Showing papers in "Quantitative Finance in 2014"

Filling in the blanks: network structure and interbank contagion

Abstract: The network pattern of financial linkages is important in many areas of banking and finance. Yet, bilateral linkages are often unobserved, and maximum entropy serves as the leading method for estimating counterparty exposures. This paper proposes an efficient alternative that combines information-theoretic arguments with economic incentives to produce more realistic interbank networks that preserve important characteristics of the original interbank market. The method loads the most probable links with the largest exposures consistent with the total lending and borrowing of each bank, yielding networks with minimum density. When used in a stress-testing context, the minimum-density solution overestimates contagion, whereas maximum entropy underestimates it. Using the two benchmarks side-by-side defines a useful range that bounds the cost of contagion in the true interbank network when counterparty exposures are unknown.

Hawkes model for price and trades high-frequency dynamics

Abstract: We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by four kernels associated with, respectively, the trade arrival self-excitation, the price changes mean reversion, the impact of trade arrivals on price variations and the feedback of price changes on trading activity. It allows one to account for both stylized facts of market price microstructure (including random time arrival of price moves, discrete price grid, high-frequency mean reversion, correlation functions behaviour at various time scales) and the stylized facts of market impact (mainly the concave-square-root-like/relaxation characteristic shape of the market impact of a meta-order). Moreover, it allows one to estimate the entire market impact profile from anonymous market data. We show that these kernels can be empirically estimated from the empirical conditional mean intensities. We p...

Robust risk measurement and model risk

Abstract: Financial risk measurement relies on models of prices and other market variables, but models inevitably rely on imperfect assumptions and estimates, creating model risk. Moreover, optimization decisions, such as portfolio selection, amplify the effect of model error. In this work, we develop a framework for quantifying the impact of model error and for measuring and minimizing risk in a way that is robust to model error. This robust approach starts from a baseline model and finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a precise constraint on the plausibility of the deviation. Using relative entropy to constrain model distance leads to an explicit characterization of worst-case model errors; this characterization lends itself to Monte Carlo simulation, allowing straightforward calculation of bounds on model error with very little computational effort beyond that required to evaluate performance under the baseline nominal model. Thi...

Arbitrage-free SVI volatility surfaces

Abstract: In this article, we show how to calibrate the widely used SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data

Expected Returns: An Investor’s Guide to Harvesting Market Rewards

Abstract: by Antti Ilmanen. Wiley Finance, 2011, Hardcover. ISBN 978-1-119-99072-7. Ilmanen’s guide to harvesting market premia is first and foremost intensely practitioner oriented; it is indeed an indispen...

Completeness, interconnectedness and distribution of interbank exposures—a parameterized analysis of the stability of financial networks

Abstract: This paper assesses the impact of a certain structure of interbank exposures on the stability of a stylized financial system. Given a certain balance sheet structure of financial institutions, a large number of valid matrices of interbank exposures is created by a random generator. Assuming a certain loss given default, domino effects are simulated. The main results are, first, that financial stability depends not only on the completeness and interconnectedness of the network, but also on the distribution of interbank exposures within the system (measured by entropy). Second, looking at random graphs, the sign of the correlation between the degree of equality of the distribution of claims and financial stability depends on the connectivity of the financial system as well as on additional parameters that affect the vulnerability of the system to interbank contagion. Third, the more concentrated the assets are within a money center model, the less stable it is. Fourth, a money center model with asset concen...

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Abstract: We consider the portfolio selection problem in the accumulation phase of a defined contribution (DC) pension scheme. We solve the mean–variance portfolio selection problem using the embedding technique pioneered by Zhou and Li [Appl. Math. Optimiz., 2000, 42, 19–33] and show that it is equivalent to a target-based optimization problem, consisting of the minimization of a quadratic loss function. We support the use of the target-based approach in DC pension funds for three reasons. Firstly, it transforms the difficult problem of selecting the individual's risk-aversion coefficient into the easier task of choosing an appropriate target. Secondly, it is intuitive, flexible and adaptable to the member's needs and preferences. Thirdly, it produces final portfolios that are efficient in the mean–variance setting. We address the issue of the comparison between an efficient portfolio and a portfolio that is optimal according to the more general criterion of maximization of the expected utility (EU). The two natur...

