Analytic approximations for multi-asset option pricing

We derive general analytic approximations for pricing European basket and rainbow options on N assets. The key idea is to express the option’s price as a sum of prices of various compound exchange options, each with different pairs of subordinate multi- or single-asset options. The underlying asset prices are assumed to follow lognormal processes, although our results can be extended to certain other price processes for the underlying. For some multi-asset options a strong condition holds, whereby each compound exchange option is equivalent to a standard single-asset option under a modified measure, and in such cases an almost exact analytic price exists. More generally, approximate analytic prices for multi-asset options are derived using a weak lognormality condition, where the approximation stems from making constant volatility assumptions on the price processes that drive the prices of the subordinate basket options. The analytic formulae for multi-asset option prices, and their Greeks, are defined in a recursive framework. For instance, the option delta is defined in terms of the delta relative to subordinate multi-asset options, and the deltas of these subordinate options with respect to the underlying assets. Simulations test the accuracy of our approximations, given some assumed values for the asset volatilities and correlations. Finally, a calibration algorithm is proposed and illustrated.

Real option pricing in mixed-use development projects

The application of real options theory to commercial real estate has developed rapidly during the last 15 Years. In particular, several pricing models have been applied to value real options embedded in development projects. In this study we use a case study of a mixed use development scheme and identify the major implied and explicit real options available to the developer. We offer the perspective of a real market application by exploring different binomial models and the associated methods of estimating the crucial parameter of volatility. We include simple binomial lattices, quadranomial lattices and demonstrate the sensitivity of the results to the choice of inputs and method.

Pricing the options inherent in leased commercial property: a UK case study

This paper sets out the findings of a group of research and development projects carried out at the Department of Real Estate & Planning at the University of Reading and at Oxford Property Systems over the period 1999 – 2003. The projects have several aims: these are to identify the fundamental drivers of the pricing of different lease terms in the UK property sector; to identify current and best market practice and uncover the main variations in lease terms; to identify key issues in pricing lease terms; and to develop a model for the pricing of rent under a variety of lease variations. From the landlord’s perspective, the main factors driving the required ‘compensation’ for a lease term amendment include expected rental volatility, expected probability of tenant vacation, and the expected costs of tenant vacation. These data are used in conjunction with simulation technology to reflect the options inherent in certain lease types to explore the required rent adjustment. The resulting cash flows have interesting qualities which illustrate the potential importance of option pricing in a non-complex and practical way.

Modelling niches of arbitrary shape in genetic algorithms using Niche Linkage in the Dynamic Niche Clustering framework

We present some additions to a fuzzy variable radius niche technique called Dynamic Niche Clustering (DNC) (Gan and Warwick, 1999; 2000; 2001) that enable the identification and creation of niches of arbitrary shape through a mechanism called Niche Linkage. We show that by using this mechanism it is possible to attain better feature extraction from the underlying population.

Dynamic Niche Clustering: a fuzzy variable radius niching technique for multimodal optimisation in GAs

This paper describes the recent developments and improvements made to the variable radius niching technique called Dynamic Niche Clustering (DNC). DNC is fitness sharing based technique that employs a separate population of overlapping fuzzy niches with independent radii which operate in the decoded parameter space, and are maintained alongside the normal GA population. We describe a speedup process that can be applied to the initial generation which greatly reduces the complexity of the initial stages. A split operator is also introduced that is designed to counteract the excessive growth of niches, and it is shown that this improves the overall robustness of the technique. Finally, the effect of local elitism is documented and compared to the performance of the basic DNC technique on a selection of 2D test functions. The paper is concluded with a view to future work to be undertaken on the technique.