Volatility Parameter Research Articles

A New Spin on the Jumbo/Conforming Loan Rate Differential

This article uses house-price transaction data to estimate volatility in house prices. The volatility parameter is an input into a mortgage-pricing model that is used to simulate the contract interest rate that balances the mortgage contract. By segmenting the house-price transaction into high- and low-valued homes, we are able to estimate a theoretical jumbo/conforming loan rate differential. Simulation results demonstrate that the differences in volatility between high- and low-priced homes can produce a contract loan rate differential, holding all else constant. The article also presents a discussion of the problems inherent to estimating volatilities form assets with infrequent trades and long holding periods.

High Frequency Deutsche Mark-US Dollar Returns: FIGARCH Representations and Non Linearities

This article considers the use of the long memory volatility process, FIGARCH, in representing Deutschemark - US dollar spot exchange rate returns for both high and low frequency returns data. The FIGARCH model is found to be the preferred specification for both high frequency and daily returns data, with similar values of the long memory volatility parameter across frequencies, which is indicative of returns being generated by a self similar process. The BDS test for non-linearity is applied to the residuals of the model for the high frequency returns. No evidence is found to suggest that the procedure for filtering the high frequency returns to remove the intraday periodicity has induced any non-linearities in the residuals; and the FIGARCH specification is found to be adequate.

Long Memory in Stock-Market Trading Volume

This article examines consistent estimation of the long-memory parameters of stock-market trading volume and volatility. The analysis is carried out in the frequency domain by tapering the data instead of detrending them. The main theoretical contribution of the article is to prove a central limit theorem for a multivariate two-step estimator of the memory parameters of a nonstationary vector process. Using robust semiparametric procedures, the long-memory properties of trading volume for the 30 stocks in the Dow Jones Industrial Average index are analyzed. Two empirical results are found. First, there is strong evidence that stock-market trading volume exhibits long memory. Second, although it is found that volatility and volume exhibit the same degree of long memory for most of the stocks, there is no evidence that both processes share the same long-memory component.

American Options Exercise Boundary When the Volatility Changes Randomly

The American put option exercise boundary has been studied extensively as a function of time and the underlying asset price. In this paper we analyze its dependence on the volatility, since the Black and Scholes model is used in practice via the (varying) implied volatility parameter. We consider a stochastic volatility model for the underlying asset price. We provide an extension of the regularity results of the American put option price function and we prove that the optimal exercise boundary is a decreasing function of the current volatility process realization.

Effects of Surface Tension and Binary Diffusion on Pool Boiling of Dilute Solutions: An Experimental Assessment

Pool boiling heat transfer with dilute binary mixtures introduces two additional effects due to binary diffusion, and due to change in the surface tension. The secondary effects due to changes in contact angle and wetting characteristics may also play a role. The present study focuses on identifying these effects for dilute aqueous solutions of ethylene glycol. Pool boiling experiments are conducted to generate data in the range of one to ten percent mass fraction. It is found that in the low concentration region, the binary diffusion effects are insignificant for aqueous solutions of ethylene glycol, and a slight improvement in heat transfer coefficient is observed over the pure water value. The binary diffusion effects are related to a volatility parameter, V1. The heat transfer coefficient does not degrade in the region where V1 < 0.03, and the surface tension does not change appreciably compared to pure water value. This points to the possibility that the changes in contact angle and wetting characteristics play an important role in the pool boiling heat transfer.

Stain resistance in resilient sheet flooring applications: The role of the plasticizer

AbstractStain resistance, or more properly, appearance retention, is a complex phenomenon in resilient sheet flooring applications. The process can be complex, involving the plasticizer, the overall toughness (or abrasion resistance) of the wear layer, and the thermoplastic nature of plasticized PVC. This paper explores the plasticizer related portions of the stain resistance phenomenon. Data are presented to illustrate relationships between stain resistance and plasticizer structure, concentration, extraction resistance, volatility, and solubility parameter.

Capturing all the information in foreign currency option prices: solving for one versus two implied variables

The information content of option prices has traditionally been expressed in an implied volatility parameter which is characterized as capturing the markets expectations about future volatility of the underlying asset. Researchers normally solve for an implied volatility alone. A more recent trend has been to solve for both an implied interest rate and standard deviation simultaneously. This study compares the proficiency of these two techniques in capturing the information in the market prices of foreign currency options. The results show that solving for two implied variables consistently yields less information than solving for an implied volatility alone. This raises the implication that by trying to reduce one source of bias by solving for two variables simultaneously, researchers may be introducing a more serious source of error resulting in a dilution of the available information.

Do Reuters spreads reflect currencies' differences in global trading activity?

