Capturing UK real estate volitility

Volatility, or the variability of the underlying asset, is one of the key fundamental components of property derivative pricing and in the application of real option models in development analysis. There has been relatively little work on volatility in real terms of its application to property derivatives and the real options analysis. Most research on volatility stems from investment performance (Nathakumaran & Newell (1995), Brown & Matysiak 2000, Booth & Matysiak 2001). Historic standard deviation is often used as a proxy for volatility and there has been a reliance on indices, which are subject to valuation smoothing effects. Transaction prices are considered to be more volatile than the traditional standard deviations of appraisal based indices. This could lead, arguably, to inefficiencies and mis-pricing, particularly if it is also accepted that changes evolve randomly over time and where future volatility and not an ex-post measure is the key (Sing 1998). If history does not repeat, or provides an unreliable measure, then estimating model based (implied) volatility is an alternative approach (Patel & Sing 2000). This paper is the first of two that employ alternative approaches to calculating and capturing volatility in UK real estate for the purposes of applying the measure to derivative pricing and real option models. It draws on a uniquely constructed IPD/Gerald Eve transactions database, containing over 21,000 properties over the period 1983-2005. In this first paper the magnitude of historic amplification associated with asset returns by sector and geographic spread is looked at. In the subsequent paper the focus will be upon model based (implied) volatility.

A simplified pricing model for volatility futures

We develop a general model to price VIX futures contracts. The model is adapted to test both the constant elasticity of variance (CEV) and the Cox–Ingersoll–Ross formulations, with and without jumps. Empirical tests on VIX futures prices provide out-of-sample estimates within 2% of the actual futures price for almost all futures maturities. We show that although jumps are present in the data, the models with jumps do not typically outperform the others; in particular, we demonstrate the important benefits of the CEV feature in pricing futures contracts. We conclude by examining errors in the model relative to the VIX characteristics

Finite departure from convective quasi-equilibrium: periodic cycle and discharge-recharge mechanism

A simple self–contained theory is proposed for describing life cycles of convective systems as a discharge–recharge process. A closed description is derived for the dynamics of an ensemble of convective plumes based on an energy cycle. The system consists of prognostic equations for the cloud work function and the convective kinetic energy. The system can be closed by intro ducing a functional relationship between the convective kinetic energy and the cloud–base mass flux. The behaviour of this system is considered under a bulk simplification. Previous cloud–resolving mo delling as well as bulk statistical theories for ensemble convective systems suggest that a plausible relationship would be to assume that the convective kinetic energy is linearly proportional to the cloud–base mass flux. As a result, the system reduces to a nonlinear dynamical system with two dependent variables, the cloud–base mass flux and the cloud work function. The fully nonlinear solution of this system always represents a periodic cycle regardless of the initial condition under constant large–scale forcing. Importantly, the inclusion of energy dissipation in this model does not in itself lead the system to an equilibrium.