Analytic valuation formulas for range notes and an affine term structure model with jump risks

We derive analytic valuation formulas for range accrual notes and spread range accrual notes under an affine term structure model with jump risks. We show that the value of a range accrual note can be significantly affected by the choice of interest rate model and the arrival intensity of jump risks. We also show that misuse of the correlation between reference rates of a spread range accrual note may lead traders and risk managers to mispricing of the note.     

Out-of-sample density forecasts with affine jump diffusion models

We conduct out-of-sample density forecast evaluations of the affine jump diffusion models for the S&P 500 stock index and its options’ contracts. We also examine the time-series consistency between the model-implied spot volatilities using options & returns and only returns. In particular, we focus on the role of the time-varying jump risk premia. Particle filters are used to estimate the model-implied spot volatilities. We also propose the beta transformation approach for recursive parameter updating. Our empirical analysis shows that the inconsistencies between options & returns and only returns are resolved by the introduction of the time-varying jump risk premia. For density forecasts, the time-varying jump risk premia models dominate the other models in terms of likelihood criteria. We also find that for medium-term horizons, the beta transformation can weaken the systematic effect of misspecified AJD models using options & returns.     

Volatility dynamics for the S&P 500: Further evidence from non-affine,multi-factor jump diffusions

We apply Markov chain Monte Carlo methods to time series data on S&P 500 index returns, and to its option prices via a term structure of VIX indices, to estimate 18 different affine and non-affine stochastic volatility models with one or two variance factors, and where jumps are allowed in both the price and the instantaneous volatility. The in-sample fit to the VIX term structure shows that the second (stochastic long-term volatility) factor is required to fit the VIX term structure. Out-of-sample tests on the fit to individual option prices, as well as in-sample tests, show that the inclusion of jumps is less important than allowing for non-affine dynamics. The estimation and testing periods together cover more than 21 years of daily data.     

A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model

We consider the problem of pricing European exotic path-dependent derivatives on an underlying described by the Heston stochastic volatility model. Lipton has found a closed form integral representation of the joint transition probability density function of underlying price and variance in the Heston model. We give a convenient numerical approximation of this formula and we use the obtained approximated transition probability density function to price discrete path-dependent options as discounted expectations. The expected value of the payoff is calculated evaluating an integral with the Monte Carlo method using a variance reduction technique based on a suitable approximation of the transition probability density function of the Heston model. As a test case, we evaluate the price of a discrete arithmetic average Asian option, when the average over n = 12 prices is considered, that is when the integral to evaluate is a 2n = 24 dimensional integral. We show that the method proposed is computationally efficient and gives accurate results.     

A jump diffusion model for VIX volatility options and futures

Volatility indices are becoming increasingly popular as a measure of market uncertainty and as a new asset class for developing derivative instruments. Although jumps are widely considered as a salient feature of volatility, their implications for pricing volatility options and futures are not yet fully understood. This paper provides evidence indicating that the time series behaviour of the VIX index is well approximated by a mean reverting logarithmic diffusion with jumps. This process is capable of capturing stylized facts of VIX dynamics such as fast mean-reversion at higher levels, level effects of volatility and large upward movements during times of market stress. Based on the empirical results, we provide closed-form valuation models for European options written on the spot and forward VIX, respectively.     

Tempered stable and tempered infinitely divisible GARCH models

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation. This model, which we refer to as the rapidly decreasing tempered stable (RDTS) GARCH model, takes into account empirical facts that have been observed for stock and index returns, such as volatility clustering, non-zero skewness, and excess kurtosis for the residual distribution. We review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, we can find the risk-neutral price process, thereby allowing application to option-pricing. We propose algorithms to generate scenarios based on GARCH models with CTS and RDTS innovations. To investigate the performance of these GARCH models, we report parameter estimates for the Dow Jones Industrial Average index and stocks included in this index. To demonstrate the advantages of the proposed model, we calculate option prices based on the index.     

