Jon Danielsson

Stochastic volatility in asset prices. Estimation with simulated maximum likelihood

Abstract The stochastic volatility model is used to estimate daily asset price dynamics. The model is estimated by integrating latent volatility out of the joint density of prices and volatility to obtain the marginal density of prices. Due to high number of dimensions of the integral, no conventional integration technique is applicable. A Monte Carlo method, called simulated maximum likelihood, is used to obtain the marginal density, where the latent variable is simulated conditional on available information. The model is estimated by 2022 observations from the S & P 500 index. For comparison ARCH type models are estimated with the same data.

Value-at-Risk and Extreme Returns

We propose a semi-parametric method for unconditional Value-at-Risk (VaR) evaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non-parametric empirical distribution function. A comparison of methods on a portfolio of stock and option returns reveals that at the 5% level the RiskMetrics analysis is best, but for predictions of low probability worst outcomes, it strongly underpredicts the VaR while the semi-parametric method is the most accurate.

Tail index and quantile estimation with very high frequency data

Precise estimation of the tail shape of forex returns is of critical importance for proper risk assessment. We improve upon the efficiency of conventional estimators that rely on a first order expansion of the tail shape, by using the second order expansion. Here we advocate a moments estimator for the second term. The paper uses both Monte Carlo simulations and the high frequency foreign exchange recordings collected by the Olsen corporation to illustrate the technique.

The emperor has no clothes: Limits to risk modelling

Abstract This paper considers the properties of risk measures, primarily value-at-risk (VaR), from both internal and external (regulatory) points of view. It is argued that since market data is endogenous to market behavior, statistical analysis made in times of stability does not provide much guidance in times of crisis. In an extensive survey across data classes and risk models, the empirical properties of current risk forecasting models are found to be lacking in robustness while being excessively volatile. For regulatory use, the VaR measure may give misleading information about risk, and in some cases may actually increase both idiosyncratic and systemic risk.

An academic response to Basel II

It is our view that the Basel Committee of Banking Supervision, in its Basel II proposals, has failed to address many of the key deficiencies of the global financial regulatory system and even created the potential for new sources of instability. This document highlights our concerns that the failure of the proposals to address key issues can have destabilising effects and thus harm the global financial system. In particular, there is considerable scope for under-estimation of financial risk, which may lead to complacency on the part of policy makers and insufficient understanding of the likelihood of a systematic crisis. Furthermore, it is unfortunate that the Basel Committee has not considered how financial institutions will react to the new regulations. Of special concern is how the proposed regulations would induce the harmonisation of investment decisions during the crises with the consequence of destabilising rather than stabilising the global financial system.

Real trading patterns and prices in spot foreign exchange markets

Most of the existing empirical literature on FX market microstructure uses indicative quote data derived from Reuters EFX Screens. This paper examines the adequacy of such data as proxies for firm, tradeable quotes. We present a comparison of prices (and volumes) derived from Reuters D2000-2 electronic inter-dealer broking system with contemporaneous data from EFX. Tick-by-tick data is available from both sources, covering October 6-10, 1997. Our main comparative results are as follows. EFX midquote returns are consistently more volatile than their D2000-2 counterparts and display strong moving average effects which are not present in the D2000-2 returns. EFX spreads bear little or no relation to the inside spreads derived from D2000-2. In terms on information flows, D2000-2 returns lead those on EFX by up to 3 minutes and, further contribute around 90% of all information impounded in quotes. A bivariate GARCH analysis also indicates a dominant role for D2000-2 in price discovery. On the positive side, however, EFX quotation frequency correlates well with D2000-2 transaction frequency.

Multivariate stochastic volatility models: Estimation and a comparison with VGARCH models

Abstract A multivariate stochastic volatility (MSV) model is presented together with an estimation method. Estimation of the MSV model requires specialized estimation techniques since the volatility is a dynamic latent variable. The simulated maximum likelihood technique is expanded to allow for estimation of models with multiple latent variables and is applied to the MSV model. The MSV model is compared with a multivariate GARCH model. The MSV model has fewer parameters and higher likelihood values than the multivariate GARCH models. The univariate models are compared in a Monte Carlo experiment where the likelihood domination is confirmed.

