It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a...

Comonotone additivity for two price economy bid and ask prices motivates combining bid prices for call options with the ask prices for puts and the converse to construct two densities (termed lower and upper) reflected by these prices. Bilateral gamma models are fit to estimate these the lower...

Lower and upper prudent valuations in two price economies obtained on sufficiently distorting physical probabilities for returns to horizons matching option maturities straddle the market prices of options. Market prices are then modeled as geometric averages of the extremal valuations. Upper...

Two new indices for financial diversity are proposed. The first is aggregative and evaluates distance from a single factor driving returns. The second evaluates how fast correlation with a stock rises as the stock falls. Both measures are here risk neutral. The CRI is also compared with coVaR....

In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive to speed-ups of several orders of magnitude by deploying machine learning techniques based on Gaussian process...