RISK
Uncertainty beyond a single number
What risk measures reveal, what they hide, and how decisions change at the boundary.
Quantitative thinking · markets · systems
Quantitative Finance Through Systems Thinking.
I investigate quantitative ideas across models, markets, risk, probability, and engineering—then explain what is worth understanding and keeping.
A current question
Where duration meets uncertainty.
Long-lived commitments often meet short-lived assumptions. The resulting gap is where quantitative reasoning becomes most useful.
RISK · VALUATION · SYSTEMS
Explore writingFIGURE 01Conceptual · Illustrative
Fields of inquiry
Three questions behind the work.
Recurring lenses for the writing: how uncertainty is measured, how models enter decisions, and how market structure shapes outcomes.
MODELS
Models inside decision systems
How assumptions, controls, feedback, and validation determine whether a model is useful.
MARKETS
Structure beneath market outcomes
How incentives, constraints, probability, and engineering shape what we observe.
Visual glossary
One idea, in context.
Black–Scholes Option Pricing is the glossary's most connected concept: it links market assumptions and probability to volatility, option risk, and model validation.
Connections for Black–Scholes Option Pricing
Black–Scholes Option PricingYOU ARE HERE
Built onArbitrage and No-ArbitrageBlack–Scholes valuation rests on dynamic replication and the exclusion of arbitrage.
Built onGeometric Brownian Motion (GBM)The classical Black–Scholes model assumes GBM dynamics for the underlying asset.
Built onRisk-Neutral Measure (Intuition)Black–Scholes prices the discounted derivative payoff under risk-neutral dynamics.
Foundation ofGreeks and Risk FactorsBlack–Scholes provides the canonical analytical setting for understanding option Greeks.
Foundation ofImplied Volatility Smile and SurfaceImplied volatility is obtained by inverting a benchmark option-pricing formula such as Black–Scholes across strikes and maturities.
Extended byStochastic Volatility (Heston) and Characteristic FunctionsHeston extends the constant-volatility Black–Scholes framework by making variance stochastic.
Built on · Arbitrage and No-Arbitrage
Black–Scholes valuation rests on dynamic replication and the exclusion of arbitrage.
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About
I am Vahab.
My background spans quantitative finance and control systems engineering. I use this publication to examine ideas that sit between models, markets, and real decisions.
More about this work“Better questions lead to a deeper understanding.”
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