Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model

The rough Bergomi (rBergomi) model, introduced recently in Bayer et al. [Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits empirical implied volatility surfaces. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is to use the Monte Carlo (MC) simulation for pricing. Despite recent advances in the MC method in this context, pricing under the rBergomi model is still a time-consuming task. To overcome this issue, we have designed a novel, hierarchical approach, based on: (i) adaptive sparse grids quadrature (ASGQ), and (ii) quasi-Monte Carlo (QMC). Both techniques are coupled with a Brownian bridge construction and a Richardson extrapolation on the weak error. By uncovering the available regularity, our hierarchical methods demonstrate substantial computational gains with respect to the standard MC method. They reach a sufficiently small relative error tolerance in the price estimates across different parameter constellations, even for very small values of the Hurst parameter. Our work opens a new research direction in this field, i.e. to investigate the performance of methods other than Monte Carlo for pricing and calibrating under the rBergomi model.     

The Valuation Accuracy of the Price-Earnings and Price-Book Benchmark Valuation Methods

This paper evaluates the valuation accuracy of the price-earnings (P/E), the price-book (P/B) and a combined price-earnings and price-book (P/E-P/B) benchmark valuation methods. Performance of the benchmark valuation methods relies on the definition of comparable firms. In this paper, comparable firms are selected based on industry membership, size and return on equity as well as combinations of industry membership with size and with return on equity. We find that within the P/E and P/B benchmark valuation methods, the best definition of the comparable firms are based on industry membership combined with return on equity. However, only the industry membership is necessary to define the comparable firms for the combined P/E-P/B method. In sum, the results suggest that, when firm's value is unknown, the combined P/E-P/B valuation approach selecting comparable firms based on industry membership performs the best among all the approaches evaluated in this paper.We also find that the P/E benchmark valuation method performs better than the P/B benchmark valuation method and the combined method outperforms either the P/E or the P/B method. These results imply that earnings are more important than book value as a single-number firm valuator over our sample years (from 1973 to 1992) and that both earnings and book values are value relevant, one does not substitute perfectly for the other.     

Analytical approximations for the critical stock prices of American options: a performance comparison

Many efficient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the quadratic approximation. We compare our methods with existing analytical methods including the quadratic approximations in Barone-Adesi and Whaley (J Finance 42:301–320, 1987) and Barone-Adesi and Elliott (Stoch Anal Appl 9(2):115–131, 1991), the lower bound approximation in Broadie and Detemple (Rev Financial Stud 9:1211–1250, 1996), the tangent approximation in Bunch and Johnson (J Finance 55(5):2333–2356, 2000), the Laplace inversion method in Zhu (Int J Theor Appl Finance 9(7):1141–1177, 2006b), and the interpolation method in Li (Working paper, 2008). Both of our methods give much more accurate critical stock prices than all the existing methods above.     

商业化背景下开行债券发行成本问题研究

商业化转型将大幅度提高国开行债券融资成本.债券融资成本的提高是否超出了国开行的容忍度,直接关系到国开行转型能否成功,以及转型后的类型,战略发展方向等一系列问题.本文采用“价值补偿”的方法测度了失去国家信用后开行债券的发行成本,然后以盈亏临界点为目标测度了开行债券发行成本的生存容忍度,以银行业平均资产收益率为目标测度了开...     

Empirical Evaluation of Asset–Pricing Models: A Comparison of the SDF and Beta Methods

The stochastic discount factor (SDF) method provides a unified general framework for econometric analysis of asset–pricing models. There have been concerns that, compared to the classical beta method, the generality of the SDF method comes at the cost of efficiency in parameter estimation and power in specification tests. We establish the correct framework for comparing the two methods and show that the SDF method is as efficient as the beta method for estimating risk premiums. Also, the specification test based on the SDF method is as powerful as the one based on the beta method.     

Measuring relative volatility in high-frequency data under the directional change approach

We introduce a new approach in measuring relative volatility between two markets based on the directional change (DC) method. DC is a data-driven approach for sampling financial market data such that the data are recorded when the price changes have reached a significant amplitude rather than recording data under a predetermined timescale. Under the DC framework, we propose a new concept of DC micro-market relative volatility to evaluate relative volatility between two markets. Unlike the time-series method, micro-market relative volatility redefines the timescale based on the frequency of the observed DC data between the two markets. We show that it is useful for measuring the relative volatility in micro-market activities (high-frequency data).     

Statistical properties of demand fluctuation in the financial market

Numerical integration methods for stochastic volatility models in financial markets are discussed. We concentrate on two classes of stochastic volatility models where the volatility is either directly given by a mean-reverting CEV process or as a transformed Ornstein–Uhlenbeck process. For the latter, we introduce a new model based on a simple hyperbolic transformation. Various numerical methods for integrating mean-reverting CEV processes are analysed and compared with respect to positivity preservation and efficiency. Moreover, we develop a simple and robust integration scheme for the two-dimensional system using the strong convergence behaviour as an indicator for the approximation quality. This method, which we refer to as the IJK (137) scheme, is applicable to all types of stochastic volatility models and can be employed as a drop-in replacement for the standard log-Euler procedure.     