A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features, volatility smile, and volatility clustering observed empirically for the Dow Jones Industrial Average (DJIA) and its component stocks. Using 10 years of stock return data, we confirm the existence of jump intensity switching and clustering, illustrate transition probabilities, and verify superior empirical fit over competing Poisson-style models.     

Point and Figure charting: A computational methodology and trading rule performance in the S&P 500 futures market

This paper empirically contributes to the existing trading rule literature by providing a methodology for the calculation of Point and Figure charts using ultra-high-frequency data and tests trading rules using eight objective, pre-defined trading rules on S&P 500 futures contracts traded between 1990 and 1998. To assess the robustness of reported profits, a bootstrapping adjustment was conducted to determine the forecasting power of the PF trading rules. The results producing mixed statistical significance with some rules proving significant while many others were not.     

Return and Maturity Relationships for Treasury Auctions: Evidence from Turkey

The relationship between the interest rate and the maturity of newly issued bonds provides information on the debt dynamics of an economy as well as on the sustainability of its debt. Such information is crucial especially for countries that have debt‐rollover concerns due to financial stress and/or macroeconomic instability. This study investigates the relationship between treasury auction maturity, which also dictates the debt maturity, and auction interest rates. When the Turkish treasury auction data from 1988 to 2004 are analysed, a reciprocal linkage between auction interest rates and maturities can be observed, especially for the 1995–2000 period, when there were chronic high inflation, high political uncertainty, high public deficits and unsuccessful attempts at stabilisation. This suggests that under an adverse shock, the Treasury decreases the auction maturity in order not to increase interest rates too much. A change in this reciprocal relationship is also reported for the post‐2001 era, which is characterised by decreasing inflation, higher political stability, lower public deficits and successful stabilisation attempts.     

A closer look at financial development and income distribution

This paper analyzes the under-investigated relationship uniting financial development and income distribution. We use a novel approach taking into account for the first time the specific channels linking banks, capital markets and income inequality, the time-varying nature of the relationship, and reciprocal causality. We construct a set of annual indicators of banking and capital market size, robustness, efficiency and international integration. We then estimate the determinants of income distribution using a panel Bayesian structural vector autoregressive (SVAR) model, for a set of 49 countries over the 1994-2002 period. We uncover a significant causality running from financial sector development to income distribution. In addition, the banking sector seems to exert a stronger impact on inequality. Finally, the relationship appears to depend on the characteristics of the financial sector, rather than on its size.     

A comparison of MAD and CVaR models with real features

In this paper we consider two different mixed integer linear programming models for solving the single period portfolio selection problem when integer stock units, transaction costs and a cardinality constraint are taken into account. The first model has been formulated by using the maximization of the worst conditional expectation as objective function. The second model is based on the maximization of the safety measure corresponding to the mean absolute deviation. Extensive computational results are provided to compare the financial characteristics of the optimal portfolios selected by the two models on real data from European stock exchange markets. Some simple heuristics are also introduced that provide efficient and effective solutions when an optimal integer solution cannot be found in a reasonable amount of time.     

Scaling models for the severity and frequency of external operational loss data

According to Basel II criteria, the use of external data is indispensable to the implementation of an advanced method for calculating operational risk capital. This article investigates how the severity and frequencies of external losses are scaled for integration with internal data. We set up an initial model designed to explain the loss severity by taking into account potential selection bias in the external data. Estimation results show that many variables have significant power in explaining the loss amount. We use them to develop a normalization formula. We develop a zero-inflated count-data model to scale the loss frequency. We compute an operational VaR and we conduct out-of-sample backtesting.     

Fuzzy logic and financial risk. A proposed classification of financial risk to the cooperative sector

Applying fuzzy logic to financial indicators is not a well disseminated proposal in the accounting field. This methodology allows observing the results of financial ratios with a broader perspective, showing neither completely true nor completely false results, since they can take an undetermined truthfulness value within a set of values, applying the fuzzy logic theory. The objective of this work is to introduce the reader to the application of fuzzy logic on financial risk indicators, using the ratios of one of the sector one cooperatives of Ecuador, and thus validate the level of relevance of this indicator when compared to the standardized objective of the CAMEL model and its risk rating. To apply this theory, linguistic variables were used, the ranges of which were evaluated in 0–1 scales. It was determined that the fuzzy methodology, applied to financial risks, presents a greater level of relevance toward a good credit rating, ensuring a low level of risk and a very good solvency. However, in periods of low economic activity it would stagnate in this level due to the increased risk.     

