Arbitrage-Free Smoothing of the Implied Volatility Surface

The pricing accuracy and pricing performance of local volatility models crucially depends on absence of arbitrage in the implied volatility surface: an input implied volatility surface that is not arbitrage-free invariably results in negative transition probabilities and/ or negative local volatilities, and ultimately, into mispricings. The common smoothing algorithms of the implied volatility surface cannot guarantee the absence arbitrage. Here, we propose an approach for smoothing the implied volatility smile in an arbitrage-free way. Our methodology is simple to implement, computationally cheap and builds on the well-founded theory of natural smoothing splines under suitable shape constraints. Unlike other methods, our approach also works when input data are scarce and not arbitrage-free. Thus, it can easily be integrated into standard local volatility pricers.Arbitrage-Free Smoothing, Volatility, Implied Volatility Surface

Fitting the Smile Revisited: A Least Squares Kernel Estimator for the Implied Volatility Surface

Nonparametric methods for estimating the implied volatility surface or the implied volatility smile are very popular, since they do not impose a specific functional form on the estimate. Traditionally, these methods are two-step estimators. The first step requires to extract implied volatility data from observed option prices, in the second step the actual fitting algorithm is applied. These two-step estimators may be seriously biased when option prices are observed with measurement errors. Moreover, after the nonlinear transformation of the option prices the error distribution will be complicated and less tractable. In this study, we propose a one-step estimator for the implied volatility surface based on a least squares kernel smoother of the Black-Scholes formula. Consistency and the asymptotic distribution of the estimate are provided. We demonstrate the estimator using German DAX index option data to recover the smile and the implied volatility surface

Multivariate volatility models

Multivariate Volatility Models belong to the class of nonlinear models for financial data. Here we want to focus on multivariate GARCH models. These models assume that the variance of the innovation distribution follows a time dependent process conditional on information which is generated by the history of the process. In this chapter we demonstrate how to use the bigarch quantlet of XploRe to estimate the conditional covariance of a bivariate (high frequency) return process. In particular we consider a system of exchange rates of two currencies measured against the US Dollar (USO), namely the Deutsche Mark (DEM) and the British Pound Sterling (GBP). For this example process we compare the dynamic properties of the bivariate model with univariate GARCH specifications where cross sectional dependecies are ignored. Moreover, to illustrate the scope of the bivariate model we employ the estimated model to price call options written on foreign exchange rates

Price variability and price dispersion in a stable monetary environment: Evidence from German retail markets

We investigate the relationship between inflation and price variation using highly disaggregated, weekly price data for consumption goods recorded in Germany during 1995, a low inflation period. We find a significant positive correlation between the rates of price change and price dispersion, both at the level of individual products and product groups. However, we find no correlation between the rates of price change and price variability. Together with results from similar studies, Tommasi (1993) and Parsley (1996), a remarkable pattern emerges: When aggregate nominal shocks are small, only price dispersion is correlated with price changes. As the rate of inflation rises, both variability and dispersion become affected. During hyperinflation, systematic movements of price dispersion seem to disappear. We conclude that price dispersion is best explained by microeconomic frictions in price adjustment, whereas price variability appears to be related to costly price search and information problems

The analysis of implied volatilities

The analysis of volatility in financial markets has become a first rank issue in modern financial theory and practice: Whether in risk management, portfolio hedging, or option pricing, we need to have a precise notion of the market's expectation of volatility. Much research has been done on the analysis of realized historic volatilities, Roll (1977) and references therein. However, since it seems unsettling to draw conclusions from past to expected market behavior, the focus shifted to implied volatilities, Dumas, Fleming and Whaley (1998). To derive implied volatilities the Black and Scholes (BS) formula is solved for the constant volatility parameter a using observed option prices. This is a more natural approach as the option value is decisively determined by the market's assessment of current and future volatility. Hence implied volatility may be used as an indicator for market expectations over the remaining lifetime of the option. It is well known that the volatilities implied by observed market prices exhibit a pattern that is far different from the flat constant one used in the BS formula. Instead of finding a constant volatility across strikes, implied volatility appears to be non flat, a stylized fact which has been called smile effect. In this chapter we illustrate how implied volatilities can be analyzed. We focus first on a static and visual investigation of implied volatilities, then we concentrate on a dynamic analysis with two variants of principal components and interpret the results in the context of risk management

