-point distribution. The P50 represents the model's best estimate of where an auction will clear. The P10 and P90 define actionable boundaries — a statistically derived floor below which bids are unlikely to be filled, and a ceiling above which overpayment risk rises sharply.

The width of the interval itself carries information: tight bands indicate high model confidence; wide bands flag instruments where behavioral uncertainty dominates and manual review is warranted.

Infrastructure

Built for institutional speed.

Compute

Edge-Native Execution

The pricing engine runs entirely at the edge — no round-trip to a central server. Compute-intensive valuation routines are compiled to WebAssembly for near-native execution speed within sub-5ms response budgets.

Data

7+ Years of Auction Records

Behavioral models are trained on a curated archive of Taiwan CB auction outcomes spanning multiple market cycles, regimes, and issuer cohorts — providing the statistical depth required to generalize beyond recent history.

Deployment

ONNX Model Inference

ML models are exported to the open ONNX interchange format and deployed for low-latency inference at the network edge — decoupling the training environment from the production serving stack.

See the engine in action.

The Auction Workbench puts the full pricing stack at your fingertips — adjust inputs, stress-test assumptions, and inspect the full P10/P50/P90 output distribution in real time.

Open Workbench Request a Demo