Psychological determinants of financial buffer saving: the influence of financial risk tolerance and regulatory focus

With governments redistributing more responsibilities unto citizens, individuals have an increasing need for financial resources acting as a buffer against life’s setbacks and unexpected expenditures. The purpose of this study was to examine psychological determinants of saving for a financial buffer, for which a theoretical model was formulated based on the theory of planned behaviour with three new, domain-specific psychological constructs: financial risk tolerance, regulatory focus and perceived saving barriers. Data were collected with an online questionnaire that utilised convenience and snowball sampling to target both students and working individuals (N = 272). Regression analyses offered support for the proposed model, showing that participants’ financial risk tolerance (i.e. an individual’s attitude towards financial risk taking) was significantly associated with their subjective financial knowledge and regulatory focus. Furthermore, perceived financial self-efficacy and financial risk tolerance both predicted participants’ intention to save for a financial buffer. In turn, perceived financial self-efficacy and saving intention predicted self-reported saving behaviour. Importantly, perceived saving barriers mediated the relationship between saving intention and self-reported saving behaviour. In line with the proposed model, results also showed that a specific attitude-based construct (financial risk tolerance) is a considerably better predictor of saving intention than general measures of attitude towards saving. This study is also the first to demonstrate that regulatory focus influences financial risk tolerance. Implications of these findings for stimulating saving behaviour are discussed.     

On measuring volatility and the GARCH forecasting performance

We apply a new algorithm based on Fourier analysis to compute the volatility of a diffusion process. By using simulations of the continuous-time GARCH model, we show that our method performs well in computing integrated volatility. We show that linear interpolation of high frequency observations induces a downward bias in estimating integrated volatility. By measuring ex post volatility with our method, we find that the forecasting performance of the GARCH model is improved with respect to what is established when classical methods are employed. These results are confirmed by the analysis of exchange rate high frequency time series.     

Test of recent advances in extracting information from option prices

A large literature exists on techniques for extracting probability distributions for future asset prices from option prices. No definitive method has been developed however. The parametric ‘mixture of normals’, and non-parametric ‘smoothed implied volatility’ methods remain the most widespread approaches. These though are subject to estimation errors due to discretization, truncation, and noise. Recently, several authors have derived ‘model free’ formulae for computing the moments of the risk neutral density (RND) directly from option prices, without first estimating the full density. The accuracy of these formulae is studied here for the first time. The Black-Scholes formula is used to generate option prices, and error curves for the first 4 moments of the RND are computed using the ‘model-free’ formulae. It is found that, in practice, the formulae are prone to large and economically significant errors, because they contain definite integrals that can only be solved numerically. We show that without mathematically equivalent expressions with analytical solutions the formulae are difficult to deploy effectively in practice.     

American option valuation: new bounds, approximations, and a comparison of existing methods

We develop lower and upper bounds on the prices of Americancall and put options written on a dividend-paying asset. Weprovide two option price approximations one based on the lowerbound (termed LBA) and one based on both bounds (termed LUBA).The LUBA approximation has an average accuracy comparable toa l,000-step binomial tree. We introduce a modification of thebinomial method (termed BBSR) that is very simple to implementand performs remarkably well. We also conduct a careful large-scaleevaluation of many recent methods for computing American optionprices.     

A sovereign risk index for the Eurozone based on stochastic dominance

We propose a new method to assess sovereign risk in Eurozone countries using an approach that relies on consistent tests for stochastic dominance efficiency. The test statistics and the estimators are computed using mixed integer programming methods. Our analysis is based on macroeconomic fundamentals and their importance in accounting for sovereign risk. The results suggest that net international investment position/GDP and public debt/GDP are the main contributors to country risk in the Eurozone. We also conduct ranking analysis of countries for fiscal and external trade risk. We find a positive correlation between our rankings of the most vulnerable countries and the S&P’s ratings, whereas the correlation for other countries is weaker.     

Financial weather derivatives for corn production in Northern China: A comparison of pricing methods

The focus in this study is on the pricing of financial derivatives for hedging weather risks in crop production. Employing data from an earlier study, we compare different methods for pricing weather derivative options based on growing degree days (GDDs). We employ average daily temperatures to derive GDDs using three approaches: (1) An econometric approach with a sine function; (2) Monte Carlo simulation with a sine function and three methods to estimate the mean-reversion parameter; and (3) a historic approach (burn analysis) based on a 10-year moving average of GDDs. Results indicate that the historical average method provides the best fit, followed by the stochastic process with a high mean reversion speed, and, finally, the approach using the econometrically estimated sine function. Depending on the method used, premiums for weather derivative options vary from $21.27 to $24.39 per GDD index contract.     