Forming priors for DSGE models (and how it affects the assessment of nominal rigidities)

We discuss prior elicitation for the parameters of dynamic stochastic general equilibrium (DSGE) models, and provide a method for constructing prior distributions for a subset of these parameters from beliefs about steady-state relationships and second moments of the endogenous variables. The empirical application documents how the specification of the prior distribution affects our assessment of the relative importance of price and wage rigidities in a New Keynesian DSGE model.     

Derivative prices from interest rate models: results for Canada, Hong Kong, and United States

In this paper, we compute implied bond and contingent claim prices from the CKLS, Vasicek, CIR, and BS interest rate models using historical estimates for Canada, Hong Kong, and the United States. We find that default-free bond prices and contingent claim prices are sensitive to the assumed model used for these currencies, and that for Canada the CIR is the best, for Hong Kong the Vasicek and CIR models, and for the US the BS model.     

M‐PRESS‐CreditRisk: Microprudential and Macroprudential Capital Requirements for Credit Risk under Systemic Stress

M‐PRESS‐CreditRisk is a novel stress testing approach that can help authorities gauge banks' capital adequacy related to credit risk. For the first time, it combines the assessment of microprudential capital requirements under Pillars 1 and 2 and macroprudential buffers in a unified, coherent framework. Its core element is an advanced credit portfolio model—SystemicCreditRisk—built upon a rich, nonlinear dependence structure for correlated bank portfolios. The model is applied to a sample of 12 systemically important German banking groups and delivers measures for systemic credit risk and the banks' contributions to it in both baseline and stress scenarios.     

Unravelling the complexity of collective mental models: A method for developing and analysing scenarios in multi-organisational contexts

In multi-organisational contexts, scenario building has been used to engage stakeholders in a critical discussion on issues of mutual importance, and to gain their support with regards to possible future responses. A review of existing literature suggests that much has been written regarding the process of scenario development and the benefits of the process, but the detailed analysis of scenario building outcomes, which encompass a large number of issues and their complex interconnections, has not been made explicit for studying and enhancing understanding of a complex societal problem. This paper presents a systematic method for analysing such complex outcomes in order to facilitate reflective thinking on important issues within the wider context for policy development. The method was employed in a series of participative scenario development workshops, which yielded several causal maps around the theme of construction industry skills. A collective map merging the individual subject-specific causal maps was created to help provide a more holistic overview of the pertinent issues surrounding the construction skills debate. The analysis of this collective map promotes a better understanding of the issue in the wider context, the consequence of possible future events and actions, and of the pre-requisition required for certain events/desired outcomes to take place. The main benefit that could be derived from the method is the opportunity to help facilitate and encourage debate and discussion amongst key stakeholders regarding scenario theme, in this case skills improvement within construction. Due to its flexibility and adaptability, the method could potentially be applied to other areas requiring longer range planning and which contain multiple stakeholder perspectives.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

A general theory of controllability and expectations anchoring for small-open economies

Rational expectations are often used as an argument against policy activism, as they may undermine or neutralize the policymaker’s actions. Although this sometimes happens, rational expectations do not always imply policy invariance or ineffectiveness. In fact, in certain circumstances rational expectations can enhance our power to control an economy over time. In those cases, policy announcements can be used to extend the impact of conventional policy instruments. We present a general forward-looking policy framework and use it to provide a formal rationale for testing when policymakers can and cannot expect to be able to manage expectations. To describe the relevance of our results applications are shown for policy design in small-open economies. Those are the cases where domestic policies are at their weakest and our ability to influence expectations most constrained.