Ground-breaking recent work by Carr and Lee extends well-known results for variance swaps to arbitrary functions of realized variance, provided a zero-correlation assumption is made. We give a detailed mathematical analysis of some of their computations and work out the cases of volatility swaps...

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...

We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread conjecture is given.

It is known that Heston's stochastic volatility model exhibits moment explosion, and that the critical moment s+ can be obtained by solving (numerically) a simple equation. This yields a leading-order expansion for the implied volatility at large strikes: σBS(k, T)2T ∼ Ψ(s+ - 1) × k (Roger...

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...

Motivated by marginals-mimicking results for It\^o processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely $\mathcal{L}(Z_t|Y_t...

A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied volatility surface; (ii) computation of the local volatility based...

We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal...

<title>Abstract</title>We consider the three-factor double mean reverting (DMR) option pricing model of Gatheral [<italic>Consistent Modelling of SPX and VIX Options</italic>, 2008], a model which can be successfully calibrated to both VIX options and SPX options simultaneously. One drawback of this model is that calibration...