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

Monte Carlo analysis of methods for extracting risk-neutral densities with affine jump diffusions

YesThis paper compares several widely-used and recently-developed methods to extract risk-neutral densities (RND) from option prices in terms of estimation accuracy. It shows that positive convolution approximation method consistently yields the most accurate RND estimates, and is insensitive to the discreteness of option prices. RND methods are less likely to produce accurate RND estimates when the underlying process incorporates jumps and when estimations are performed on sparse data, especially for short time-to-maturities, though sensitivity to the discreteness of the data differs across different methods

Option Pricing Kernels and the ICAPM

We estimate the parameters of pricing kernels that depend on both aggregate wealth and state variables that describe the investment opportunity set, using FTSE 100 and S&P 500 index option returns as the returns to be priced. The coefficients of the state variables are highly significant and remarkably consistent across specifications of the pricing kernel, and across the two markets. The results provide further evidence that, consistent with Merton's (1973) Intertemporal Capital Asset Pricing Model, state variables in addition to market risk are priced

Analogy making and the structure of implied volatility skew

An analogy based option pricing model is put forward. If option prices are determined in accordance with the analogy model, and the Black Scholes model is used to back-out implied volatility, then the implied volatility skew arises, which flattens as time to expiry increases. The analogy based stochastic volatility and the analogy based jump diffusion models are also put forward. The analogy based stochastic volatility model generates the skew even when there is no correlation between the stock price and volatility processes, whereas, the analogy based jump diffusion model does not require asymmetric jumps for generating the skew

Option prices under Bayesian learning: implied volatility dynamics and predictive densities

This paper shows that many of the empirical biases of the Black and Scholes option pricing model can be explained by Bayesian learning effects. In the context of an equilibrium model where dividend news evolve on a binomial lattice with unknown but recursively updated probabilities we derive closed-form pricing formulas for European options. Learning is found to generate asymmetric skews in the implied volatility surface and systematic patterns in the term structure of option prices. Data on S&P 500 index option prices is used to back out the parameters of the underlying learning process and to predict the evolution in the cross-section of option prices. The proposed model leads to lower out-of-sample forecast errors and smaller hedging errors than a variety of alternative option pricing models, including Black-Scholes and a GARCH model

Inductively coupled plasma mass spectrometric detection for multielement flow injection analysis and elemental speciation by reversed-phase liquid chromatography

The feasibility of using an inductively coupled plasma mass spectrometer as a muitieiement detector for flow injection analysis (FIA) and ion-pair reversed-phase liquid chromatography was investigated. Sample introduction was by uitrasonk nebulization with aerosol desolvation. Absolute detecton limits for FIA ranged from 0.01 to 0.1 ng for most elements using 10-pL injections. Over 30 elements were surveyed for their response to both anionic and cationic ion pairing reagents. The separation and selective detection of various As and Se species were demonstrated, yielding detection limits near 0.1 ng (as element) for ail six species present. Determination of 15 elements in a single injection with multiple ion monitoring produced shniiar detection limits. Isotope ratios were measured with sufficient precision (better than 2%) and accuracy (about 1 %) on eluting peaks of Cd and Pb to demonstrate that liquid chromatographyhductively coupled plasma mass spectrometry should make speciation studies with stable tracer isotopes feasible