Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka~[Adv.~Math.~Econ.~6, 69--83, 2004] and Lyons--Victoir~[Proc.~R.~Soc.\\Lond.~Ser.~A 460, 169--198, 2004], involve the solution to numerous auxiliary ordinary differential equations. With focus on the Ninomiya-Victoir...

The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in Financial and Actuarial Mathematics.) In...

Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka [<italic>Adv. Math. Econ</italic>., 2004, <bold>6</bold>, 69--83] and Lyons--Victoir [<italic>Proc. R. Soc. Lond. Ser. A</italic>, 2004, <bold>460</bold>, 169--198], involve the solution to numerous auxiliary ordinary differential equations (ODEs). With focus on the Ninomiya--Victoir...

From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough...