Singular Fourier–Padé series expansion of European option prices

We apply a new numerical method, the singular Fourier–Padé (SFP) method invented by Driscoll and Fornberg [Numer. Algorithms, 2001, 26, 77–92; The Gibbs Phenomenon in Various Representations and Applications, 2011], to price European-type options in Lévy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with non-smooth probability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. Moreover, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques.     

Data for outcome payments or information for care? A sociotechnical analysis of the management information system in the implementation of a social impact bond

ABSTRACT

Social Impact Bonds (SIBs) are a policy intervention designed to explicitly link the activity of social interventions to outcome payments. Despite a burgeoning literature on SIBs there is a lack of evidence in relation to the information system characteristics and accounting mechanisms of SIBs. Applying a multi-dimensional sociotechnical lens to a case study of a SIB allows us to reveal the current problematic convergence of public management and information systems. The authors found that an information system within a SIB is introduced and adapted to increasingly prioritize the production of data for payment over documenting care accounts to support improved provision. The ?ndings of this paper also suggest that claims of SIBs as an innovation are limited as they are subject to the familiar problems of New Public Management practice, in the way they shape the design and use of the data in governance, management and service delivery practices.     

The Impact of the Inpatient Prospective Payment System and Diagnosis-Related Groups

Abstract

The outpatient prospective payment system for the Medicare program became effective Aug. 1, 2000, as mandated by the Balanced Budget Act of 1997. This outpatient program complements Medicare’s inpatient prospective payment system, which was introduced in 1983. A survey of the literature over the past 20 years is undertaken to review the effects of the inpatient prospective payment system and diagnosis-related groups (DRGs) on inpatient hospital utilization, expenditures, and outcomes. The level of the DRG payment has been questioned, as well as the process of adjusting the payment levels from one year to the next. In addition, past research has speculated that the DRG classification may not be sensitive to severity and is subject to coding ambiguities. These conclusions can be used as input to future research on the new outpatient program, as well as updating research on the inpatient program.     

Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

The representation of American options prices under stochastic volatility and jump-diffusion dynamics

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [Rev. Financial Stud., 1993, 6, 327–343], and by a Poisson jump process as introduced by Merton [J. Financial Econ., 1976, 3, 125–144]. Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalizes in an intuitive way the structure of the solution to the corresponding European option pricing problem obtained by Scott [Math. Finance, 1997, 7(4), 413–426], but here in the case of a call option and constant interest rates.     

A Risk Model with Multilayer Dividend Strategy

Abstract

In recent years various dividend payment strategies for the classical collective risk model have been studied in great detail. In this paper we consider both the dividend payment intensity and the premium intensity to be step functions depending on the current surplus level. Algorithmic schemes for the determination of explicit expressions for the Gerber-Shiu discounted penalty function and the expected discounted dividend payments are derived. This enables the analytical investigation of dividend payment strategies that, in addition to having a sufficiently large expected value of discounted dividend payments, also take the solvency of the portfolio into account. Since the number of layers is arbitrary, it also can be viewed as an approximation to a continuous surplus-dependent dividend payment strategy. A recursive approach with respect to the number of layers is developed that to a certain extent allows one to improve upon computational disadvantages of related calculation techniques that have been proposed for specific cases of this model in the literature. The tractability of the approach is illustrated numerically for a risk model with four layers and an exponential claim size distribution.     

The micro-price: a high-frequency estimator of future prices

The micro-price estimated using high-frequency data is empirically a better predictor of short-term prices than the mid-price or the weighted mid-price     

A comment on the role of prices for excludable public goods

Blomquist and Christensen [(2005). The role of prices for excludable public goods, International Tax and Public Finance, 12 ,61–79] argue that welfare is initially decreasing in the price of an excludable public good and that the case for a positive price for an excludable public good price is weak. We argue that this result follows from their particular characterization of the public good and that an alternative and equally reasonable characterization overturns their result. Hence, the policy case for a positive price on the public good is stronger than Blomquist and Christiansen suggest. JEL Classification H21 · H41     

Financial Deepening,Asset Price Inflation,and Economic Convergence: Empirical Analysis Based on China’s Experience

Abstract

In this study, we test for convergence in financial development and economic growth in China’s financial deepening reform process by using system GMM method. The results show strong evidence of the mutually interactive and systematic relationship between financial development and economic growth, and the system is in a condition of long-run divergence. The main cause of divergence in the system changed after 2008 from financial depression to asset price expansion. This study provides evidence that the government should intensify financial deepening reforms and pay attention to financial resource flows to prevent excessive asset price expansion.     

Non-constant rates and over-diffusive prices in a simple model of limit order markets

Abstract

Using simple particle models of limit order markets, we argue that the mid-term over-diffusive price behaviour is due to the variability of market order and limit order rates. Several rules for rate changes are considered. We obtain analytical results for bid-ask spread properties, Hurst plots and price increment correlation functions.     

