Central limit theorem for the multilevel Monte Carlo Euler method

This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg-Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the limiting variance in the central limit theorem of the algorithm. A complexity of the multilevel Monte Carlo algorithm is carried out.Comment: Published in at http://dx.doi.org/10.1214/13-AAP993 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Working Paper 118 - Assessment of the Trade Finance Market in Africa Post-Crisis

The financial crisis, which began to hit the trade finance markets in 2008, caused a sharp slow-down in trade in 2008 and 2009. The tightening of global credit reduced capital inflows and curtailed the availability of trade finance. This sudden shortage of trade finance negatively impacted African economies. In response, the African Development Bank (AfDB) established, on March 2009, a multiphase USD 1 billion Trade Finance Initiative (TFI). As part of the Trade Finance Initiative, AfDB commissioned a trade finance survey conducted three times between 2009 and 2010. The financial institutions contacted during these market surveys are listed at the end of this document. During this research, banks in Senegal, Burkina Faso, Ghana, Nigeria, Egypt, Morocco, Kenya, South Africa, Tanzania and Rwanda were contacted. In addition, financial institutions active in the international and regional trade finance markets based in the USA, UK, France, Germany and the Netherlands were contacted. Finally, development finance institutions active in supporting trade both within Africa and without were interviewed. Generally trade operations officers, international department management, treasury officers or senior commercial bankers were contacted. Participants were asked to: • Describe their trade finance related activities • Describe the state of the market for trade finance products • Describe how availability of facilities has changed •Describe how terms and conditions of facilities have changed •Discuss overall economic activity in their markets • Discuss potential roles for AfDB to play to facilitate access to trade finance The overall conclusions of these surveys are: • African trade grew rapidly during the pre-crisis period, spurred by growing south-south trade and the emergence of Asia as a major purchaser of African raw materials and primary products. Anecdotally, it appears that trade finance was increasingly available during this period. • The crisis has had a negative impact on African trade due to falling demand for African primary product exports. Trade finance availability was sharply constrained during the initial crisis period. • It is difficult to discern real trends in African trade finance as markets remain highly volatile. Liquidity and risk appetite vary widely across markets and counterparties. Across all markets, trade finance tenors have shortened. • There is an overall decrease in demand for trade products due to decreased economic activity but a higher proportion of the current transactions are using trade instruments. • International commercial banks that historically provided confirmation lines for trade instruments remain risk averse and seek to maintain/increase returns. • Low income countries and the smaller Regional Member Countries are hit hardest by the lack of availability of trade finance due to higher perceived risk, even for low risk transactions. • Basel II related capital allocation rules will have a negative impact on the cost and availability of trade finance across the continent. • Multilateral Development Banks in other regions play a variety of roles to support trade finance availability, from which AfDB could learn some lessons. • The African Development Bank can have a significant impact on trade finance availability and, consequently, RMC economic performance over the short/medium term.

Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily bounded variation with a L\'evy measure concentrated on $(-1,\infty)$. We prove strong consistency and asymptotic normality for all admissible parameter values except one, where we show only weak consistency and mixed normal (but non-normal) asymptotic behavior. It turns out that the volatility of the price process is a measurable function of the price process. We also present some numerical illustrations to confirm our results.Comment: 51 pages, 3 figure