Lessons from a collapse of a financial system

The paper draws lessons from the collapse of Iceland’s banking system in October 2008. The rapid expansion of the banking system following its privatization in the early 2000s is explained, as well as the inherent fragility due to the size of the banking system relative to the domestic economy and the central bank’s reserves, market manipulation enabling bank capital to expand rapidly and the weak and understaffed public institutions. Most of Iceland’s banking system was traditionally in state hands but was privatized and sold to politically favoured entities at the turn of the century, with laws and regulations subsequently changed to facilitate the expansion of the banking system. Political connections and the tacit support of the authorities enabled senior bank managers and key shareholders to extract significant private benefits while shifting risk to domestic and foreign taxpayers and foreign creditors. These problems were exacerbated by symptoms of what the paper terms the small country syndrome. The size of the banking sector made the central bank incapable of serving as the lender of last resort. The domestic supervisor, the central bank and the ministries in charge of economic affairs were understaffed and lacking in experience in how to manage a large financial sector. The rapid growth was also ultimately unsustainable due to high levels of leverage and a weak capital base due to both the rapid expansion of balance sheets and lending to finance investment in own shares. The episode demonstrates the importance of closely monitoring rapidly growing financial institutions and even possibly slowing growth when institutions are systemically important. One lesson to be drawn from the crisis relates to the role of politics in a financial crisis. The Icelandic authorities as a matter of policy encouraged the creation of an international banking centre. This involved the privatization and deregulation of the banking system, rules and regulations being relaxed and the neglect of financial supervision. Another lesson is that floating exchange rates can be hazardous in the presence of large capital flows. The central bank raised interest rates during the boom years in order to meet an inflation target. This created an interest rate differential with other countries that encourages a large volume of carry trades and incentivized domestic agents to borrow in foreign currency. Both conspired to create an asset price bubble, excessive currency appreciation and – counter-intuitively – high inflation. The result was that monetary policy as conducted was ineffective at curbing domestic demand. The eventual large depreciation of the currency made a large section of the economy insolvent. Finally, there are lessons about the European passport system in financial services and the common market. The Icelandic banks had the right to set up branches in the European Union by means of the passport on the explicit assumption that home regulators were exercising adequate controls. The collapse of the banks left the United Kingdom and the Netherlands with significant costs, demonstrating the inherent weakness in the passport when one member country can undercut the supervisory standards of other member countries. For the passport system to work, the home supervisor must be trustworthy. — Sigridur Benediktsdottir, Jon Danielsson and Gylfi Zoega

On time-scaling of risk and the square-root-of-time rule

Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk. A common method for this purpose, though only correct when returns are iid normal, is the square–root–of–time rule where an estimated quantile of a return distribution is scaled to a lower frequency by the square-root of the time horizon. The aim of this paper is to examine time scaling of risk when returns follow a jump diffusion process. It is argued that a jump diffusion is well-suited for the modeling of systemic risk, which is the raison d’etre of the Basel capital adequacy proposals. We demonstrate that the square–root–of–time rule leads to a systematic underestimation of risk, whereby the degree of underestimation worsens with the time horizon, the jump intensity and the confidence level. As a result, even if the square–root–of–time rule has widespread applications in the Basel Accords, it fails to address the objective of the Accords.(This abstract was borrowed from another version of this item.)

Incentives for effective risk management

Under the new Capital Accord, banks choose between two different types of risk management systems, the standard or the internal rating based approach. The paper considers how a banks preference for a risk management system is affected by the presence of supervision by bank regulators. The model uses a principal–agent setting between a banks owner and its risk management. The main conclusion is that previously unregulated institutions can be expected to switch to the lower quality standard approach subsequent to becoming regulated, i.e., the presence of regulation may induce a bank to decrease the quality of its risk management system.