# Black-Scholes-Merton Framework ⎊ Area ⎊ Greeks.live --- ## What is the Framework of Black-Scholes-Merton Framework? The Black-Scholes-Merton framework provides a foundational mathematical model for pricing European-style options, establishing a theoretical value based on five key inputs. This model, originally developed for traditional equities, assumes a specific stochastic process for the underlying asset price, enabling the calculation of a fair premium. Its core principle relies on constructing a risk-free portfolio by continuously adjusting a hedge position, thereby eliminating market risk. ## What is the Assumption of Black-Scholes-Merton Framework? A critical assumption of the Black-Scholes-Merton model is the log-normal distribution of asset returns, implying that price movements are continuous and follow a random walk. The framework also assumes constant volatility and interest rates over the option's life, alongside the ability to execute continuous, frictionless hedging. These assumptions create a theoretical environment where arbitrage opportunities are absent, allowing for a single, definitive option price. ## What is the Application of Black-Scholes-Merton Framework? In the cryptocurrency derivatives market, the Black-Scholes-Merton framework serves as a benchmark for pricing, despite significant deviations from its core assumptions. Traders and quantitative analysts often adapt the model by incorporating empirical adjustments, such as using implied volatility surfaces to account for the volatility skew observed in crypto options. While the model's theoretical perfection is compromised by market microstructure factors like high transaction costs and discontinuous trading, it remains a vital tool for risk management and delta hedging strategies. --- ## [Greeks Sensitivity Measures](https://term.greeks.live/term/greeks-sensitivity-measures/) Meaning ⎊ Sensitivity measures provide the quantitative framework for managing risk and hedging directional exposure within decentralized crypto derivatives. ⎊ Term ## [Capital Cost Modeling](https://term.greeks.live/term/capital-cost-modeling/) Meaning ⎊ Capital Cost Modeling establishes the mathematical baseline for pricing risk and liquidity in decentralized derivative markets. ⎊ Term ## [Volatility Index Modeling](https://term.greeks.live/term/volatility-index-modeling/) Meaning ⎊ Volatility Index Modeling quantifies market-implied risk to automate margin requirements and enable pure volatility trading in decentralized markets. ⎊ Term ## [Option Valuation Model Comparisons](https://term.greeks.live/term/option-valuation-model-comparisons/) Meaning ⎊ Option valuation models provide the mathematical foundation for pricing risk and ensuring solvency within decentralized derivative markets. ⎊ Term ## [Option Sensitivity Measures](https://term.greeks.live/term/option-sensitivity-measures/) Meaning ⎊ Option sensitivity measures quantify non-linear risk, enabling precise hedging and systemic stability in decentralized derivative markets. ⎊ Term ## [Asset Price Modeling](https://term.greeks.live/term/asset-price-modeling/) Meaning ⎊ Asset Price Modeling establishes the quantitative framework for valuing decentralized derivatives and maintaining systemic stability in volatile markets. ⎊ Term ## [Volatility Arbitrage Risk Modeling](https://term.greeks.live/term/volatility-arbitrage-risk-modeling/) Meaning ⎊ Volatility Arbitrage Risk Modeling quantifies pricing gaps between implied and realized volatility to stabilize decentralized derivative strategies. ⎊ Term ## [Gamma Exposure Monitoring](https://term.greeks.live/term/gamma-exposure-monitoring/) Meaning ⎊ Gamma Exposure Monitoring quantifies dealer hedging requirements to predict structural market volatility and identify critical liquidity thresholds. ⎊ Term ## [Greeks Analysis Derivatives](https://term.greeks.live/term/greeks-analysis-derivatives/) Meaning ⎊ Greeks Analysis Derivatives provide the mathematical framework required to quantify and manage risk sensitivities within decentralized financial systems. ⎊ Term ## [Quantitative Modeling Applications](https://term.greeks.live/term/quantitative-modeling-applications/) Meaning ⎊ Quantitative modeling transforms market uncertainty into precise risk metrics, enabling the structural integrity of decentralized derivative markets. ⎊ Term ## [Risk-Adjusted Return Optimization](https://term.greeks.live/term/risk-adjusted-return-optimization/) Meaning ⎊ Risk-Adjusted Return Optimization enables the precise calibration of derivative positions to maximize capital efficiency within decentralized markets. ⎊ Term ## [Probabilistic