Journal of Derivatives 

About: Journal of Derivatives is an academic journal published by Pageant Media US. The journal publishes majorly in the area(s): Volatility (finance) & Valuation of options. It has an ISSN identifier of 1074-1240. Over the lifetime, 683 publications have been published receiving 23711 citations.

Techniques for Verifying the Accuracy of Risk Measurement Models

Abstract: Risk exposures are typically quantified in terms of a "value at risk" (VaR) estimate. A VaR estimate corresponds to a specific critical value of a portfolio's potential one-day profit and loss distribution. Given their functions both as internal risk management tools and as potential regulatory measures of risk exposure, it is important to assess and quantify the accuracy of an institution's VaR estimates. This study considers the formal statistical procedures that could be used to assess the accuracy of VaR estimates. The analysis demonstrates that verification of the accuracy of tail probability value estimates becomes substantially more difficult as the cumulative probability estimate being verified becomes smaller. In the extreme, it becomes virtually impossible to verify with any accuracy the potential losses associated with extremely rare events. Moreover, the economic importance of not being able to reliably detect an inaccurate model or an under-reporting institution potentially becomes much more pronounced as the cumulative probability estimate being verified becomes smaller. It does not appear possible for a bank or its supervisor to reliably verify the accuracy of an institution's internal model loss exposure estimates using standard statistical techniques. The results have implications both for banks that wish to assess the accuracy of their internal risk measurement models as well as for supervisors who must verify the accuracy of an institution's risk exposure estimate reported under an internal models approach to model risk.

An Overview of Value at Risk

Abstract: This article gives a broad and accessible overview o f models o f value at risk (WR), a popular measure o f the market risk of afinancialfirm’s “book,” the list ofpositions in various instruments that expose the firm to financial risk. Roughly speaking, the value at risk o f a portjolio is the loss in market value over a given time period, such as one day or two weeks, that is exceeded with a small probability, such as 1%. We focus narrowly on the market risk associated with changes in the prices or rates of underlying traded instruments. Traditionally, this would include such aspects o f credit risk as the risk o f changes in the spreads ofpublicly traded corporate and sovereign bonds. In order to maintain a narrow focus, however, I/aR does not traditionally include, and we do not review here, the risk ofdefdult on long-term derivative contracts. We begin with models o f the distribution ofunderlying market returns and ofvolatility, emphasizing the roles o f price jumps and o f stochastic volatility in determining the ‘ffatness” o f the tails o f the distributions o f returns in various markets. We then turn to methods for approximating the value at risk o f derivatives, using numerical approximations based on delta andgamma. Estimation o f the value at risk o f a portjolio ofpositions is then discussed, beginning with the choice of which risk factors to include. A n extensive numerical example illustrates the accuracy of various alternative methods, allowing for correlated jumps in the underlying market prices. Finally, we review “scenario analysis,” which treats the potential losses associated with particular scenarios, such as a given parallel shiji o f a yield curve or a given change in volatility.

Valuation of a CDO and an n-th to Default CDS Without Monte Carlo Simulation

Abstract: Many of the new credit derivative products are based on default experience for a portfolio of financial instruments. These include collateralized debt obligations (CDOs) and similar tranched credit products, and “n-th to default swaps.” Devising good default risk models for single-name credits has been challenging enough, but applying them to credit portfolios introduces much greater complexity, because of the critical importance of correlation. The most common valuation technology is Monte Carlo simulation, but with many bonds, each of which is subject to both correlated and idiosyncratic risk factors, the simulation is time-consuming and limited in scope. In this article, Hull and White offer two straightforward approximation techniques for evaluating default risk within the industry-standard “copula“ model that eliminate simulation of the idiosyncratic risks. Their approach greatly accelerates the solution while still allowing a large degree of flexibility in the choice of factor correlation structure and probability distributions. For example, Student-t distributed shocks that have fatter tails than the normal are easily accommodated.

A Guide to Volatility and Variance Swaps

Abstract: Trading in derivatives has caused investors, and especially market makers, to be concerned with the volatility of asset returns along with their direction. Uncertain and time-varying volatility imparts risk to an otherwise hedged position, and volatility risk is not easy to manage with ordinary instruments. Volatility swaps are a new class of derivative, for which an asset9s volatility itself is the underlying. This article describes how volatility swaps work, and derives pricing and hedging equations for them. Interestingly, the natural derivative instrument in this family would be based on variance, rather than volatility, since a variance swap can be replicated (pretty well) by a static portfolio of ordinary European calls and puts on the price of the underlying asset. The authors also show how to set up a volatility hedge when the available traded options exhibit a smile or skew pattern.