In this note we show that the inclusion of funding costs and collateralization into the valuation of derivatives (via replication) is analogue to the modelling of cross-currency and quantoed claimes, where the role of the FX process is taken by a “fund exchange process”. Hence, classical cross-currency (alternatively risky curve models) may be used to construct rich models for (stochastic) funding. In an appendix we make two remarks motivating the use of a dedicated funding curve.

Two denizens of wilmott.com document their quest to win a data mining contest that required estimating the probability of a binary response variable given 3,751 training samples described on 1,776 dimensions. The contest's log-loss scoring metric provided strong incentives for high-confidence estimates but also strong penalties for over-confident estimates - a pay-off structure also found in strategic investment decisions. The contest offered a low-risk environment for learning in which the only thing we could lose was our dignity, not our capital. We delved into the combined effects of the curse of dimensionality and small sample sizes on the geometries of sub-regions in a high-D space. We created methods to test if a given projection or sub-region was statistically useful for classifying a data point. This work Illustrated five key lessons and many issues associated with data mining and statistical estimation in the era of “Big Data.”

Portfolio optimisation is computationally intensive and has potential for performance improvement. This paper examines the effects of evaluating large numbers of proposed solutions in parallel for use with direct search optimization. This leads to a method that has considerable performance increase. A GPU implementation demonstrates an order of magnitude performance improvement over the best available multi-threaded CPU. The new algorithm and GPU combined offer a performance increase of more than 60× compared to CPU.