Parsimonious HJM modelling for multiple yield curve dynamics

Abstract: The opinions here expressed are solely those of the authors and do not represent in any way those of their employers. Classical interest-rate models were formulated to satisfy by construction, no-a...

Estimation methods for expected shortfall

Abstract: Introduced in the 1980s, value at risk has been a popular measure of financial risk. However, value at risk suffers from a number of drawbacks as measure of financial risk. An alternative measure referred to as expected shortfall was introduced in late 1990s to circumvent these drawbacks. Much theory have been developed since then. The developments have been most intensive in recent years.However, we are not aware of any comprehensive review of known estimation methods for expected shortfall. We feel it is timely that such a review is written. This paper (containing six sections and over 140 references) attempts that task with emphasis on recent developments. We expect this review to serve as a source of reference and encourage further research with respect to measures of financial risk.

Closed form spread option valuation

Abstract: This paper considers the valuation of a spread call when asset prices are log-normal. The implicit strategy of the Kirk formula is to exercise if the price of the long asset exceeds a given power function of the price of the short asset. We derive a formula for the spread call value, conditional on following this feasible, but non-optimal, exercise strategy. Numerical investigations indicate that the lower bound produced by our formula is extremely accurate. The precision is much greater than the Kirk formula. Moreover, optimizing with respect to the strategy parameters (which corresponds to the Carmona–Durrleman procedure) yields only a marginal improvement of accuracy (if any).

Longevity hedge effectiveness: a decomposition

Abstract: We use a case study of a pension plan wishing to hedge the longevity risk in its pension liabilities at a future date. The plan has the choice of using either a customised hedge or an index hedge, with the degree of hedge effectiveness being closely related to the correlation between the value of the hedge and the value of the pension liability. The key contribution of this paper is to show how correlation and, therefore, hedge effectiveness can be broken down into contributions from a number of distinct types of risk factors. Our decomposition of the correlation indicates that population basis risk has a significant influence on the correlation. But recalibration risk as well as the length of the recalibration window are also important, as is cohort effect uncertainty. Having accounted for recalibration risk, additional parameter uncertainty has only a marginal impact on hedge effectiveness. Finally, the inclusion of Poisson risk only starts to become significant when the smaller population falls below a...

Asset price bubbles: a survey

Abstract: Why do asset price bubbles continue to appear in various markets? What types of events give rise to bubbles and why do arbitrage forces fail to quickly burst them? Do bubbles have real economic consequences and should policy makers do more to prevent them? This paper provides an overview of recent literature on bubbles, with significant attention given to behavioral models and rational models with frictions. The latest U.S. real estate bubble is described in the context of this literature.

A regime-switching Heston model for VIX and S&P 500 implied volatilities

Abstract: Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies have examine whether there is significantly greater risk premium in VIX option prices compared with S&P 500 option prices. We address this issue by proposing and analysing a stochastic volatility model with regime switching. The basic Heston model cannot capture VIX-implied volatilities, as has been documented. We show that the incorporation of sharp regime shifts can bridge this shortcoming. We take advantage of asymptotic and Fourier methods to make the extension tractable, and we present a fit to data, both in times of crisis and relative calm, which shows the effectiveness of the regime switching.

Can utility optimization explain the demand for structured investment products

Abstract: In this paper, we first show that for classical rational investors with correct beliefs and constant absolute or constant relative risk aversion, the utility gains from structured products over and above a portfolio consisting of the risk-free asset and the market portfolio are typically much smaller than their fees. This result holds irrespectively of whether the investors can continuously trade the risk-free asset and the market portfolio at no costs or whether they can just buy the assets and hold them to maturity of the structured product. However, when considering behavioural utility functions, such as prospect theory, or investors with incorrect beliefs (arising from probability weighting or probability misestimation), the utility gain can be sizable.

