# Past Nomura Seminar

1 May 2009
14:15
to
8 May 2009
14:15
Elyes Jouini
Abstract
Can investors with irrational beliefs be neglected as long as they are rational on average ? Does unbiased disagreement lead to trades that cancel out with no consequences on prices, as implicitly assumed by the traditional models ? We show in this paper that there is an important impact of unbiased disagreement on the behavior of financial markets, even though the pricing formulas are "on average" (over the states of the world) unchanged. In particular we obtain time varying, mean reverting and countercyclical (instead of constant in the standard model) market prices of risk, mean reverting and procyclical (instead of constant) risk free rates, decreasing (instead of flat) yield curves in the long run, possibly higher returns and higher risk premia in the long run (instead of a flat structure), momentum in stock returns in the short run, more variance on the state price density, time and state varying (instead of constant) risk sharing rules, as well as more important and procyclical trading volumes. These features seem consistent with the actual (or desirable) behavior of financial markets and only result from the introduction of unbiased disagreement.
• Nomura Seminar
11 March 2009
14:15
Paul Glasserman
Abstract
We analyze the impact of portfolio rebalancing frequency on the measurement of risk over a moderately long horizon. This problem arises from an incremental capital charge recently proposed by the Basel Committee on Banking Supervision. The new risk measure calculates VaR over a one-year horizon at a high confidence level and assigns different rebalancing frequencies to different types of assets to capture potential illiquidity. We analyze the difference between discretely and continuously rebalanced portfolios in a simple model of asset dynamics by examining the limit as the rebalancing frequency increases. This leads to alternative approximations at moderate and extreme loss levels. We also show how to incorporate multiple scales of rebalancing frequency in the analysis
• Nomura Seminar
6 March 2009
14:15
Peter Imkeller
Abstract
A financial market model is considered on which agents (e.g. insurers) are subject to an exogenous financial risk, which they trade by issuing a risk bond. Typical risk sources are climate or weather. Buyers of the bond are able to invest in a market asset correlated with the exogenous risk. We investigate their utility maximization problem, and calculate bond prices using utility indi®erence. This hedging concept is interpreted by means of martingale optimality, and solved with BSDE and Malliavin's calculus tools. Prices are seen to decrease as a result of dynamic hedging. The price increments are interpreted in terms of diversification pressure.
• Nomura Seminar
27 February 2009
14:15
Abstract
My talk will be about optimal investment in Kabanov's model of currency exchange with transaction costs. The model is general enough to allow a random, discontinuous bid-offer spread. The investor wishes to maximize their &quot;direct&quot; utility of consumption, which is measured in terms of consumption assets linked to some (but not necessarily all) of the traded currencies. The analysis will centre on two conditions under which the existence of a dual minimiser leads to the existence of an optimal terminal wealth. The first condition is a well known, but rather unintuitive, condition on the utility function. The second weaker, and more natural condition is that of &quot;asymptotic satiability&quot; of the value function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer. This is joint work with Luciano Campi.
• Nomura Seminar
20 February 2009
14:15
Aurélien Alfonsi
Abstract
This paper presents weak second and third order schemes for the Cox-Ingersoll-Ross (CIR) process,  without any restriction on its <br /> parameters. At the same time, it gives a general   recursive <br /> construction method to get weak second-order schemes that extends the one introduced by Ninomiya and Victoir. Combining these both results, this allows to propose a second-order scheme for more general affine diffusions. Simulation examples are given to illustrate the convergence of these schemes on CIR and Heston models<br /> <br />
• Nomura Seminar
13 February 2009
14:15
Monique Jeanblanc
Abstract
Seminar also with N. El Karoui and Y. Jiao Dynamic modelling of default time for one single credit has been largely studied in the literature. For the pricing and hedging purpose, it is important to describe the price dynamics of credit derivative products. To this end, one needs to characterize martingales in the various filtrations and calculate conditional expectations by taking into account of default information, often modelized by a filtration $\bf{ D}$ generated by the jump process related to the default time $\tau$. A general principle is to work with some reference filtration $\bf F$ which is often generated by some given processes. The calculations are then achieved by a formal passage between the enlarged filtration and the reference one on the set $\{\tau>t\}$ and the models are developed on the filtration $\bf F$. In this paper, we are interested in what happens after a default occurs, i.e., on the set $\{\tau\leq t\}$. The motivation is to study the impact of a default event on the market, which will be important in a multi-credits setting. To this end, we adopt a new approach which is based on the knowledge of conditional survival probabilities. Inspired by the enlargement of filtration theory, we assume that the conditional law of $\tau$ admits a density. We also present how our computations can be used in a multi-default setting.
• Nomura Seminar
6 February 2009
14:15
Marek Musiela
Abstract
Since summer 2007 financial markets moved in unprecedented ways. Volatility was extremely high. Correlations across the board increased dramatically. More importantly, also much deeper fundamental changes took place. In this talk we will concentrate on the following two aspects, namely, inter-bank unsecured lending at LIBOR and 40% recovery. Before the crisis it was very realistic for the banks to consider that risk free rate of inter-bank lending, and hence also of funding, is equivalent to 3M LIBOR. This logic was extended to terms which are multiples of 3M via compounding and to arbitrary periods by interpolation and extrapolation. Driven by advances in financial mathematics arbitrage free term structure models have been developed for pricing of interest rate exotics, like LIBOR Market Model (or BGM). We explain how this methodology was challenged in the current market environment. We also point to mathematical questions that need to be addressed in order to incorporate in the pre-crisis pricing and risk management methodology the current market reality. We also discuss historically validated and universally accepted pre-crisis assumption of 40% recovery. We expose its inconsistency with the prices observed now in the structured credit markets. We propose ways of addressing the problem and point to mathematical questions that need to be resolved.
• Nomura Seminar
30 January 2009
14:15
Damir Filipovic
Abstract
This paper provides a unifying approach for valuing contingent claims on a portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable (T; x)-bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded x at maturity T, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Background market risk as well as feedback contagion effects of the loss process are taken into account. Moreover, we show that any ex- ogenous specification of the volatility and contagion parameters actually yields a unique consistent loss process and thus an arbitrage-free family of (T; x)-bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of doubly stochastic affine term structure models.
• Nomura Seminar