Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at­the­money options increases, on average, with maturity). We account for both using Gram­Charlier...

We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts...

Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at-the-money options increases, on average, with maturity). We account for both using Gram-Charlier...

We develop a new option pricing framework that tightly integrates with how institutional investors manage options positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no-arbitrage constraints on its current shape. Within this framework, we...

Risk premia are related to price probability ratios or for continuous time pure jump processes the ratios of jump arrival rates under the pricing and physical measures. The variance gamma model is employed to synthesize densities with risk premia seen as the ratio of the three parameters. The...

Index option pricing on world market indices are investigated using Lévy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a Rally Before a...

At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution...

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...

Minimal discounted distorted expectations across a range of stress levels are employed to model risk acceptability in markets. Interactions between discounting and stress levels used in measure changes are accommodated by lowering discount rates for the higher stress levels. Acceptability...

With increasing appreciation of the fact that stock return variance is stochastic and variance risk is heavily priced, the industry has created a series of variance derivative products to span variance risk. The variance swap contract is the most actively traded of these products. It pays at...