The effect of corporate social responsibility on stock performance: new evidence for the USA and Europe

Abstract: This paper provides new empirical evidence for the effect of corporate social responsibility on corporate financial performance. In contrast to former studies, we examine two different regions, namely the USA and Europe, and disentangle firm and sector specific impacts. Our econometric analysis shows that environmental and social activities of a firm compared with other firms within the industry are valued by financial markets in both regions. However, the respective positive effects on average monthly stock returns between 2003 and 2006 are more robust in the USA and, in addition, non-linear. Our analysis furthermore points to biased parameter estimates if incorrectly specified econometric models are applied: the seemingly significantly negative effect of environmental and social performance of the industry to which a firm belongs strongly declines and mostly becomes insignificant if the explanation of stock performance is based on the Fama–French three-factor or the Carhart four-factor models instead of...

The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies

Abstract: Over 200 years ago, the Industrial Revolution bent the curve of human development by almost 90°. The authors refer to this period of dramatic technological progress as the ‘first machine age’. Now ...

Portfolio performance evaluation with loss aversion

Abstract: In this paper we consider a loss-averse investor equipped with a specific, but still quite general, utility function motivated by behavioral finance. We show that, under certain concrete assumptions concerning the form of this utility, one can derive closed-form solutions for the investor's portfolio performance measure. We investigate the effects of loss aversion and demonstrate its important role in performance measurement. The framework presented in this paper also provides a sound theoretical foundation for all known performance measures based on partial moments of the distribution.

A Principal Component Approach to Measuring Investor Sentiment in China

Abstract: This paper develops a new investor sentiment index for the Chinese stock market. The index is constructed via the principal component approach (PCA), taking six important economic and market factors into consideration. The sentiment index serves as a threshold variable in a threshold autoregressive model to identify the stock market regimes. Our findings show that the Chinese stock market can be divided into three regimes: namely, a high-return volatile regime, a low-return stable regime and a neutral regime. The sentiment index is shown to have good out-of-sample predictability.

Jump detection with wavelets for high-frequency financial time series

Abstract: This paper introduces a new nonparametric test to identify jump arrival times in high frequency financial time series data. The asymptotic distribution of the test is derived. We demonstrate that the test is robust for different specifications of price processes and the presence of the microstructure noise. A Monte Carlo simulation is conducted which shows that the test has good size and power. Further, we examine the multi-scale jump dynamics in US equity markets. The main findings are as follows. First, the jump dynamics of equities are sensitive to data sampling frequency with significant underestimation of jump intensities at lower frequencies. Second, although arrival densities of positive jumps and negative jumps are symmetric across different time scales, the magnitude of jumps is distributed asymmetrically at high frequencies. Third, only 20% of jumps occur in the trading session from 9:30 AM to 4:00 PM, suggesting that illiquidity during after-hours trading is a strong determinant of jumps.

Doing Capitalism in the Innovation Economy

Abstract: Doing Capitalism in the Innovation Economy, by William H. Janeway, Cambridge University Press (2012). Hardback. ISBN: 978-1-107-03125-8. After his doctorate at Cambridge University, William H. Jane...

Pairs trading: optimal thresholds and profitability

Abstract: Since its birth in the 1980s, pairs trading have been popular as a statistical arbitrage strategy among major investment banks and hedge funds. Despite the high average annualized excess return, wh...

Cardinality versus q-Norm Constraints for Index Tracking

Abstract: Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can be set up to determine the optimal index replicating portfolio. In this paper, we propose an alternative based on imposing a constraint on the q-norm (0 < q < 1) of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimization viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimization problems. The empirical analysis of real-world financial data allows us to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset ...

Mean-variance cointegration and the expectations hypothesis

Abstract: The present paper sheds further light on a well-known (alleged) violation of the expectations hypothesis of the term structure (EHT): the frequent finding of unit roots in interest rate spreads. We show that the EHT implies (i) that the nonstationarity stems from the holding premium, which is hence (ii) cointegrated with the spread. In a stochastic discount factor framework, we model the premium as being driven by the integrated variance of excess returns. Introducing the concept of mean-variance cointegration, we actually find cointegration relations between the conditional first and second moment of US bond data.

Pricing of geometric Asian options under Heston's stochastic volatility model

Abstract: In this work, it is assumed that the underlying asset price follows Heston's stochastic volatility model and explicit solutions for the prices of geometric Asian options with fixed and floating strikes are derived. This approach has to deal with the derivation of the generalized joint Fourier transform of a square-root process and of three different weighted integrals of the square-root process with constant, linear and quadratic weights. Numerical implementation results for the complicated expressions are presented, together with the computational stability and efficiency of the method.