Returns to scale and asset prices

The q‐theory of investment is proposed to explain firm growth effects, where previous papers identify a negative effect of firm growth, including asset growth, real investment and net share issuance, on future stock returns. This paper uses returns to scale from the production function to test the dynamic q‐theory, which predicts that the firm growth effect is theoretically weaker for firms with decreasing returns to scale (DRS) than for non‐DRS firms. Our empirical results generally support the prediction of dynamic q‐theory. However, we find that the dynamic q‐theory explains little of the value, momentum and ROE effects from the standpoint of returns to scale.     

General approximation schemes for option prices in stochastic volatility models

In this paper we develop a general method for deriving closed-form approximations of European option prices and equivalent implied volatilities in stochastic volatility models. Our method relies on perturbations of the model dynamics and we show how the expansion terms can be calculated using purely probabilistic methods. A flexible way of approximating the equivalent implied volatility from the basic price expansion is also introduced. As an application of our method we derive closed-form approximations for call prices and implied volatilities in the Heston [Rev. Financial Stud., 1993, 6, 327–343] model. The accuracy of these approximations is studied and compared with numerically obtained values.     

On investment in funds

Abstract

The purpose of this paper is to determine how large a capital risk a monetary institution is incurring by receiving capital payments under obligation to yield a fixed guaranteed interest until a prescribed date, even if the market rate of interest should fall below the rate guaranteed, and to investigate to what extent the risk is decreased if it is possible to invest the payment first received at a rate of interest exceeding the rate guaranteed.     

Quadratic Hawkes processes for financial prices

We introduce and establish the main properties of QHawkes (‘Quadratic’ Hawkes) models. QHawkes models generalize the Hawkes price models introduced in Bacry and Muzy [Quant. Finance, 2014, 14(7), 1147–1166], by allowing feedback effects in the jump intensity that are linear and quadratic in past returns. Our model exhibits two main properties that we believe are crucial in the modelling and the understanding of the volatility process: first, the model is time-reversal asymmetric, similar to financial markets whose time evolution has a preferred direction. Second, it generates a multiplicative, fat-tailed volatility process, that we characterize in detail in the case of exponentially decaying kernels, and which is linked to Pearson diffusions in the continuous limit. Several other interesting properties of QHawkes processes are discussed, in particular the fact that they can generate long memory without necessarily being at the critical point. A non-parametric fit of the QHawkes model on NYSE stock data shows that the off-diagonal component of the quadratic kernel indeed has a structure that standard Hawkes models fail to reproduce. We provide numerical simulations of our calibrated QHawkes model which is indeed seen to reproduce, with only a small amount of quadratic non-linearity, the correct magnitude of fat-tails and time reversal asymmetry seen in empirical time series.     

Are there Social Spillovers in Consumers’ Security Assessments of Payment Instruments?

Even though security of payments has long been identified as an important aspect of the consumer payment experience, recent literature fails to appropriately assess the extent of social spillovers among payment users. We test for the existence and importance of such spillovers by analyzing whether social influence affects consumers’ perceptions of the security of payment instruments. Based on a 2008–2014 annual panel data survey of consumers, we find strong evidence of social spillovers in payment markets: others’ perceptions of security of payment instruments exert a positive influence on one’s own payment security perceptions. The significant and robust results imply that a consumer’s assessments of security converge to his peers’ average assessment: a 10 percent change in the divergence between one’s own security rating and peers’ average rating will result in a 7 percent change in one’s own rating in the next period. The results are robust to many specifications and do not change when we control for actual fraud or crime data. Our results indicate that spillovers rather than reflection appear to be the cause, although separating the two causes is very difficult (Manski 1993). In particular, the spillovers are stronger for people who experience an exogenous shock to security perception, people who have more social interactions, and younger consumers, who are more likely to be influenced by social media. We also examine the effects of social spillovers on payment behavior (that is, on decisions regarding payment adoption and use). Our results indicate that social spillovers have a rather limited impact on payment behavior, as others’ perceptions seem to affect one’s own payment behavior mainly indirectly through the effect on one’s own perceptions.     

American-style options in jump-diffusion models: estimation and evaluation

We propose dynamic programming coupled with finite elements for valuing American-style options under Gaussian and double exponential jumps à la Merton [J. Financ. Econ., 1976, 3, 125–144] and Kou [Manage. Sci., 2002, 48, 1086–1101], and we provide a proof of uniform convergence. Our numerical experiments confirm this convergence result and show the efficiency of the proposed methodology. We also address the estimation problem and report an empirical investigation based on Home Depot. Jump-diffusion models outperform their pure-diffusion counterparts.     

A structural Heath–Jarrow–Morton framework for consistent intraday spot and futures electricity prices

The framework is based on stochastic processes with economic interpretations and is consistent with the initial forward price curve     

New model valuating for life assurances with invalidity benefits

Abstract

In a paper in this journal 1977, pp. 106–109 I described a technique splitting the risk element of a life assurance from the saving element. This technique can be extended to assurances with invalidity benefits. In Denmark, life assurances often include exemption of premium payment in case of invalidity caused by accident or disease.