risk.hpp

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#pragma once
 
#include <vector>
 
namespace quant::risk {
 
// Compute historical VaR and CVaR (Expected Shortfall) from a vector of P&L samples
// alpha in (0,1), e.g., 0.99 for 99% VaR
struct VarEs {
    double var;
    double cvar;
};
 
VarEs var_cvar_from_pnl(const std::vector<double>& pnl, double alpha);
 
// Monte Carlo VaR under GBM for a single asset position
// Returns VaR/CVaR of horizon P&L for position size (positive long)
VarEs var_cvar_gbm(double spot, double mu, double sigma, double horizon_years, double position,
                   unsigned long num_sims, unsigned long seed, double alpha);
 
// Portfolio VaR/CVaR under joint normal/Gaussian copula (Cholesky)
// mu, sigma, weights have size N; corr is N x N row-major correlation matrix
VarEs var_cvar_portfolio(const std::vector<double>& mu, const std::vector<double>& sigma,
                         const std::vector<double>& corr, const std::vector<double>& weights,
                         double horizon_years, unsigned long num_sims, unsigned long seed, double alpha);
 
// Backtest statistics for VaR exceptions
struct BacktestStats {
    double alpha;    // VaR confidence
    unsigned long T; // total trials
    unsigned long N; // number of exceptions
    double lr_pof;   // Kupiec POF LR statistic (df=1)
    double p_pof;    // p-value for POF
    double lr_ind;   // Christoffersen independence LR (df=1)
    double p_ind;    // p-value for independence
    double lr_cc;    // Combined conditional coverage LR (df=2)
    double p_cc;     // p-value for combined
};
 
// Compute Kupiec (POF) and Christoffersen (independence) tests from exception sequence (0/1)
BacktestStats kupiec_christoffersen(const std::vector<int>& exceptions, double alpha);
 
// t-Student VaR/CVaR for a single asset P&L over a horizon
VarEs var_cvar_t(double mu, double sigma, double nu, double horizon_years, double position,
                 unsigned long num_sims, unsigned long seed, double alpha);
 
} // namespace quant::risk