Modeling](https://term.greeks.live/term/probabilistic-modeling/) Meaning ⎊ Probabilistic modeling provides the mathematical foundation for quantifying uncertainty and managing risk in volatile decentralized derivative markets. ⎊ Term ## [Rho Calculation](https://term.greeks.live/term/rho-calculation/) Meaning ⎊ Rho Calculation quantifies an option premium's sensitivity to interest rate fluctuations, vital for risk management in decentralized finance markets. ⎊ Term ## [Cryptocurrency Volatility Index](https://term.greeks.live/term/cryptocurrency-volatility-index/) Meaning ⎊ The Cryptocurrency Volatility Index provides a standardized measure of market uncertainty, essential for pricing risk in decentralized derivatives. ⎊ Term ## [Time Decay Mitigation](https://term.greeks.live/term/time-decay-mitigation/) Meaning ⎊ Time decay mitigation functions as a systematic defense against the erosive effects of theta, preserving capital efficiency in volatile crypto markets. ⎊ Term ## [Put Option Valuation](https://term.greeks.live/term/put-option-valuation/) Meaning ⎊ Put option valuation provides the mathematical framework to quantify and transfer downside risk within decentralized financial markets. ⎊ Term ## [Delta Gamma Vega Rho Exposure](https://term.greeks.live/term/delta-gamma-vega-rho-exposure/) Meaning ⎊ Delta Gamma Vega Rho Exposure quantifies derivative risk sensitivities to maintain stability and capital efficiency in volatile crypto markets. ⎊ Term ## [Predictive Modeling Strategies](https://term.greeks.live/term/predictive-modeling-strategies/) Meaning ⎊ Predictive modeling strategies enable participants to quantify market probabilities and manage systemic risks within decentralized derivative ecosystems. ⎊ Term ## [Options Market Volatility](https://term.greeks.live/term/options-market-volatility/) Meaning ⎊ Options market volatility quantifies future price uncertainty, acting as the fundamental driver for derivative pricing and systemic risk management. ⎊ Term ## [Delta Gamma Vanna Hedging](https://term.greeks.live/term/delta-gamma-vanna-hedging/) Meaning ⎊ Delta Gamma Vanna Hedging provides a robust framework to neutralize multi-dimensional risk in volatile digital asset derivative portfolios. ⎊ Term ## [Options Greek Calculation](https://term.greeks.live/term/options-greek-calculation/) Meaning ⎊ Options Greek Calculation quantifies derivative risk sensitivities to enable precise, automated hedging within decentralized financial systems. ⎊ Term ## [Quantitative Strategies](https://term.greeks.live/term/quantitative-strategies/) Meaning ⎊ Quantitative strategies utilize mathematical modeling to automate risk management and capture value within decentralized derivative markets. ⎊ Term ## [Portfolio Delta Management](https://term.greeks.live/definition/portfolio-delta-management/) The systematic monitoring and adjustment of a portfolio's aggregate price sensitivity to maintain a target risk profile. ⎊ Term ## [Delta Hedging Flow Signals](https://term.greeks.live/term/delta-hedging-flow-signals/) Meaning ⎊ Delta hedging flow signals serve as critical indicators of institutional risk management, dictating short-term price dynamics in derivative markets. ⎊ Term ## [Implied Volatility Forecasting](https://term.greeks.live/term/implied-volatility-forecasting/) Meaning ⎊ Implied volatility forecasting provides the mathematical foundation for pricing market uncertainty within decentralized derivative ecosystems. ⎊ Term ## [Vega Hedging Techniques](https://term.greeks.live/term/vega-hedging-techniques/) Meaning ⎊ Vega hedging neutralizes portfolio sensitivity to volatility shifts, securing capital against rapid repricing in decentralized derivative markets. ⎊ Term ## [Options Pricing Accuracy](https://term.greeks.live/term/options-pricing-accuracy/) Meaning ⎊ Options pricing accuracy ensures derivative premiums reflect real-time risk, essential for maintaining systemic stability in decentralized markets. ⎊ Term ## [Backtesting Financial Models](https://term.greeks.live/term/backtesting-financial-models/) Meaning ⎊ Backtesting financial models quantifies the performance and risk of trading strategies by subjecting them to historical and simulated market stress. ⎊ Term ## [Vega Exposure Assessment](https://term.greeks.live/term/vega-exposure-assessment/) Meaning ⎊ Vega Exposure Assessment quantifies portfolio sensitivity to implied volatility, essential for maintaining solvency in decentralized derivatives. ⎊ Term ## [Rho Risk Factors](https://term.greeks.live/term/rho-risk-factors/) Meaning ⎊ Rho risk factors quantify the impact of fluctuating interest rates on