Quantitative Finance · Derivatives · Volatility · Risk

From research papers to reproducible quantitative tools.

Research-driven quantitative tools for derivatives pricing, volatility analytics, tail risk, and actuarial finance.

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100+research publications

4core technology tracks

2013–2026continuous research program

Core capabilities

One research platform, four connected technology tracks.

Organized around institutional workflows rather than individual papers.

Option Surface & Implied Risk

Arbitrage-aware smoothing, implied-volatility inversion, risk-neutral density and option-implied quantiles.

Learn more → 02

Derivative Pricing & Risk Engine

CTMC, transform and semi-analytical methods for vanilla, barrier, Asian, American and volatility-linked contracts.

Learn more → 03

Equity–Volatility Joint Calibration

Joint SPX/VIX market calibration using implied-tree and stochastic-volatility research.

Learn more → 04

Insurance & Annuity Analytics

Variable annuity pricing, VIX-linked fees, long-term-care riders and risk measures.

Learn more →

Built for transparent validation

Every result should come with the assumptions that produced it.

The goal is not a black-box product page. Each example should expose inputs, model scope, numerical settings, benchmark error, runtime and failure states.

See the validation template →

example.py

from cuiquant import SurfaceAnalyzer

model = SurfaceAnalyzer(
  asset="equity",
  exercise="american"
)

result = model.fit(option_chain)

print(result.diagnostics)
# arbitrage_residual
# quote_adjustment
# convergence_status
# runtime_ms

Research examples

Start with hard, falsifiable questions.

All examples

SURFACE

Can sparse American quotes form a consistent surface?

Compare raw and adjusted quotes, constraint residuals and bid-ask deviations.

IMPLIED RISK

What downside distribution is embedded in option prices?

Recover risk-neutral density, CDF and quantiles with explicit coverage diagnostics.

PRICING

Why does barrier monitoring frequency change value?

Separate contract differences from numerical error using benchmarked comparisons.

Academic foundation

Research depth across derivatives, volatility, stochastic simulation and actuarial finance.

Professor Zhenyu Cui is an Associate Professor of Financial Engineering at Stevens Institute of Technology, with a research program spanning derivatives pricing, volatility modeling, computational finance and insurance.

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