A new estimation of the long-run impact of trading activity on bid–ask spreads in the foreign exchange markets is undertaken with a short panel containing around-the-clock Reuters quotes and global transaction volumes. Individual and time effects are accounted for in an unbalanced random effects model. In line with liquidity effect explanations the volume parameter is found to have a (weakly) significant negative sign, whereas the volatility parameter is positive. Structural parameters are stable over time, while residuals are groupwise heteroscedastic. Reuters quoting (`tick') frequency is also tested as a measure of trading activity with very similar results.)

Boiling Heat Transfer With Binary Mixtures: Part II—Flow Boiling in Plain Tubes

Flow boiling heat transfer with pure fluids comprises convective and nucleate boiling components. In flow boiling of binary mixtures, in addition to the suppression effects present in pool boiling, the presence of flow further modifies the nucleate boiling characteristics. In the present work, the flow boiling correlation by Kandlikar (1990, 1991b) for pure fluids is used as the starting point, and the mixture effects derived in Part I (Kandlikar, 1998) of this paper are incorporated. Three regions are defined on the basis of a volatility parameter, V1 = (cp/ΔhLG)(k/D12)1/2|(y1 − x1)dT/dx1|. They are: region I—near azeotropic, region II—moderate diffusion-induced suppression, and region III—severe diffusion-induced suppression. The resulting correlation is able to correlate over 2500 data points within 8.3 to 13.3 percent mean deviation for each data set. Furthermore, the α–x trend is represented well for R-12/R-22, R-22/R-114, R-22/R-152a, R-500, and R-132a/R-123 systems. Electrically heated stainless steel test sections as well as fluid-heated copper test sections are both covered under this correlation.

Volatility misspecification, option pricing and superreplication via coupling

Consider the performance of an options writer who misspecifies the dynamics of the price process of the underlying asset by overestimating asset price volatility. When does he overprice the option? If he follows the hedging strategy suggested by his model, when does the terminal value of his strategy dominate the option payout? We show that both these events happen if the option payoff is a convex function of the price of the underlying at maturity. The proofs involve the simple, powerful and intuitive techniques of coupling. 1. Robust hedging and superreplication. The standard approach in mathematical finance, and particularly in the pricing of derivative securities, is to begin by writing down a stochastic model, which is assumed, without comment, to correctly and precisely specify the dynamics of the underlying asset. Arbitrage theory, backed by change of measure techniques and martingale representation theorems, then allows options to be priced and hedged. The fairness of the price and the success of the hedge depend crucially on the truth of the underlying model. The purpose of this article is to consider the implications of a misspecification of the dynamics of the asset price process. In particular, if the options writer uses an incorrect model, when does he overcharge for the option? Further, if he attempts to hedge using this incorrect model, can he still replicate (or rather superreplicate) the option payoff? (A superreplicating strategy is a dynamic hedging strategy which generates a terminal wealth which stochastically dominates the option payout.) It is well known that the price of a call option in the Black-Scholes model is an increasing function of the volatility parameter and that this monotonicity property extends to all European options with convex payoff profiles. We generalize this result to prove a price comparison theorem for pairs of models with stochastic volatilities. We have in mind the scenario where one model is used by the options writer to price and hedge options, and the second model represents the (unknown) truth.

Generalized Binomial Trees

We consider the problem of consistently pricing new options given the prices of related options on the same stock. The Black-Scholes formula and standard binomial trees can only accommodate one related European option which then effectively specifies the volatility parameter. Implied binomial trees can accommodate only related European options with the same time-to-expiration. The generalized binomial trees introduced here can accommodate any kind of related options (European, American, or exotic) with different times-to-expiration.

Local parametric analysis of hedging in discrete time

When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained from a novel estimation procedure, namely local parametric estimation. In the latter, the weights of the duplicating portfolio are estimated by fitting parametric models (in this paper, Black-Scholes) in the neighborhood of the derivative's moneyness and maturity. Local parametric estimation directly incorporates the error from hedging in discrete time. Results are shown where the root mean square tracking error is reduced up to 41% for short-maturity options. The performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters. The root mean square tracking error is thereby reduced by about 18% for long-maturity options. Plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the Black-Scholes model when hedging in discrete time. In particular, there is a sharp ‘smile’ effect in the relation between estimated volatility and moneyness for short-maturity options, as well as a significant ‘wave’ effect in the relation with maturity for deep out-of-the-money options.

