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...

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...

<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...

In this article, we show how to calibrate the widely used SVI parameterization of the implied volatility smile in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form...

With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren–Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.