Methodology and Implementation of Value-at-Risk Measures in Emerging Fixed-Income Markets with Infrequent Trading.

This paper deals with the issue of calculating daily Value-at-Risk (VaR) measures within an environment of thin trading. Our approach focuses on fixed income portfolios with low frequency of transactions in which the missing data problem makes VaR measures difficult to calculate. We propose and implement a methodology to calculate VaR measures with an incomplete panel of prices. The methodology is composed of three phases: Phase I, generates a complete panel of prices, using a term-structure dynamic model of interest rates. Phase II, calculates portfolio VaR measures with several alternative methods using the complete panel data generated in phase I. Phase III, shows how to back-test the VaR measures obtained in phase II using the original incomplete panel of prices. We provide an empirical implementation of the methodology for the Chilean fixed income market. The proposed methodology seems to provide reliable VaR measures for thinly traded markets addressing an important issue for financial risk management in emerging markets.Risk, Value-at-Risk, Fixed Income, Incomplete Panels, Term- Structure Dynamic Models, Extreme Value, GARCH, Kalman Filter.

Risk Management with Thinly Traded Securities: Methodology and Implementation

Thinly traded securities exist in both emerging and well developed markets. However, plausible estimations of market risk measures for portfolios with infrequently traded securities have not been explored in the literature. We propose a methodology to calculate market risk measures based on the Kalman filter which can be used on incomplete datasets. We implement our approach in a fixed- income portfolio within a thin trading environment. However, a similar approach may be also applied to other markets with thinly traded securities. Our methodology provides reliable market risk measures in portfolios with infrequent trading.

Can oil prices help estimate commodity futures prices? The cases of copper and silver

There is an extensive literature on modeling the stochastic process of commodity futures. It has been shown that models with several risk factors are able to adequately fit both the level and the volatility structure of observed transactions with reasonable low errors. One of the characteristics of commodity futures markets is the relatively short term maturity of their contracts, typically ranging for only a few years. This poses a problem for valuing long term investments that require extrapolating the observed term structure. There has been little work on how to effectively do this extrapolation and in measuring its errors. (Cortazar et al., 2008a) and (Cortazar et al., 2008b) propose a multicommodity model that jointly estimates two commodities, one with much longer maturity futures contracts than the other, showing that futures prices of one commodity may be useful information for estimating the stochastic process of another. They implement the procedure using highly correlated commodities like WTI and Brent. In this paper we analyze using prices of long term oil futures contracts to help estimate long term copper and silver future prices. We start by analyzing the performance of the (Cortazar et al., 2008a) and (Cortazar et al., 2008b) multicommodity model, now applied to oil-copper and oil-silver which have much lower correlation than the WTI-Brent contracts. We show that for these commodities with lower correlation the multicommodity model seems not to be effective. We then propose a modified multicommodity model with a much simpler structure which is easier to estimate and that uses the non-stationary long term process of oil to help estimate long term copper and silver futures prices, achieving a much better fit than using available individual or multicommodity models.Commodity futures Price estimation Copper Silver Oil

A Compound Option Model of Production and Intermediate Inventories.

This article extends the option approach to valuing real assets by modeling the firm as a two-stage process with bounded output rates, in which the output of the first stage may be held as work-in-process. In this setting, the real asset becomes a compound option, which, if exercised, gives the option to finish the work-in-process and sell the output as its final payoff. The existence of intermediate inventories may arise as an optimal investment strategy for exploiting possible future price increases. The framework allows us to analyze the effect of uncertainty on output rates and the effect of interest rates changes on inventory levels. Copyright 1993 by University of Chicago Press.