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.

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).

Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

Calibration of stochastic volatility models via second order approximation: the Heston model case

Using a suitable Hull and White type formula we develop a methodology to obtain asecond order approximation to the implied volatility for very short maturities. Using thisapproximation we accurately calibrate the full set of parameters of the Heston model. Oneof the reasons that makes our calibration for short maturities so accurate is that we alsotake into account the term-structure for large maturities. We may say that calibration isnot "memoryless", in the sense that the option's behavior far away from maturity doesinfluence calibration when the option gets close to expiration. Our results provide a wayto perform a quick calibration of a closed-form approximation to vanilla options that canthen be used to price exotic derivatives. The methodology is simple, accurate, fast, andit requires a minimal computational cost.

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.

On the goodness of fit of Kirk's formula for spread option prices

In this paper we investigate the goodness of fit of the Kirk's approximation formula for spread option prices in the correlated lognormal framework. Towards this end, we use the Malliavin calculus techniques to find an expression for the short-time implied volatility skew of options with random strikes. In particular, we obtain that this skew is very pronounced in the case of spread options with extremely high correlations, which cannot be reproduced by a constant volatility approximation as in the Kirk's formula. This fact agrees with the empirical evidence. Numerical examples are given.

A signaling mechanism coupling netrin-1/deleted in colorectal cancer chemoattraction to SNARE-mediated exocytosis in axonal growth cones

Directed cell migration and axonal guidance are essential steps in neural development. Both processes are controlled by specific guidance cues that activate the signaling cascades that ultimately control cytoskeletal dynamics. Another essential step in migration and axonal guidance is the regulation of plasmalemma turnover and exocytosis in leading edges and growth cones. However, the cross talk mechanisms linking guidance receptors and membrane exocytosis are not understood. Netrin-1 is a chemoattractive cue required for the formation of commissural pathways. Here, we show that the Netrin-1 receptor deleted in colorectal cancer (DCC) forms a protein complex with the t-SNARE (target SNARE) protein Syntaxin-1 (Sytx1). This interaction is Netrin-1 dependent both in vitro and in vivo, and requires specific Sytx1 and DCC domains. Blockade of Sytx1 function by using botulinum toxins abolished Netrin-1-dependent chemoattraction of axons in mouse neuronal cultures. Similar loss-of-function experiments in the chicken spinal cord in vivo using dominant-negative Sytx1 constructs or RNAi led to defects in commissural axon pathfinding reminiscent to those described in Netrin-1 and DCC loss-of-function models. We also show that Netrin-1 elicits exocytosis at growth cones in a Sytx1-dependent manner. Moreover, we demonstrate that the Sytx1/DCC complex associates with the v-SNARE (vesicle SNARE) tetanus neurotoxin-insensitive vesicle-associated membrane protein (TI-VAMP) and that knockdown of TI-VAMP in the commissural pathway in the spinal cord results in aberrant axonal guidance phenotypes. Our data provide evidence of a new signaling mechanism that couples chemotropic Netrin-1/DCC axonal guidance and Sytx1/TI-VAMP SNARE proteins regulating membrane turnover and exocytosis.

A signaling mechanism coupling netrin-1/deleted in colorectal cancer chemoattraction to SNARE-mediated exocytosis in axonal growth cones