Clustering financial time series with variance ratio statistics

Abstract: This study introduces a new distance measure for clustering financial time series based on variance ratio test statistics. The proposed metric attempts to assess the level of interdependence of time series from the point of view of return predictability. Simulation results show that this metric aggregates time series according to their serial dependence structure better than a metric based on the sample autocorrelations. An empirical application of this approach to international stock market returns is presented. The results suggest that this metric discriminates stock markets reasonably well according to size and the level of development. Furthermore, despite the substantial evolution of individual variance ratio statistics, the clustering pattern remains fairly stable across different time periods.

Assessing dependence between financial market indexes using conditional time-varying copulas: applications to Value at Risk (VaR)

Abstract: We analyse the dynamic dependence structure between broad stock market indexes from the United States (S&P500), Britain (FTSE100), Brazil (BOVESPA) and Mexico (PCMX). We employ Patton’s [Int. Econ. Rev., 2006, 2, 527–556] conditional copula setting and additionally observe the impact of different copula functions on Value at Risk (VaR) estimation. We conclude that the dependence between BOVESPA and the other indexes has intensified since the beginning of 2007. In our case the particular copula form is not crucial for VaR estimation. A goodness-of-fit test based on the parametric bootstrap is also applied. The best fits are obtained via time constant Student-t and time-varying Normal copulas.

Do fear indices help predict stock returns

Abstract: This study investigates the forecasting power of implied volatility indices on forward looking returns Prior studies document that negative innovations to returns are associated with increasing implied volatility of the underlying indices; thus, suggesting a possible relationship between extremely high levels of implied volatility and positive short term returns We investigate this issue by examining the predictive power of three implied volatility indices, VIX, VXN and VDAX, on the underlying index returns We extend previous research by also focusing on characterised selected stocks and examine the relationship between implied volatility indices and future returns across different sectors and classified portfolios Our findings suggest that implied volatility indices are good predictors of 20-days and 60-days forward looking returns and illustrate insignificant predictive power for very short term (1-day and 5-days) returns

Optimal liquidation in dark pools

Abstract: We consider a large trader seeking to liquidate a portfolio using both a transparent trading venue and a dark pool. Our model captures the price impact of trading in transparent traditional venues as well as the execution uncertainty of trading in a dark pool. The unique optimal execution strategy uses both venues continuously. The order size in the dark pool can over- or underrepresent the portfolio size depending on adverse selection and the correlation structure of the assets in the portfolio.

Myopic loss aversion, reference point, and money illusion

Abstract: We use the portfolio selection model presented in He and Zhou [Manage. Sci., 2011, 57, 315–331] and the NYSE equity and US treasury bond returns for the period 1926–1990 to revisit Benartzi and Thaler’s myopic loss aversion theory. Through an extensive empirical study, we find that in addition to the agent’s loss aversion and evaluation period, his reference point also has a significant effect on optimal asset allocation. We demonstrate that the agent’s optimal allocation to equities is consistent with market observation when he has reasonable values of degree of loss aversion, evaluation period and reference point. We also find that the optimal allocation to equities is sensitive to these parameters. We then examine the implications of money illusion for asset allocation. Finally, we extend the model to a dynamic setting.

Pricing credit default swaps with bilateral value adjustments

Abstract: The paper studies the problem of computing adjustments for bilateral counterparty risk for a standard CDS in a three-factor first-passage time default risk model. Extending the existing literature that gives analytical expression for the transition probability density function (or Green’s function) for two-dimensional Brownian motions absorbed at the boundaries in the positive quadrant, this paper gives a semi-analytical expression for Green’s function for three-dimensional Brownian motions absorbed at first exit time from the positive octant. This is done by separating the problem into a radial and an angular part, of which the latter is universal and depends only on the correlation matrix. These mathematical results are then used to provide semi-analytical expressions for bilateral CVA/DVA of a credit default swap. An example of market data is analysed in detail and it is shown that these value adjustments can be surprisingly large.