激光二极管阵列的窄线宽、可调谐输出

外腔反馈的激光二极管阵列(LDA)可获得窄线宽、可调谐的光谱输出。外腔由快轴准直镜、准直光学系统和闪耀光栅组成。由于阵列中各发光单元的排列弯曲导致不同波长的光原路返回,引起谱线展宽,在输出光路中加入光谱滤波器,使激光二极管阵列的线宽进一步窄化。这样,激光二极管阵列的输出光谱由自由运转时的2 nm压缩到0.12 nm,在恒定温度23 ℃时,实现了激光在806～818 nm的调谐,调谐范围达12 nm。

Asymmetric Smiles, Leverage Effects and Structural Parameters.

In this paper, we characterize the asymmetries of the smile through multiple leverage effects in a stochastic dynamic asset pricing framework. The dependence between price movements and future volatility is introduced through a set of latent state variables. These latent variables can capture not only the volatility risk and the interest rate risk which potentially affect option prices, but also any kind of correlation risk and jump risk. The standard financial leverage effect is produced by a cross-correlation effect between the state variables which enter into the stochastic volatility process of the stock price and the stock price process itself. However, we provide a more general framework where asymmetric implied volatility curves result from any source of instantaneous correlation between the state variables and either the return on the stock or the stochastic discount factor. In order to draw the shapes of the implied volatility curves generated by a model with latent variables, we specify an equilibrium-based stochastic discount factor with time non-separable preferences. When we calibrate this model to empirically reasonable values of the parameters, we are able to reproduce the various types of implied volatility curves inferred from option market data.

Empirical Assessment of an Intertemporal Option Pricing Model with Latent variables

This paper assesses the empirical performance of an intertemporal option pricing model with latent variables which generalizes the Hull-White stochastic volatility formula. Using this generalized formula in an ad-hoc fashion to extract two implicit parameters and forecast next day S&P 500 option prices, we obtain similar pricing errors than with implied volatility alone as in the Hull-White case. When we specialize this model to an equilibrium recursive utility model, we show through simulations that option prices are more informative than stock prices about the structural parameters of the model. We also show that a simple method of moments with a panel of option prices provides good estimates of the parameters of the model. This lays the ground for an empirical assessment of this equilibrium model with S&P 500 option prices in terms of pricing errors.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

Linewidth reduction in a large-smile laser diode array

We present theory and simulations for a spectral narrowing scheme for laser diode arrays (LDAs) that employs optical feedback from a diffraction grating. We calculate the effect of the so-called smile of the LDA and show that it is possible to reduce the effect by using a cylindrical lens set at an angle to the beam. The scheme is implemented on a 19-element LDA with smile of 7.6 mu m and yields frequency narrowing from a free-running width of 2 to 0.15 nm. The experimental results are in good agreement with the theory. (c) 2005 Optical Society of America.