Measuring fair capital adequacy holdings for banks: The case of Taiwan

An option-theoretical framework was employed to solve the level of capital at which Taiwan's deposit insurer would just break even in guaranteeing the deposits of individual banks. The method is applied to ten banks in Taiwan yearly from 1985 to 1992. Asset value and volatility parameters were estimated using the maximum likelihood method via market-based equity data. These critical values were then applied as inputs in Merton's (7) deposit insurance pricing model towards yielding the fair levels of capital adequacy for each individual bank. The estimates showed that, except for in 1989, most of the sample banks were inadequately capitalized. Additionally, estimates of adequate levels of capital for the four commercial banks were found to generally exceed 10 billion NT (US$ 400 million). This finding indicates that the 10 billion NT initial capital requirement now imposed on new commercial banks, though generally perceived as high by the public, may actually not be adequate.

An empirical investigation of the two-factor Brennan-Schwartz term structure model

This paper studies the pricing behaviors of default-free bonds based on the two-factor model by Brennan and Schwartz (1979), where a short-term spot rate and a long-term consol rate are the state variables. The logarithm of these two factors is assumed to follow a linear transformation of an Ornstein-Uhlenbeck process. An exact discrete time model is derived to estimate the parameters in the process. The model prices are then numerically solved. The sensitivity analysis indicates that the long-rate process, especially the long-rate volatility parameter, is important in characterizing the term structure of interest rates.

A simple class of square-root interest-rate models

An analytically tractable class of square-root interest-rate models is introduced. Algebraic expressions are found for the drift and volatility parameters of the short rate in terms of initial yield and volatility curves. Explicit formulae are derived for bond, Arrow-Debreu, and European and American bond options.

Physical properties and evaporation characteristics of nonaqueous insecticide formulations, spray diluents and adjuvant/co-solvent mixtures

Abstract Three chemical insecticides, tebufenozide, permethrin and diflubenzuron, and a bacterial control agent, Bacillus thuringiensis var. kurstaki, were mixed with oil‐based carrier diluents or diluent oil mixtures to provide several spray formulations. In addition, two adjuvants, Triton® X‐114 and glycerol, were mixed with hydroxylic co‐solvents to provide adjuvant/co‐solvent mixtures. All of these liquids were tested for their evaporation behaviour using a gravimetric method. The data were subjected to linear regression analysis to determine three volatility parameters, i.e., evaporation rate (ER), nonvolatile components (NVC%) and half‐life of evaporation, T1/2. In addition, a new equation was developed to determine the fourth volatility parameter, mean loss of mass per min (MLMPM). Viscosity (η) and surface tension (γ), were also measured to determine the relationships of the two physical properties with the four volatility parameters. Viscosity showed a better correlation with the volatility param...

Volatility Shifts in Stock Market Returns : A Look at Emerging Markets

The volatility or risk parameter, usually defined as the standard deviation of stock returns, forms the cornerstone of contemporary finance theories. Reliability of results obtained from various financial decision making models depends on the stability, finiteness, and accuracy of risk estimates. This paper by Broca examines the stability of this parameter using weekly market data over 1990-91 in respect of 17 emerging markets identified by the International Finance Corporation. Through an application of nonparametric test procedures, the study detects variance heterogeneity for 6 out of 17 markets. Though not pervasive, a review of major political-economic events over the sample period, with special reference to the Gulf crisis of August 1990, is attempted to partly validate empirical findings.

Unit root tests with conditional heteroskedasticity

This paper considers the finite-sample accuracy (size) of the Dickey-Fullerunit root tests when the errors are conditionally heteroskedastic. We consider the specific case that the error variance follows a GARCH (1,1) model. The Dickey-Fuller tests tend to overreject in the presence of GARCH errors, but the problem is not very serious except when the variance process is nearly degenerate (in the sense that the ratio of the GARCH intercept to the initial variance is near zero) and the volatility parameter is large.

Ultrasonic degradation of polymer solutions—III. The effect of changing solvent and solution concentration

This paper presents part of a comprehensive study of the ultrasonic degradation of polystyrene solutions. The efficiency of the process with changing concentration was studied in toluene and methyl butyrate and was found to decrease at higher concentration. In addition, degradations were performed in 13 solvents and the variations correlated in terms of the volatility and thermodynamic parameters of the solvent. The results are explained in terms of a mechanism involving shear forces generated around collapsing cavitation bubbles.

Improving the Parkinson Method of Estimating Security Price Volatilities

The author proposes a new method for estimating the volatility parameters of security prices, which is an improvement of the estimation method by M. Parkinson (1980). The author assumes that the security prices follow the geometric Brownian motion. However, contrary to the setting of Parkinson, the geometric Brownian motion may have nonzero drift terms. The author shows that the efficiency of his estimator is about 10 in comparison with the standard sample variance estimator. Since the efficiency of the estimator by Parkinson is about 4.91, his estimation method may considerably improve the estimation methods already known in financial economics. Copyright 1992 by University of Chicago Press.