# Past Nomura Seminar

20 February 2014
16:00
to
17:30
Abstract
In this work, we want to construct the solution $(Y,Z,K)$ to the following BSDE $$\begin{array}{l} Y_t=\xi+\int_t^Tf(s,Y_s,Z_s)ds-\int_t^TZ_sdB_s+K_T-K_t, \quad 0\le t\le T, \\ {\mathbf E}[l(t, Y_t)]\ge 0, \quad 0\le t\le T,\\ \int_0^T{\mathbf E}[l(t, Y_t)]dK_t=0, \\ \end{array}$$ where $x\mapsto l(t, x)$ is non-decreasing and the terminal condition $\xi$ is such that ${\mathbf E}[l(T,\xi)]\ge 0$. This equation is different from the (classical) reflected BSDE. In particular, for a solution $(Y,Z,K)$, we require that $K$ is deterministic. We will first study the case when $l$ is linear, and then general cases. We also give some application to mathematical finance. This is a joint work with Philippe Briand and Romuald Elie.
• Nomura Seminar
13 February 2014
16:00
to
17:30
Peter Tankov
Abstract
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is the strategy for which this constant has the highest possible value. Our definition of optimal arbitrage is similar to the one in Fenrholz and Karatzas (2010), where optimal relative arbitrage with respect to the market portfolio is studied. In this work we present a systematic method to construct market models where the optimal arbitrage strategy exists and is known explicitly. We then develop several new examples of market models with arbitrage, which are based on economic agents' views concerning the impossibility of certain events rather than ad hoc constructions. We also explore the concept of fragility of arbitrage introduced in Guasoni and Rasonyi (2012), and provide new examples of arbitrage models which are not fragile in this sense. References: Fernholz, D. and Karatzas, I. (2010). On optimal arbitrage. The Annals of Applied Probability, 20(4):1179–1204. Guasoni, P. and Rasonyi, M. (2012). Fragility of arbitrage and bubbles in diffusion models. preprint.
• Nomura Seminar
6 February 2014
16:00
to
17:30
Mike Tehranchi
Abstract
There are many financial models used in practice (CIR/Heston, Vasicek, Stein-Stein, quadratic normal) whose popularity is due, in part, to their analytically tractable asset pricing. In this talk we will show that it is possible to generalise these models in various ways while maintaining tractability. Conversely, we will also characterise the family of models which admit this type of tractability, in the spirit of the classification of polynomial term structure models.
• Nomura Seminar
28 January 2014
12:30
Abstract
The finance literature documents a relation between labor income and the cross-section of stock returns. One possible explanation for this is the hedging decisions of investors with relative wealth concerns. This implies a negative risk premium associated with stock returns correlated with local undiversifiable wealth, since investors are willing to pay more for stocks that help their hedging goals. We find evidence that is consistent with these regularities. In addition, we show that the effect varies across geographic areas depending on the size and variability of undiversifiable wealth, proxied by labor income.
• Nomura Seminar
23 January 2014
16:00
to
17:30
Johannes Muhle-Karbe
Abstract
An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to optimal execution problems and to other market frictions such as proportional and fixed transaction costs.
• Nomura Seminar
6 December 2013
16:00
Abstract
Worst-case portfolio optimization has been introduced in Korn and Wilmott (2002) and is based on distinguishing between random stock price fluctuations and market crashes which are subject to Knightian uncertainty. Due to the absence of full probabilistic information, a worst-case portfolio problem is considered that will be solved completely. The corresponding optimal strategy is of a multi-part type and makes an investor indifferent between the occurrence of the worst possible crash and no crash at all. We will consider various generalizations of this setting and - as a very recent result - will in particular answer the question "Is it good to save for bad times or should one consume more as long as one is still rich?"
• Nomura Seminar
29 November 2013
16:00
Abstract
We construct a model for asset price in a limit order book, which captures on one hand main stylized facts of microstructure effects, and on the other hand is tractable for dealing with optimal high frequency trading by stochastic control methods. For this purpose, we introduce a model for describing the fluctuations of a tick-by-tick single asset price, based on Markov renewal process. We consider a point process associated to the timestamps of the price jumps, and marks associated to price increments. By modeling the marks with a suitable Markov chain, we can reproduce the strong mean-reversion of price returns known as microstructure noise. Moreover, by using Markov renewal process, we can model the presence of spikes in intensity of market activity, i.e. the volatility clustering. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formulae for the mean signature plot, and show the diffusive behavior of our model at large scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with empirical data on futures Euribor and Eurostoxx. In a second part, we use a dynamic programming approach to our semi Markov model applied to the problem of optimal high frequency trading with a suitable modeling of market order flow correlated with the stock price, and taking into account in particular the adverse selection risk. We show a reduced-form for the value function of the associated control problem, and provide a convergent and computational scheme for solving the problem. Numerical tests display the shape of optimal policies for the market making problem. This talk is based on joint works with Pietro Fodra.
• Nomura Seminar
22 November 2013
16:00
Pierre Collin-Dufresne
Abstract
We extend Kyle's (1985) model of insider trading to the case where liquidity provided by noise traders follows a general stochastic process. Even though the level of noise trading volatility is observable, in equilibrium, measured price impact is stochastic. If noise trading volatility is mean-reverting, then the equilibrium price follows a multivariate stochastic volatility `bridge' process. More private information is revealed when volatility is higher. This is because insiders choose to optimally wait to trade more aggressively when noise trading volatility is higher. In equilibrium, market makers anticipate this, and adjust prices accordingly. In time series, insiders trade more aggressively, when measured price impact is lower. Therefore, aggregate execution costs to uninformed traders can be higher when price impact is lower
• Nomura Seminar
15 November 2013
16:00
Abstract
We study optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and from expert opinions in the form of signals at random discrete time points. We use stochastic filtering to transform the original problem into an optimization problem under full information where the state variable is the filter for the Markov chain. This problem is studied with dynamic programming techniques and with regularization arguments. Finally we discuss a number of numerical experiments
• Nomura Seminar
8 November 2013
16:00
Enrico Biffis
Abstract
We consider over-the-counter (OTC) transactions with bilateral default risk, and study the optimal design of the Credit Support Annex (CSA). In a setting where agents have access to a trading technology, default penalties and collateral costs arise endogenously as a result of foregone investment opportunities. We show how the optimal CSA trades off the costs of the collateralization procedure against the reduction in exposure to counterparty risk and expected default losses. The results are used to provide insights on the drivers of different collateral rules, including hedging motives, re-hypothecation of collateral, and close-out conventions. We show that standardized collateral rules can have a detrimental impact on risk sharing, which should be taken into account when assessing the merits of standardized vs. bespoke CSAs in non-centrally cleared OTC instruments. This is joint work with D. Bauer and L.R. Sotomayor (GSU).
• Nomura Seminar