the cost of carry for decentralized options and derivative positions. ⎊ Term --- ## Raw Schema Data ```json { "@context": "https://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "name": "Home", "item": "https://term.greeks.live/" }, { "@type": "ListItem", "position": 2, "name": "Area", "item": "https://term.greeks.live/area/" }, { "@type": "ListItem", "position": 3, "name": "Black-Scholes-Merton Framework", "item": "https://term.greeks.live/area/black-scholes-merton-framework/" } ] } ``` ```json { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [ { "@type": "Question", "name": "What is the Framework of Black-Scholes-Merton Framework?", "acceptedAnswer": { "@type": "Answer", "text": "The Black-Scholes-Merton framework provides a foundational mathematical model for pricing European-style options, establishing a theoretical value based on five key inputs. 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The parts are dark blue, medium blue, cream, and green, suggesting a complex system or assembly." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/delta-gamma-vega-rho-exposure/", "url": "https://term.greeks.live/term/delta-gamma-vega-rho-exposure/", "headline": "Delta Gamma Vega Rho Exposure", "description": "Meaning ⎊ Delta Gamma Vega Rho Exposure quantifies derivative risk sensitivities to maintain stability and capital efficiency in volatile crypto markets. ⎊ Term", "datePublished": "2026-03-25T02:42:43+00:00", "dateModified": "2026-03-25T02:43:06+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-core-of-defi-market-microstructure-with-volatility-peak-and-gamma-exposure-implications.jpg", "width": 3850, "height": 2166, "caption": "A complex metallic mechanism composed of intricate gears and cogs is partially revealed beneath a draped dark blue fabric. The fabric forms an arch, culminating in a bright neon green peak against a dark background." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/predictive-modeling-strategies/", "url": "https://term.greeks.live/term/predictive-modeling-strategies/", "headline": "Predictive Modeling Strategies", "description": "Meaning ⎊ Predictive modeling strategies enable participants to quantify market probabilities and manage systemic risks within decentralized derivative ecosystems. ⎊ Term", "datePublished": "2026-03-24T20:11:33+00:00", "dateModified": "2026-03-24T20:13:40+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/high-speed-quantitative-trading-mechanism-simulating-volatility-market-structure-and-synthetic-asset-liquidity-flow.jpg", "width": 3850, "height": 2166, "caption": "A stylized 3D rendered object featuring a dark blue faceted body with bright blue glowing lines, a sharp white pointed structure on top, and a cylindrical green wheel with a glowing core. The object's design contrasts rigid, angular shapes with a smooth, curving beige component near the back." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/options-market-volatility/", "url": "https://term.greeks.live/term/options-market-volatility/", "headline": "Options Market Volatility", "description": "Meaning ⎊ Options market volatility quantifies future price uncertainty, acting as the fundamental driver for derivative pricing and systemic risk management. ⎊ Term", "datePublished": "2026-03-24T04:01:05+00:00", "dateModified": "2026-03-24T04:02:08+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-smart-contract-visualization-representing-implied-volatility-and-options-risk-model-dynamics.jpg", "width": 3850, "height": 2166, "caption": "The abstract render displays a blue geometric object with two sharp white spikes and a green cylindrical component. This visualization serves as a conceptual model for complex financial derivatives within the cryptocurrency ecosystem." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/delta-gamma-vanna-hedging/", "url": "https://term.greeks.live/term/delta-gamma-vanna-hedging/", "headline": "Delta Gamma Vanna Hedging", "description": "Meaning ⎊ Delta Gamma Vanna Hedging provides a robust framework to neutralize multi-dimensional risk in volatile digital asset derivative portfolios. ⎊ Term", "datePublished": "2026-03-24T02:32:15+00:00", "dateModified": "2026-03-24T02:32:41+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/dynamic-representation-of-layered-risk-exposure-and-volatility-shifts-in-decentralized-finance-derivatives.jpg", "width": 3850, "height": 2166, "caption": "The abstract composition features a series of flowing, undulating lines in a complex layered structure. The dominant color palette consists of deep blues and black, accented by prominent bands of bright green, beige, and light blue." