Ait-Sahalia and Lo (2000) and Panigirtzoglou and Skiadopoulos (2004) have argued that Economic VaR (E-VaR), calculated under the option market implied risk neutral density is a more relevant measure of risk than historically based VaR. As industry practice requires VaR at high confidence level of 99%, we propose Extreme Economic Value at Risk (EE-VaR) as a new risk measure, based on the General...

One of the central goals in finance is to find better models for pricing and hedging financial derivatives such as call and put options. We present a new semi-nonparametric approach to risk-neutral density extraction from option prices, which is based on an extension of the concept of mixture density networks. The central idea is to model the shape of the risk-neutral density in a flexible, non...

1 Introduction This paper is concerned with the use of stock indices futures to hedge the return on portfolios. This topic has received considerable attention in the literature, which will be briefly summarised in section 2 of the paper. First of all it is desirable to consider the nature of hedging. The main aim of hedging is assumed to be the minimisation of the variance of the return on the ...

A continuous time random walk (CTRW) imposes a random waiting time between random particle jumps. CTRW limit densities solve a fractional Fokker-Planck equation, but since the CTRW limit is not Markovian, this is not sufficient to characterize the process. This paper applies continuum renewal theory to restore the Markov property on an expanded state space, and compute the joint CTRW limit dens...