# QuantCalc Tools

> QuantCalc Tools provides verifiable quantitative calculators for options pricing, FX carry, fixed-income duration, compound CAGR, and portfolio risk metrics.

- Canonical Domain: https://quantcalctools.com
- Organization: QuantCalc Analytics Ltd.
- Full Corpus Digest: https://quantcalctools.com/llms-full.txt

## Quantitative Pricing & Options Engines

- [Black-Scholes-Merton Option Pricing, Analytical Greeks & Newton-Raphson Implied Volatility Engine](https://quantcalctools.com/articles/black-scholes-merton-implied-volatility-greeks-calculator-guide): For an at-the-money European call option with spot S = $100.00, strike K = $100.00, time to expiry T = 0.25 years (91.25 days), risk-free rate r = 4.50%, continuous dividend yield q = 1.50%, and implied volatility σ = 20.00%, the exact Black-Scholes-Merton theoretical premium is $4.3584 with Delta = +0.5299, Gamma = 0.0396, annualized Vega = $0.1978 per 1% vol, and daily Theta = -$0.0241.
- [Continuous Kelly Criterion & Fractional Half-Kelly Drawdown Probability Calculator](https://quantcalctools.com/articles/kelly-criterion-fractional-leverage-optimal-f-calculator): Optimal continuous leverage f* = (μ - r) / σ² maximizes log-wealth growth while half-Kelly cuts 50% drawdown risk by 75%.
- [FX Forward Swap Points & Covered Interest Parity (CIP) Cross-Currency Basis Calculator](https://quantcalctools.com/articles/fx-forward-points-covered-interest-parity-calculator): Computes exact ACT/360 vs ACT/365 forward outright rates F = S * [1 + r_term * d_term] / [1 + r_base * d_base].
- [Hagan SABR Stochastic Volatility Model (α, β, ρ, ν) Swaption Smile Calibration Utility](https://quantcalctools.com/articles/sabr-stochastic-volatility-hagan-smile-calibration): Asymptotic Hagan et al. (2002) implied normal and lognormal volatility approximation for interest rate caps and swaptions.
- [Garman-Kohlhagen FX Option Pricing & Pip vs. Premium-Adjusted Delta Conventions](https://quantcalctools.com/articles/garman-kohlhagen-fx-option-delta-conventions): Converts between spot delta, forward delta, and premium-adjusted delta for EUR/USD and USD/JPY 25-delta risk reversals and butterflies.
- [Cox-Ross-Rubinstein (CRR) 500-Step Binomial Tree for American Exercise Premium](https://quantcalctools.com/articles/cox-ross-rubinstein-binomial-american-option-tree): Evaluates early exercise boundaries for American puts and discrete dividend-paying single-stock call options.
- [Model-Free Variance Swap Fair Strike Replication from Out-of-the-Money Option Strips](https://quantcalctools.com/articles/variance-swap-fair-strike-vix-replication-strip): Integrates 2/T * ∫ (ΔK / K²) e^(rT) Q(K) dK across OTM puts and calls to price fair variance vs squared VIX.
- [Portfolio Reg-T vs. SPAN Cross-Margin & Futures Liquidation Threshold Calculator](https://quantcalctools.com/articles/margin-initial-maintenance-liquidation-price-simulator): Computes maintenance margin call triggers and net delta-adjusted margin offsets across correlated futures spreads.
- [Sobol Low-Discrepancy Quasi-Monte Carlo Path Pricer for Asian & Barrier Options](https://quantcalctools.com/articles/monte-carlo-antithetic-sobol-quasi-random-pricer): Reduces standard error at O(N⁻¹ log^d N) convergence speed compared to O(N⁻¹/²) pseudo-random sampling.