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/options-greek-calculation/", "url": "https://term.greeks.live/term/options-greek-calculation/", "headline": "Options Greek Calculation", "description": "Meaning ⎊ Options Greek Calculation quantifies derivative risk sensitivities to enable precise, automated hedging within decentralized financial systems. ⎊ Term", "datePublished": "2026-03-24T02:29:53+00:00", "dateModified": "2026-03-24T02:30:31+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-options-protocol-showing-algorithmic-price-discovery-and-derivatives-smart-contract-automation.jpg", "width": 3850, "height": 2166, "caption": "This image features a dark, aerodynamic, pod-like casing cutaway, revealing complex internal mechanisms composed of gears, shafts, and bearings in gold and teal colors. The precise arrangement suggests a highly engineered and automated system." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/quantitative-strategies/", "url": "https://term.greeks.live/term/quantitative-strategies/", "headline": "Quantitative Strategies", "description": "Meaning ⎊ Quantitative strategies utilize mathematical modeling to automate risk management and capture value within decentralized derivative markets. ⎊ Term", "datePublished": "2026-03-23T21:34:35+00:00", "dateModified": "2026-03-23T21:36:24+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-execution-of-derivative-instruments-high-frequency-trading-strategies-and-optimized-liquidity-provision.jpg", "width": 3850, "height": 2166, "caption": "A white control interface with a glowing green light rests on a dark blue and black textured surface, resembling a high-tech mouse. The flowing lines represent the continuous liquidity flow and price action in high-frequency trading environments." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/portfolio-delta-management/", "url": "https://term.greeks.live/definition/portfolio-delta-management/", "headline": "Portfolio Delta Management", "description": "The systematic monitoring and adjustment of a portfolio's aggregate price sensitivity to maintain a target risk profile. ⎊ Term", "datePublished": "2026-03-23T16:56:49+00:00", "dateModified": "2026-03-25T05:20:12+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/structured-derivatives-portfolio-visualization-for-collateralized-debt-positions-and-decentralized-finance-liquidity-provision.jpg", "width": 3850, "height": 2166, "caption": "A stylized 3D representation features a central, cup-like object with a bright green interior, enveloped by intricate, dark blue and black layered structures. The central object and surrounding layers form a spherical, self-contained unit set against a dark, minimalist background." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/delta-hedging-flow-signals/", "url": "https://term.greeks.live/term/delta-hedging-flow-signals/", "headline": "Delta Hedging Flow Signals", "description": "Meaning ⎊ Delta hedging flow signals serve as critical indicators of institutional risk management, dictating short-term price dynamics in derivative markets. ⎊ Term", "datePublished": "2026-03-22T12:43:20+00:00", "dateModified": "2026-03-22T12:44:23+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/interoperability-architecture-illustrating-synthetic-asset-pricing-dynamics-and-derivatives-market-liquidity-flows.jpg", "width": 3850, "height": 2166, "caption": "A close-up view reveals a series of smooth, dark surfaces twisting in complex, undulating patterns. Bright green and cyan lines trace along the curves, highlighting the glossy finish and dynamic flow of the shapes." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/implied-volatility-forecasting/", "url": "https://term.greeks.live/term/implied-volatility-forecasting/", "headline": "Implied Volatility Forecasting", "description": "Meaning ⎊ Implied volatility forecasting provides the mathematical foundation for pricing market uncertainty within decentralized derivative ecosystems. ⎊ Term", "datePublished": "2026-03-22T04:17:56+00:00", "dateModified": "2026-03-22T04:20:06+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/quantifying-volatility-cascades-in-cryptocurrency-derivatives-leveraging-implied-volatility-analysis.jpg", "width": 3850, "height": 2166, "caption": "A smooth, continuous helical form transitions in color from off-white through deep blue to vibrant green against a dark background. The glossy surface reflects light, emphasizing its dynamic contours as it twists." