We construct “Hybrid Value at Risk” (HYVAR) that is an arbitrary mixture of Historical VAR and Monte Carlo VAR. The procedure is capable of retaining both the correlation matrix of the original time series and also jumps/‘fat tails'. For this reason HYVAR provides more realistic scenarios,...

A common scenario risk analysis employs a multiple factor model with assumed changes in the factors to obtain changes in non-factor variables. This analysis is sometimes designated as a “predictive stress scenario”. We choose to designate the factor model as a multifactor “CAPM” model,...

The Macro Micro (MM) model contains different time scales and deals with risk as it occurs in the real world, especially trend risk. A new methodology - Singular Spectrum Analysis (SSA) – is introduced to identify historical trends, trend volatilities, and noise-reduced trend-trend...

We describe some details of extensions of the Macro Micro (MM) model. Applications include a long-term real-world PFE risk simulation, including realistic quasi-random Macro trends. The details elaborated here include the use of the 3rd order skew Green function to obtain micro mean reversion, a...

Interest-rate structured products and over-the-counter derivatives are like an immense, dense jungle that's grown from a small bare patch of earth in 30 years. From virtually nothing in the late 1970s, the notional value of interest-rate contracts reached $458 trillion - about eight times the...

Despite the recent market upheavals, the OTC derivatives markets continue to comprise one of the largest components of the financial markets, with an overall outstanding notional of $547 trillion in December 2008, 70% of which are in interest rate derivatives. As of June 2009, this grew to $605...

Exotic interest rate derivatives are hard to value. Care must be taken to make sure that sources of volatility that impact the contingent claim are properly modeled, and that appropriate relationships are maintained between the underlying rates involved.In this presentation, we outline the...

The most widely used option pricing model is the Black-Scholes model.We motivate an alternative option pricing model called the Variance Gamma (VG) model and demonstrate its implementation in the Bloomberg system

We review and detail the causes of errors in numerical differentiation, including roundoff error, convexity error, cancellation error and correlated errors. We discuss methods for improving accuracy, including step size selection and smoothing techniques, as well as a number of approaches...