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accuracy accurate VaR measure accurate VaR model accurately reﬂects Adam Copeland Ana Aizcorbe Andreas Lehnert Andrew Cohen April assess Athanasios Orphanides August average loss Backtesting Procedures bankís Berger Brian Sack contingency table coverage and independence Covitz current regulatory framework December deﬁned detect Economics Discussion Series Egon Zakrajsek Empirical estimate example February Federal Reserve Board Finance and Economics function based backtests Hao Zhou Historical Simulation hit function hit sequence hit series inaccurate increase independence property independence test Inﬂation January joint test July Kevin Moore Kupiec Test loss function based market risk capital Markov test Monetary Policy November October Pearsonís Q test POF test portfolio risk power of Pearsonís Prices proﬁt or loss proﬁts and losses quantile function quantiles reported VaR measure risk management sample satisﬁed Speciﬁcally systematic under reporting Takeshi Kimura test of unconditional tests that examine three risk models unconditional coverage property unit interval Value-at-Risk violation occurs volatility