• It is not widely emphasized in the literature that derivatives are complex random quantities which should, by custom, be characterized by their probability density functions. • It is understood that Black-Scholes style of derivatives pricing represents an expected value, i.e. the...

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram-Charlier series expansion, known as the Gauss-Hermite expansion. This expansion converges for...

We develop an ex-ante measure of expected stock returns based on analyst price targets. We then show that ex-ante measures of volatility, skewness, and kurtosis implied from stock option prices are positively related to the cross section of ex-ante expected stock returns. While expected returns...

Most of the empirical studies on stochastic volatility dynamics favor the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model is reported to be able to capture the volatility skew evolution better than...

This paper provides a number of relevant guidelines to build a consistent Volatility Smile accounting for the FX market conventions. This consistency is understood as fitting a model which is able to price vanilla options across all possible strikes given the knowledge of a few market...

The stock options implied volatility skew reflects both the structural risk characteristics of the underlying company and the short-term information flow about the stock price movement. This paper builds a semi-structural cross-sectional option pricing model to separate the structural risk...

Option prices seem to behave in ways inconsistent with the Black-Scholes model. Implied volatility varies with the strike price in a parabolic shape that is often called the volatility 'smile.' My objective in this paper is to identify implied probability distributions that might explain this...

The prices of derivatives contracts can be used to estimate ‘risk-neutral' probability density functions that give an indication of the weight investors place on different future prices of their underlying assets, were they risk-neutral. In the likely case that investors are risk-averse, this...