## Fixed Income Duration & Portfolio Risk

- [Fixed-Income Macaulay Duration, Modified Duration, DV01 & Convexity Taylor Approximation Engine](https://quantcalctools.com/articles/macaulay-modified-duration-convexity-bond-yield-calculator): A 10-year semi-annual coupon bond with $1,000 par value, 4.25% annual coupon rate, and 4.18% yield-to-maturity (YTM) prices at $1,005.67 (100.567% clean price) with a Macaulay Duration of 8.24 years, Modified Duration of 8.07 years, DV01 of $0.8116 per $1,000 par, and Convexity of 76.42 years².
- [Portfolio Parametric VaR, Expected Shortfall (CVaR) & Cornish-Fisher Skewness-Kurtosis Expansion](https://quantcalctools.com/articles/parametric-var-expected-shortfall-cornish-fisher-calculator): For a $100 million multi-asset portfolio with annualized volatility σ = 14.0%, daily skewness S = -0.65, and excess kurtosis K = 2.40, the 99% 10-day Gaussian Value-at-Risk (VaR) is $6.44 million, whereas the Cornish-Fisher fat-tail adjusted 99% 10-day VaR rises to $8.51 million (+32.1%) and 97.5% Expected Shortfall (ES) equals $7.89 million under Basel III FRTB standards.
- [Annualized Sharpe, Sortino, Calmar & Lo (2002) Autocorrelation-Adjusted Sharpe Calculator](https://quantcalctools.com/articles/sharpe-sortino-calmar-omega-ratio-performance-engine): Adjusts annualized Sharpe ratios for serial return autocorrelation ρ₁ to prevent overstating illiquid credit and hedge fund alphas.
- [Nelson-Siegel-Svensson (NSS) 6-Parameter Sovereign Yield Curve Interpolation Engine](https://quantcalctools.com/articles/nelson-siegel-svensson-yield-curve-spline-fitter): Fits instantaneous forward rates and zero-coupon discount factors across 1M to 30Y sovereign bond benchmarks.
- [Black-Litterman Equilibrium Implied Returns & Bayesian View Posterior Allocation Engine](https://quantcalctools.com/articles/black-litterman-bayesian-portfolio-posterior-optimizer): Blends CAPM market-cap equilibrium excess returns Π = λΣw_mkt with subjective investor view matrices P and confidence Ω.
- [One-Factor Hull-White & Cox-Ingersoll-Ross (CIR) Mean-Reverting Short-Rate Simulator](https://quantcalctools.com/articles/vasicek-cir-hull-white-short-rate-bond-option-pricer): Calibrates mean reversion speed a and short-rate volatility σ to initial zero-coupon bond prices.
- [ISDA Standard CDS Model: Bootstrapping Survival Probabilities & Hazard Rates from Par Spreads](https://quantcalctools.com/articles/credit-default-swap-cds-hazard-rate-bootstrapping): Extracts piecewise-constant hazard rates λ_t assuming 40% senior unsecured recovery rate and quarterly IMM coupon dates.
- [Bollerslev GARCH(1,1) vs. RiskMetrics EWMA (λ=0.94) Conditional Volatility Forecaster](https://quantcalctools.com/articles/garch-1-1-ewma-lambda-volatility-forecasting-engine): Estimates long-run variance persistence α + β and half-life of volatility shocks in daily equity and FX series.
- [Merton (1974) Structural Credit Model: Asset Volatility, Distance-to-Default & EDF Calculator](https://quantcalctools.com/articles/merton-structural-distance-to-default-pd-calculator): Treats corporate equity as a European call option on firm assets V_A to solve implied asset value and 1-year default probability.
- [Exact Money-Weighted XIRR vs. Time-Weighted Return (TWR) GIPS Performance Engine](https://quantcalctools.com/articles/compound-annual-growth-rate-cagr-xirr-cashflow-solver): Reconciles Modified Dietz, exact daily TWR sub-period linking, and irregular cash-flow XIRR under GIPS 2020 standards.
- [U.S. TIPS & UK Index-Linked Gilt CPI Index Ratio & Real Yield Cash-Flow Calculator](https://quantcalctools.com/articles/inflation-linked-tips-real-yield-index-ratio-calculator): Calculates reference CPI interpolation (3-month lag) and inflation-adjusted principal accretions to maturity.
- [Principal Component Analysis (PCA) 2s5s10s Butterfly & Steepener Regression Hedge Ratios](https://quantcalctools.com/articles/pca-yield-curve-level-slope-curvature-hedge-ratios): Neutralizes PC1 (Level, 88% variance) and PC2 (Slope, 9% variance) to isolate pure PC3 curvature carry in 2s5s10s fly trades.

## Knowledge Graph & Regulated Entities

- [CME Group Inc. (NASDAQ:CME) — Entity Profile & Regulatory Dossier](https://quantcalctools.com/entities/cme-group-derivatives-exchange): The world’s largest financial derivatives exchange operator, clearing SOFR futures, E-mini S&P 500 options, U.S. Treasury futures, and NYMEX commodities via CME Clearing. (Jurisdiction: United States / Global Clearing; Oversight: U.S. Commodity Futures Trading Commission (CFTC); Wikidata: Q1023876).
- [Myron S. Scholes (Black-Scholes-Merton PDE Architect) (NOBEL-ECON-1997) — Entity Profile & Regulatory Dossier](https://quantcalctools.com/entities/fischer-black-myron-scholes): Nobel laureate economist and co-author of the Black-Scholes-Merton stochastic partial differential equation for dynamic delta-hedging and contingent claims pricing. (Jurisdiction: International Quantitative Standards; Oversight: Academic & ISDA Derivatives Valuation Standard; Wikidata: Q295412).
- [Black-Scholes-Merton Continuous Dividend Greeks Engine (QCALC-BSM-V4) — Entity Profile & Regulatory Dossier](https://quantcalctools.com/entities/black-scholes-merton-greeks-engine): Analytical European option valuation and first/second-order Greeks (Delta, Gamma, Vega, Theta, Rho, Vanna, Volga) calculator with continuous dividend yield q. (Jurisdiction: United Kingdom / Global; Oversight: ISDA Equity Derivatives Definitions; Wikidata: Q709907).
- [FCA SYSC 15A & MiFID II RTS 6 Algorithmic Model Governance License (FCA-RTS6-MODEL) — Entity Profile & Regulatory Dossier](https://quantcalctools.com/entities/fca-mifid-ii-RTS-27-28-algorithmic-validation): Regulatory compliance and model risk management framework governing algorithmic pricing engines, pre-trade risk limits, and stress-testing backtests. (Jurisdiction: United Kingdom & European Union; Oversight: UK Financial Conduct Authority (FCA) / ESMA; Wikidata: Q1416838).