A three parameter stochastic process, termed the variance gamma process, that generalizes
Brownian motion is developed as a model for the dynamics of log stock prices. Theprocess …

We propose a direct and robust method for quantifying the variance risk premium on financial
assets. We show that the risk-neutral expected value of return variance, also known as the …

… The VG option pricing model is described in detail in Madan, Carr, and Chang [9], who
document that this process effectively removes the smile observed when plotting Black Scholes …

Much research has been directed towards forecasting the volatility 1 of various
macroeconomic variables such as stock indices, interest rates and exchange rates. However, …

We describe the construction and characterization of a genomically recoded organism (GRO).
We replaced all known UAG stop codons in Escherichia coli MG1655 with synonymous …

We document a surprising pattern in S&P 500 option prices. When implied volatilities are
graphed against a standard measure of moneyness, the implied volatility smirk does not flatten …

While American calls on non-dividend-paying stocks may be valued as European, there is
no completely explicit exact solution for the values of American puts. We use a technique …

We investigate the importance of diffusion and jumps in a new model for asset returns. In
contrast to standard models, we allow for jump components displaying finite or infinite activity …

The breadth of genomic diversity found among organisms in nature allows populations to
adapt to diverse environments 1 , 2 . However, genomic diversity is difficult to generate in the …

Three processes reflecting persistence of volatility are initially formulated by evaluating
three Lévy processes at a time change given by the integral of a mean‐reverting square root …