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/vega-hedging-techniques/", "url": "https://term.greeks.live/term/vega-hedging-techniques/", "headline": "Vega Hedging Techniques", "description": "Meaning ⎊ Vega hedging neutralizes portfolio sensitivity to volatility shifts, securing capital against rapid repricing in decentralized derivative markets. ⎊ Term", "datePublished": "2026-03-22T02:56:28+00:00", "dateModified": "2026-03-22T02:57:15+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-core-of-defi-market-microstructure-with-volatility-peak-and-gamma-exposure-implications.jpg", "width": 3850, "height": 2166, "caption": "A complex metallic mechanism composed of intricate gears and cogs is partially revealed beneath a draped dark blue fabric. The fabric forms an arch, culminating in a bright neon green peak against a dark background." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/options-pricing-accuracy/", "url": "https://term.greeks.live/term/options-pricing-accuracy/", "headline": "Options Pricing Accuracy", "description": "Meaning ⎊ Options pricing accuracy ensures derivative premiums reflect real-time risk, essential for maintaining systemic stability in decentralized markets. ⎊ Term", "datePublished": "2026-03-21T19:25:16+00:00", "dateModified": "2026-03-21T19:25:39+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-algorithmic-execution-engine-for-options-payoff-structure-collateralization-and-volatility-hedging.jpg", "width": 3850, "height": 2166, "caption": "The image showcases a high-tech mechanical cross-section, highlighting a green finned structure and a complex blue and bronze gear assembly nested within a white housing. Two parallel, dark blue rods extend from the core mechanism." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/backtesting-financial-models/", "url": "https://term.greeks.live/term/backtesting-financial-models/", "headline": "Backtesting Financial Models", "description": "Meaning ⎊ Backtesting financial models quantifies the performance and risk of trading strategies by subjecting them to historical and simulated market stress. ⎊ Term", "datePublished": "2026-03-21T16:15:17+00:00", "dateModified": "2026-03-21T16:15:35+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/high-frequency-algorithmic-execution-logic-for-cryptocurrency-derivatives-pricing-and-risk-modeling.jpg", "width": 3850, "height": 2166, "caption": "The image displays a detailed cross-section of a high-tech mechanical component, featuring a shiny blue sphere encapsulated within a dark framework. A beige piece attaches to one side, while a bright green fluted shaft extends from the other, suggesting an internal processing mechanism." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/vega-exposure-assessment/", "url": "https://term.greeks.live/term/vega-exposure-assessment/", "headline": "Vega Exposure Assessment", "description": "Meaning ⎊ Vega Exposure Assessment quantifies portfolio sensitivity to implied volatility, essential for maintaining solvency in decentralized derivatives. ⎊ Term", "datePublished": "2026-03-21T10:02:10+00:00", "dateModified": "2026-03-21T10:02:47+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/blockchain-layer-two-perpetual-swap-collateralization-architecture-and-dynamic-risk-assessment-protocol.jpg", "width": 3850, "height": 2166, "caption": "A sleek, abstract cutaway view showcases the complex internal components of a high-tech mechanism. The design features dark external layers, light cream-colored support structures, and vibrant green and blue glowing rings within a central core, suggesting advanced engineering." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/rho-risk-factors/", "url": "https://term.greeks.live/term/rho-risk-factors/", "headline": "Rho Risk Factors", "description": "Meaning ⎊ Rho risk factors quantify the impact of fluctuating interest rates on the cost of carry for decentralized options and derivative positions. ⎊ Term", "datePublished": "2026-03-21T09:21:26+00:00", "dateModified": "2026-03-21T09:21:54+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-smart-contract-visualization-representing-implied-volatility-and-options-risk-model-dynamics.jpg", "width": 3850, "height": 2166, "caption": "The abstract render displays a blue geometric object with two sharp white spikes and a green cylindrical component. This visualization serves as a conceptual model for complex financial derivatives within the cryptocurrency ecosystem." } } ], "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/interlocked-algorithmic-derivatives-and-risk-stratification-layers-protecting-smart-contract-liquidity-protocols.jpg" } } ``` --- **Original URL:** https://term.greeks.live/area/black-scholes-merton-framework/