The Moments of the Time of Ruin in Markovian Risk Models

Abstract

We present an approach based on matrix-analytic methods to find moments of the time of ruin in Markovian risk models. The approach is applicable when claims occur according to a Markovian arrival process (MAP) and claim sizes are phase distributed with parameters that depend on the state of the MAP. The method involves the construction of a sample-path-equivalent Markov-modulated fluid flow for the risk model. We develop an algorithm for moments of the time of ruin and prove the algorithm is convergent. Examples show that the proposed approach is computationally stable.     

Calibration to American options: numerical investigation of the de-Americanization method

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors.     

CAPM for estimating the cost of equity capital: Interpreting the empirical evidence

We argue that the empirical evidence against the capital asset pricing model (CAPM) based on stock returns does not invalidate its use for estimating the cost of capital for projects in making capital budgeting decisions. Because stocks are backed not only by projects in place, but also by the options to modify current projects and undertake new ones, the expected returns on stocks need not satisfy the CAPM even when expected returns of projects do. We provide empirical support for our arguments by developing a method for estimating firms' project CAPM betas and project returns. Our findings justify the continued use of the CAPM by firms in spite of the mounting evidence against it based on the cross section of stock returns.     

Reading the smile: the message conveyed by methods which infer risk neutral densities

In this study we compare the quality and information content of risk neutral densities obtained by various methods. We consider a non-parametric method based on a mixture of log–normal densities, the semi-parametric ones based on an Hermite approximation or based on an Edgeworth expansion, the parametric approach of Malz which assumes a jump-diffusion for the underlying process, and Heston's approach assuming a stochastic volatility model. We apply those models on FF/DM exchange rate options for two dates. Models differ when important news hits the market (here anticipated elections). The non-parametric model provides a good fit to options prices but is unable to provide as much information about market participants expectations than the jump-diffusion model.     

A Simple Model of Voluntary Reserve Targets with Tolerance Bands

This paper presents a version of the model of voluntary reserve targets (VRT) developed in Baughman and Carapella (2020) simplified to have a Walrasian instead of frictional interbank market. First, the model makes transparent the role of target setting in controlling the market rate. Second, the simplicity of the model allows for an analysis of the interaction between VRT and tolerance bands, which are a common tool for controlling rate variability. We find that the persistent overshooting of interbank rates observed during the Bank of England's experiment with VRT may derive from the interaction between target setting and tolerance bands, a new explanation relative to the literature. We also suggest a simple remedy.     

Detecting Accounting Fraud in Publicly Traded U.S. Firms Using a Machine Learning Approach

We develop a state-of-the-art fraud prediction model using a machine learning approach. We demonstrate the value of combining domain knowledge and machine learning methods in model building. We select our model input based on existing accounting theories, but we differ from prior accounting research by using raw accounting numbers rather than financial ratios. We employ one of the most powerful machine learning methods, ensemble learning, rather than the commonly used method of logistic regression. To assess the performance of fraud prediction models, we introduce a new performance evaluation metric commonly used in ranking problems that is more appropriate for the fraud prediction task. Starting with an identical set of theory-motivated raw accounting numbers, we show that our new fraud prediction model outperforms two benchmark models by a large margin: the Dechow et al. logistic regression model based on financial ratios, and the Cecchini et al. support-vector-machine model with a financial kernel that maps raw accounting numbers into a broader set of ratios.     

The stability of short-term interest rates pass-through in the euro area during the financial market and sovereign debt crises

We analyse the dynamics of the pass-through of banks’ marginal cost to bank lending rates over the 2008 crisis and the euro area sovereign debt crisis in France, Germany, Greece, Italy, Portugal and Spain. We measure banks’ marginal cost by their rate on new deposits, contrary to the literature that focuses on money market rates. This allows us to account for banks’ risks. We focus on the interest rate on new short-term loans granted to non-financial corporations in these countries. Our analysis is based on an error-correction approach that we extend to handle the time-varying long-run relationship between banks’ lending rates and banks’ marginal cost, as well as stochastic volatility. Our application is based on a harmonised monthly database from January 2003 to October 2014. We estimate the model within a Bayesian framework, using Markov Chain Monte Carlo methods (MCMC).We reject the view that the transmission mechanism is permanent over time. The long-run relationship moved with the sovereign debt crises to a new one, with a slower pass-through and higher bank lending rates. Its developments are heterogeneous from one country to the other. Impediments to the transmission of monetary rates depend on the heterogeneity in banks marginal costs and therefore, its risks. We also find that rates to small firms increase compared to large firms in a few countries. Using a VAR model, we show that overall, the effect of a shock on the rate of new deposits on the unexpected variances of new loans has been less important since 2010. These results confirm the slowdown in the transmission mechanism.