Directed cell migration and axonal guidance are essential steps in neural development. Both processes are controlled by specific guidance cues that activate the signaling cascades that ultimately control cytoskeletal dynamics. Another essential step in migration and axonal guidance is the regulation of plasmalemma turnover and exocytosis in leading edges and growth cones. However, the cross talk mechanisms linking guidance receptors and membrane exocytosis are not understood. Netrin-1 is a chemoattractive cue required for the formation of commissural pathways. Here, we show that the Netrin-1 receptor deleted in colorectal cancer (DCC) forms a protein complex with the t-SNARE (target SNARE) protein Syntaxin-1 (Sytx1). This interaction is Netrin-1 dependent both in vitro and in vivo, and requires specific Sytx1 and DCC domains. Blockade of Sytx1 function by using botulinum toxins abolished Netrin-1-dependent chemoattraction of axons in mouse neuronal cultures. Similar loss-of-function experiments in the chicken spinal cord in vivo using dominant-negative Sytx1 constructs or RNAi led to defects in commissural axon pathfinding reminiscent to those described in Netrin-1 and DCC loss-of-function models. We also show that Netrin-1 elicits exocytosis at growth cones in a Sytx1-dependent manner. Moreover, we demonstrate that the Sytx1/DCC complex associates with the v-SNARE (vesicle SNARE) tetanus neurotoxin-insensitive vesicle-associated membrane protein (TI-VAMP) and that knockdown of TI-VAMP in the commissural pathway in the spinal cord results in aberrant axonal guidance phenotypes. Our data provide evidence of a new signaling mechanism that couples chemotropic Netrin-1/DCC axonal guidance and Sytx1/TI-VAMP SNARE proteins regulating membrane turnover and exocytosis.

A signaling mechanism coupling netrin-1/deleted in colorectal cancer chemoattraction to SNARE-mediated exocytosis in axonal growth cones

Directed cell migration and axonal guidance are essential steps in neural development. Both processes are controlled by specific guidance cues that activate the signaling cascades that ultimately control cytoskeletal dynamics. Another essential step in migration and axonal guidance is the regulation of plasmalemma turnover and exocytosis in leading edges and growth cones. However, the cross talk mechanisms linking guidance receptors and membrane exocytosis are not understood. Netrin-1 is a chemoattractive cue required for the formation of commissural pathways. Here, we show that the Netrin-1 receptor deleted in colorectal cancer (DCC) forms a protein complex with the t-SNARE (target SNARE) protein Syntaxin-1 (Sytx1). This interaction is Netrin-1 dependent both in vitro and in vivo, and requires specific Sytx1 and DCC domains. Blockade of Sytx1 function by using botulinum toxins abolished Netrin-1-dependent chemoattraction of axons in mouse neuronal cultures. Similar loss-of-function experiments in the chicken spinal cord in vivo using dominant-negative Sytx1 constructs or RNAi led to defects in commissural axon pathfinding reminiscent to those described in Netrin-1 and DCC loss-of-function models. We also show that Netrin-1 elicits exocytosis at growth cones in a Sytx1-dependent manner. Moreover, we demonstrate that the Sytx1/DCC complex associates with the v-SNARE (vesicle SNARE) tetanus neurotoxin-insensitive vesicle-associated membrane protein (TI-VAMP) and that knockdown of TI-VAMP in the commissural pathway in the spinal cord results in aberrant axonal guidance phenotypes. Our data provide evidence of a new signaling mechanism that couples chemotropic Netrin-1/DCC axonal guidance and Sytx1/TI-VAMP SNARE proteins regulating membrane turnover and exocytosis.

Are one factor logarithmic volatility models useful to fit the features of financial data? An application to microsoft data.

This paper provides empirical evidence that continuous time models with one factor of volatility, in some conditions, are able to fit the main characteristics of financial data. It also reports the importance of the feedback factor in capturing the strong volatility clustering of data, caused by a possible change in the pattern of volatility in the last part of the sample. We use the Efficient Method of Moments (EMM) by Gallant and Tauchen (1996) to estimate logarithmic models with one and two stochastic volatility factors (with and without feedback) and to select among them.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

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.

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

This comment corrects the errors in the estimation process that appear in Martins (2001). The first error is in the parametric probit estimation, as the previously presented results do not maximize the log-likelihood function. In the global maximum more variables become significant. As for the semiparametric estimation method, the kernel function used in Martins (2001) can take on both positive and negative values, which implies that the participation probability estimates may be outside the interval [0,1]. We have solved the problem by applying local smoothing in the kernel estimation, as suggested by Klein and Spady (1993).