The ability to quickly and accurately price, hedge and calibrate financial instruments is critical for effective risk management. It could also be argued that it is essential for market efficiency, to the extent that predicted prices closely follow their intended targets and account for their most current inputs. This issue of The Journal of Risk contains papers that address both computational accuracy and empirical validation, particularly in the context of high-dimensional problems.
Estimating the variance-covariance matrix of the returns of the many thousands of securities available for investment is a key step prior to portfolio optimization. However, the reliance on history alone and on naive statistical methodology is prone to generating severely biased estimates-if it is indeed possible to produce estimates at all. In times of crisis, for example, such covariance estimates undervalue risk, but they overvalue it when crises subside. The first paper in this issue, "Incorporating forward looking market data into linear multifactor fundamental models" by Luiza Miranyan, improves on the traditional parsimonious, factor-based estimation technique by incorporating forward-looking general market indicators, including the readily available VIX index, and security-specific factors such as implied and realized volatility values.
While the paper by Miranyan assumes that a consensus on when returns are evaluated exists, the second paper, "Modeling overnight and daytime returns using a multivariate generalized autoregressive conditional heteroskedasticity copula model" by Long Kang and Simon H. Babbs, concerns the different and related dynamics of daytime and overnight returns. These are particularly essential for certain derivatives, and also reflect the microstructural difference between the two time periods. Their multivariate implementation reveals the dependence between day and night and gives empirical evidence that is consistent with asymmetric information in the market microstructure.
This time-of-day contrast is particularly illustrative of cross-currency setups. The third paper in the issue, "Efficient pricing and Greeks in the cross-currency LIBOR market model" by Chris J. Beveridge, Mark S. Joshi and Will M. Wright, tackles a high-dimensional calibration problem arising from derivatives whose values depend on currency exchange rates as well as on domestic and foreign interest rates. When, in addition, provisions for early exercise are present, the authors develop an efficient Monte Carlo simulation technique for pricing and hedging that they illustrate on power reverse dual currency swaps and cross-currency swaps.
The final paper in this issue, "Cashflow replication with mismatch constraints" by Wei Chen and Jimmy Skoglund, addresses a hedging issue in a context best represented by asset and liability risk management. While a straightforward cashflow replication would not necessarily match instruments, the authors impose matching constraints that capture essential features of the asset to be evaluated. They also develop an efficient mathematical programming technique for both valuation and hedging. Their approach offers the potential for valuing nontradable lending assets, which, as illustrated by the recent financial crisis, can lead to significant market uncertainty if not done properly.