Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

Inflation, political instability and stockmarket volatility in interwar Germany

What determined the volatility of asset prices in Germany between thewars? This paper argues that the influence of political factors has beenoverstated. The majority of events increasing political uncertainty hadlittle or no effect on the value of German assets and the volatility ofreturns on them. Instead, it was inflation (and the fear of it) that islargely responsible for most of the variability in asset returns.

Rethinking the effects of financial liberalization

During the last few decades, many emerging markets have lifted restrictions on cross-borderfinancial transactions. The conventional view was that this would allow these countries to: (i)receive capital inflows from advanced countries that would finance higher investment and growth;(ii) insure against aggregate shocks and reduce consumption volatility; and (iii) accelerate thedevelopment of domestic financial markets and achieve a more efficient domestic allocationof capital and better sharing of individual risks. However, the evidence suggests that thisconventional view was wrong.In this paper, we present a simple model that can account for the observed effects of financialliberalization. The model emphasizes the role of imperfect enforcement of domestic debts and theinteractions between domestic and international financial transactions. In the model, financialliberalization might lead to different outcomes: (i) domestic capital flight and ambiguous effectson net capital flows, investment, and growth; (ii) large capital inflows and higher investmentand growth; or (iii) volatile capital flows and unstable domestic financial markets. The modelshows how these outcomes depend on the level of development, the depth of domestic financialmarkets, and the quality of institutions.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Responsiveness of astrocytes in serum-free aggregate cultures to epidermal growth factor: dependence on the cell cycle and the epidermal growth factor concentration.

Serum-free aggregating cell cultures of fetal rat telencephalon treated with low doses (0.5 nM) of epidermal growth factor (EGF) showed a small, transient increase in DNA synthesis but no significant changes in total DNA and protein content. By contrast, treatment with high doses (13 nM) of EGF caused a marked stimulation of DNA synthesis as well as a net increase in DNA and protein content. The expression of the astrocyte-specific enzyme, glutamine synthetase, was greatly enhanced both at low and at high EGF concentrations. These results suggest that at low concentration EGF stimulates exclusively the differentiation of astrocytes, whereas at high concentration, EGF has also a mitogenic effect. Nonproliferating astrocytes in cultures treated with 0.4 microM 1-beta-D-arabinofuranosyl-cytosine were refractory to EGF treatment, indicating that their responsiveness to EGF is cell cycle-dependent. Binding studies using a crude membrane fraction of 5-day cultures showed a homogeneous population of EGF binding sites (Kd approximately equal to 2.6 nM). Specific EGF binding sites were found also in non-proliferating (and nonresponsive) cultures, although they showed slightly reduced affinity and binding capacity. This finding suggests that the cell cycle-dependent control of astroglial responsiveness to EGF does not occur at the receptor level. However, it was found that the specific EGF binding sites disappear with progressive cellular differentiation.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Why do the ithomiines (Lepidoptera, Nymphalidae) aggregate? Notes on a butterfly pocket in central Brazil

This study provides information on the species composition and the number of butterflies in different phases of an ithomiine aggregation during the 2004 dry season in central Brazil, and tests some hypotheses concerning the pocket formation. The results obtained suggest that ithomiine pockets constitute primarily an adaptation of butterflies to the adverse climatic conditions of the dry season, such as high temperatures and low air relative humidity, rather than the occurrence of large concentrations of adult food resources (flowers visited for nectar were not found in the pocket site) or defense against visually hunting predators (contrary to the prediction tested, the frequency of butterflies bearing birds beak marks on the wings significantly increased along the period of pocket formation, especially in the case of Mechanitis polymnia, the most abundant species in the pocket). Other hypotheses concerning the pocket formation are also discussed.

Asset pricing with idiosyncratic risk and overlapping generations

A number of existing studies have concluded that risk sharing allocations supported by competitive, incomplete markets equilibria are quantitatively close to first-best. Equilibrium asset prices in these models have been difficult to distinguish from those associated with a complete markets model, the counterfactual features of which have been widely documented. This paper asks if life cycle considerations, in conjunction with persistent idiosyncratic shocks which become more volatile during aggregate downturns, can reconcile the quantitative properties of the competitive asset pricing framework with those of observed asset returns. We begin by arguing that data from the Panel Study on Income Dynamics support the plausibility of such a shock process. Our estimates suggest a high degree of persistence as well as a substantial increase in idiosyncratic conditional volatility coincident with periods of low growth in U.S. GNP. When these factors are incorporated in a stationary overlapping generations framework, the implications for the returns on risky assets are substantial. Plausible parameterizations of our economy are able to generate Sharpe ratios which match those observed in U.S. data. Our economy cannot, however, account for the level of variability of stock returns, owing in large part to the specification of its production technology.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Monetary policy and exchange rate volatility in a small open economy

We lay out a small open economy version of the Calvo sticky price model, and show how the equilibrium dynamics can be reduced to simple representation in domestic inflation and the output gap. We use the resulting framework to analyze the macroeconomic implications of three alternative rule-based policy regimes for the small open economy: domestic inflation and CPI-based Taylor rules, and an exchange rate peg. We show that a key difference amongthese regimes lies in the relative amount of exchange rate volatility that they entail. We also discuss a special case for which domestic inflation targeting constitutes the optimal policy, and where a simple second order approximation to the utility of the representative consumer can be derived and used to evaluate the welfare losses associated with the suboptimal rules.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.