The regional impact of Indonesia's fiscal policy on oil and gas: Options for reform

This paper analyzes the regional impact of Indonesia's fuel policy. It discusses how the sharing of oil and gas revenue and taxes on oil and gas between the center and the regions affect sub-national fiscal position and what the regional incidence of the fuel subsidies is. It also analyzes the regional impact of president's recent proposal to discontinue subsidizing vehicle fuel aswell as the proposal to eliminate the fuel subsidies altogether and shows how the regions are affected ty these suggestions

Measuring spot variance spillovers when (co)variances are time-varying - the case of multivariate GARCH models

We propose global and disaggregated spillover indices that allow us to assess variance and covariance spillovers, locally in time and conditionally on time-t information. Key to our approach is the vector moving average representation of the half-vectorized `squared' multivariate GARCH process of the popular BEKK model. In an empirical application to a four-dimensional system of broad asset classes (equity, fixed income, foreign exchange and commodities), we illustrate the new spillover indices at various levels of (dis)aggregation. Moreover, we demonstrate that they are informative of the value-at-risk violations of portfolios composed of the considered asset classes

Audio-Tactile Integration in Congenitally and Late Deaf Cochlear Implant Users

Several studies conducted in mammals and humans have shown that multisensory processing may be impaired following congenital sensory loss and in particular if no experience is achieved within specific early developmental time windows known as sensitive periods. In this study we investigated whether basic multisensory abilities are impaired in hearing-restored individuals with deafness acquired at different stages of development. To this aim, we tested congenitally and late deaf cochlear implant (CI) recipients, age-matched with two groups of hearing controls, on an audio-tactile redundancy paradigm, in which reaction times to unimodal and crossmodal redundant signals were measured. Our results showed that both congenitally and late deaf CI recipients were able to integrate audio-tactile stimuli, suggesting that congenital and acquired deafness does not prevent the development and recovery of basic multisensory processing. However, we found that congenitally deaf CI recipients had a lower multisensory gain compared to their matched controls, which may be explained by their faster responses to tactile stimuli. We discuss this finding in the context of reorganisation of the sensory systems following sensory loss and the possibility that these changes cannot be "rewired" through auditory reafferentation

Charge Generation and Selective Separation at PbS Quantum Dot Metal Oxide Interfaces

Charge separation and transfer at the interface between layers of oleic acid capped PbS quantum dots QDs and Titanium and Indium Tin oxide TiO2 and ITO films were investigated by surface photovoltage SPV measurements. Photoluminescence PL measurements were performed in order to check for excitonic transitions and determine the QD band gaps. The QDs diameter of 4.2 nm and 5.0 nm were estimated by using the PL band gaps and the theoretical equation derived by Wang et al. [J. Chem. Phys. 87 1987 7315]. The SPV spectra of the PbS QDs TiO2 system reveal a positive charge on the PbS film surface and show three distinguished regions which demonstrate i the charge separation across QDs, ii the electron injection from QDs into TiO2 and iii the fundamental absorption in TiO2. The on set of the electron injection depends on the QD size QD band gap it shifts to lower photon energies for lower QD dimensions for higher QD band gaps . Thus, a better conduction band alignment is achieved in the latter case. In contrast to PbS QDs TiO2, the SPV spectra of the PbS QDs ITO structure reveal the negative charge on PbS surface. Moreover, the charge transfer at this interface is not observed. Instead, the SPV peculiarities in the photon energy range 1.4 3.0 eV point out to trapped holes on the ITO surface state

Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes (BS) expression with volatility in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile