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Conference on Liquidity and Credit Risk |
| Peter Bank March 16, 2012, 09:00-09:45 |
| Optimal order placement |
| Abstract:
The execution of large transactions on a financial market will typically affect market prices in an adverse manner, thus leading to possibly significant execution costs. Minimizing these costs requires to trade-off projections of future market depth vs. market resilience and vs. the urgency to trade. We present an extension of the model proposed by Obizhaeva and Wang which allows for these key market parameters to change over time and we show how to produce a closed-form solution to the resulting optimal control problem.
This is joint work with Antje Fruth. |
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| Umut Cetin March 16, 2012, 15:45-16:30 |
| Liquidity and risk aversion of market makers in Kyle's model |
| Abstract:
A continuous time version of Kyle model where the market maker is assumed to be risk averse with an exponential utility function will be presented. Within this framework we are able to characterise the equilibrium prices of risky assets and find the equilibrium levels of market depth and resiliency associated to the traded asset.
This is joint work with A. Danilova. |
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| Damir Filipovic March 16, 2012, 11:00-11:45 |
| The term structure of interbank risk |
| Abstract:
We use the term structure of spreads between rates on interest rate swaps indexed to LIBOR and overnight indexed swaps to infer a term structure of interbank risk. Using a dynamic term structure model, we decompose the term structure of interbank risk into default and non-default components. We find that, on average, from August 2007 to January 2011, the fraction of total interbank risk due to default risk increases with maturity. At the short end of the term structure, the non-default component is important in the first half of the sample period and is correlated with various measures of funding liquidity and market liquidity. Further out the term structure, the default component is the dominant driver of interbank risk throughout the sample period. These results hold true in both the USD and EUR markets and are robust to different model parameterizations and measures of interbank default risk. The analysis has implications for monetary and regulatory policy as well as for pricing, hedging, and risk-management in the interest rate swap market.
This is joint work with Anders B. Trolle. |
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| Rüdiger Frey March 15, 2012, 11:00-11:45 |
| Nonlinear Black-Scholes equations in finance: associated control problems and properties of solutions |
| Abstract: We study properties of solutions to fully nonlinear versions of the standard Black-Scholes partial differential equation. These equations have been introduced in financial mathematics in order to deal with illiquid markets or with stochastic volatility. We show that typical nonlinear Black-Scholes equations can be viewed as dynamic programming equation of an associated control problem. We establish existence and comparison results and show that the equation induces a convex risk measure on the set of all continuous terminal value claims. Moreover, we study the asymptotic behavior of solutions as market frictions get `large'. Finally the pricing of individual contracts relative to a book of derivatives is discussed. |
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| Thomas Gehrig March 16, 2012, 16:35-17:20 |
| Scattered trust - did the 2007-08 financial crisis change risk perceptions? |
| Abstract:
The paper investigates whether the financial crisis did affect risk perceptions,
and, hence, change structural parameters. By decomposing credit spreads of
US corporate bonds into the contributions by credit, equity, and liquidity risk
factors as well as structural change, the relative contribution of the change in
risk perceptions can be measured. We show that this increase is mostly due
to aversion to default risk for high-yield bonds. For low-yield bonds, the
increase is mostly due to liquidity related factors. By means of counterfactual
analysis we find that the financial crisis shifted the distribution of bond spreads
almost uniformly. This evidence is consistent with changing risk perceptions
as predicted by theories of ambiguity aversion or social learning in the case of
rare events.
This is joint work with Roland Füss and Philipp B Rindler |
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| Kathrin Glau March 15, 2012, 16:35-17:05 |
| PIDE and Fourier methods for pricing European options in Lévy models |
| Abstract:
We concentrate on the relation between time-inhomogeneous Lévy processes and evolution problems that are associated with prices of options such as calls, puts and barrier options. A major concern is to shed light on the structural affinity between the PIDE and the Fourier transform based approach for European options.
We characterize Lévy processes according to the solution spaces of associated parabolic equations. It turns out that for a wide class of processes these spaces are weighted Sobolev-Slobodeckii spaces with different indices. To classify the processes according to these spaces, we define the related Sobolev index of the process. Since it is the most convenient to work with the Fourier transform of Lévy processes, the classification is done according to the symbol i.e. the characteristic function of the process. In contrast to the criteria provided in the literature, our criteria based on the Sobolev index does not require differentiability conditions of the symbol or smoothness of the Lévy kernel, but purely translates the ellipticity condition on the infinitesimal generator to the symbol. We derive the Sobolev index for several classes of Lévy processes and compare it to the Blumenthal-Getoor index, which reveals a relation between the Sobolev index and path properties of the process. More precisely, we discuss the Sobolev index as an indicator of the smoothness of the distribution and of the unboundedness of the paths of the process. The talk is based on joint work with Ernst Eberlein |
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| Michael Gordy March 15, 2012, 09:00-09:45 |
| Stochastic time-change of default intensity models: pricing and estimation |
| Abstract:
We introduce stochastic time change to default intensity models of credit
risk as a parsimonious way to account for stochastic volatility in credit spreads.
We derive two series solutions for the survival probability function, and
show that both methods are applicable when the intensity follows the widely-used
basic affine process. This leads to straightforward and efficient
solutions to bond prices and CDS spreads. We then estimate the time-changed model on panels
of CDS spreads (across maturity and observation time) using Bayesian MCMC methods.
We find strong evidence of stochastic time change.
This is joint work with Ovidiu Costin, Min Huang, and Pawel Szerszen. |
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| Zorana Grbac March 15, 2012, 14:50-15:20 |
| Interest rate derivative valuation in a multiple-curve HJM framework |
| Abstract: In the aftermath of the 2007–09 financial crisis, a variety of spreads have developed between quantities that had been essentially the same until then, notably LIBOR-OIS spreads, LIBOR-OIS swap spreads, and basis swap spreads. In particular, it means that the LIBOR cannot be considered a risk-free rate any longer. In this work we study the valuation of the LIBOR interest rate derivatives in this multiple-curve setup. The classical approach where LIBORs were modeled as martingales under corresponding forward measures fails in this case, since a different curve has to be used for discounting. To account for the post-crisis discrepancy between a risk-free discount curve and a LIBOR fixing curve of interest rate derivatives, we resort to a defaultable HJM methodology. We develop a multiple-curve term structure model in which this discrepancy is modeled by an implied default intensity of the LIBOR contributing banks. We propose a tractable model with Vasicek volatility structure and non-negative time-inhomogeneous L\'evy processes as driving processes and derive valuation formulas for common interest rate derivatives in this setup. In view of the calibration of the model we present numerical results illustrating the flexibility of the model in producing a wide range of LIBOR-OIS swap spreads and basis swap spreads. |
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| Tony He March 16, 2012, 09:50-10:35 |
| Asset pricing under keeping up with the Joneses and heterogeneous beliefs |
| Abstract:
This paper models "keeping up with the Joneses" preferences under heterogeneous
beliefs. Agents who disagree about the growth rate of the aggregate endowment process maximize
their expected utility of consumption relative to each other. By constructing a consensus
belief, we derive agents’ share of aggregate consumption, equilibrium market price of risk and
risk-free interest rate in closed-form and provide conditions for long-run survivability of the heterogeneous
agents. Based on empirical moments of the U.S consumption data and an estimate
of the disagreement about the growth rate of aggregate consumption, we show that with a small
disagreement and reasonable risk aversion, the model is able to match both the equity premium
and risk-free rate observed in the US market. Thus, our model provides an explanation to the
equity premium and risk-free rate puzzles.
This is joint work with Lei Shi and Mi Zheng |
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| José Infante Acevedo March 15, 2012, 17:15-17:45 |
| Optimal execution and price manipulation in time dependent limit order books |
| Abstract:
In the past years, liquidity risk and market microstructure have
become hot topics in Mathematical Finance. Here, we start from
the Limit Order Book (LOB) model proposed by Alfonsi, Fruth and
Schied (AFS) in [1] and we extend this model in order to get a time-
dependent depth of the order book, while maintaining its tractability.
To be more explicit, we consider one large trader that consumes the
cheapest available orders of the LOB. Then, as in the AFS model,
new orders appears to fill the bid/ask spread, but in addition new
limit orders or order cancellations may happen.
Our main results show that under general conditions on the shape
function of the LOB, the problem of the optimal execution of large
block orders of shares by a large trader has a unique solution. As in
[1], we derived explicitly the optimal strategy for buying (or selling) a
given amount of shares before a given deadline, generalizing the results
obtained in [1]. We obtain as well a continuous time limit of the cost
and the optimal strategy for the studied models.
An important consequence is that we can then derive conditions on
the LOB dynamics that exclude the existence of Price Manipulation
Strategies (PMS). These conditions are not only interesting from a
theoretical point of view. They gives precise qualitative insights from
the point of view of a market maker. In fact, a market maker can
put (or cancel) orders in two ways: he can either put an order at a
better price (and reduce the bid ask spread) or put an order at an
existing price (and increase the depth of the LOB). Our conditions
that exclude PMS clearly indicates what a market maker should do in
order not to create manipulations strategies.
This is joint work with A. Alfonsi. References [1] Fruth A. Schied A. Alfonsi, A. Optimal execution strategies in limit order books with general shape functions. Quantitative Finance, 10(2):143–157, 2010. |
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| Florian Klöck March 16, 2012, 14:50-15:20 |
| Existence and absence of price manipulation in a market impact model with dark pool |
| Abstract:
For a market impact model, price manipulation and related notions play a role that is
similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic
investigation into such regularity issues when orders can be executed both at a traditional
exchange and in a dark pool. We characterize the regularity of a class of dark-pool models
whose market impact at the exchange is described by an Almgren-Chriss model. Conditions
include the absence of temporary cross-venue impact, the presence of full permanent crossvenue
impact, and the additional penalization of orders executed in the dark pool. When
a particular Almgren-Chriss model has been fixed, we show by a number of examples that
the regularity of the dark-pool model hinges in a subtle way on the interplay of all model
parameters and on the liquidation time constraint.
This is joint work with Alexander Schied and Yuemeng Sunz. |
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| Gechun Liang March 15, 2012, 11:50-12:20 |
| A continuous time bank run model for liquidity risk |
| Abstract: In this talk, we extend the work "A multi period bank run model for liquidity risk" by Liang, Lütkebohmert and Xiao (forthcoming) from the discrete time bank run case to the case of continuous time bank runs. A financial institution is financed by a mixture of short- and long-term debt. Short-term creditors can run on the financial institution at any time. Within this model, we incorporate rollover risk into structural credit risk models. In particular, we show that the financial institution fails because of a run by short-term creditors rather than by insolvency of the financial institution. The problem is reduced to an optimal stopping time problem, which is solved by the approaches of reflected BSDE and free-boundary PDE. |
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| Dilip Madan March 15, 2012, 14:00-14:45 |
| Tenor specific pricing |
| Abstract: Observing that pure discount projection curves are now based on a variety of tenors leads us to enquire into the possibility of theoretically deriving tenor specific zero coupon bond prices. The question then also arises on how to construct tenor specific prices for all financial contracts. Noting that in conic finance one has the law of two prices, bid and ask, that are nonlinear functions of the random variables being priced, we model dynamically consistent sequences of such prices using the theory of nonlinear expectations. The latter theory is closely connected to solutions of backward stochastic difference equations. The drivers for these stochastic difference equations are here constructed using concave distortions that implement risk charges for local tenor specific risks. It is then observed that tenor specific prices given by the mid quotes of bid and ask converge to the risk neutral price as the tenor is decreased and liquidity increased when risk charges are scaled by the tenor. Square root tenor scaling can halt the convergence to risk neutral pricing, preserving bid ask spreads in the limit. The greater liquidity of lower tenors may lead to an increase or decrease in prices depending on whether the lower liquidity of a higher tenor has a mid quote above or below the risk neutral value. Generally for contracts with a large upside and a bounded downside the prices fall with liquidity while the opposite is the case for contracts subject to a large downside and a bounded upside. |
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| Antonis Papapantoleon March 16, 2012, 11:50-12:20 |
| Affine LIBOR models with stochastic basis |
| Abstract: In this talk, we discuss how interest rate markets have developed during the ongoing financial crisis, which calls for the introduction of the so-called multi-curve interest rate models. Then, we present a multi-curve affine LIBOR model and discuss its merits for derivative pricing. |
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| Alexander Schied March 16, 2012, 14:00-14:45 |
| Stochastic solutions of some optimization problems arising in finance |
| Abstract:
In this talk, we will look at the mathematics of a couple of price impact models and analyze several optimization problems that arise in the context of algorithmic trading. These optimization problems will be formulated as (singular) control problems but solved by means of (stochastic) integral representations. This allows us in particular to work in a non-Markovian setting. Our analysis will exhibit some interesting mathematical properties of the optimal strategies. Some of these results might contribute to the evaluation of the underlying models. For instance, we will find that transience of price impact can lead to somewhat unstable optimal strategies. Some other results are of interest from a purely mathematical point of view. For example, we are led to minimizing Cartan energy forms by means of optimal control techniques.
The talk includes joint work with Aurélien Alfonsi and with Christopher Lorenz. |
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| Thorsten Schmidt March 15, 2012, 15:45-16:30 |
| Dynamic Term Structure Models with Ratings |
| Abstract:
Empirical investigations about rating transitions show typically a non-Markovian
behavior. We take this as a motivation to generalize existing models and determine
conditions for absence of arbitrage in a general forward rate model. This is the
starting point for explicit modeling approaches and we propose a semi-Markovian
model and discuss open questions.
This is joint work with J. Jakubowski and M. Nieweglowski |
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| Stephane Villeneuve March 15, 2012, 09:50-10:35 |
| Optimal liquidity management and hedging in the presence of a non-predictable investment opportunity |
| Abstract:
Both corporate liquidity management and hedging policy have been the topic of a
large academic literature in the last thirty years. The literature aimed to depart from the
benchmark of perfect capital markets (Modigliani and Miller, 1958) to explain why the
management of cash reserves and hedging are key determinants in practice to ensure the
permanence of firms. Several directions have been explored for explaining how and why
firms should hold cash reserves and hedge their risks but the literature has mainly focused
on the precautionary demand of cash holdings in order to both meet the operational needs
and avoid a costly outside raising. The literature on corporate finance has neglected the
importance of cash holdings and hedging in the determination of the optimal time to under-
take an irreversible investment. Up to now, the real option theory of irreversible investment
under uncertainty has assumed that outside funds can be raised at no cost to finance in-
vestment opportunity. As a consequence, the decision to invest is made independently of
the firm cash holdings. In the presentation, we develop a model in continuous time that
captures the dual role of cash holdings and hedging decisions.
This is joint work with Xavier Wariny |
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