Nomura Seminar
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Fri, 21/01/2011 14:15 |
Prof Josef Teichmann (ETH Zurich) |
Nomura Seminar  |
DH 1st floor SR |
| We present theory and numerics of affine processes and several of their applications in finance. The theory is appealing due to methods from probability theory, analysis and geometry. Applications are diverse since affine processes combine analytical tractability with a high flexibility to model stylized facts like heavy tails or stochastic volatility. | |||
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Fri, 28/01/2011 14:15 |
Dr Dilip Madan (University of Maryland) |
Nomura Seminar |
DH 1st floor SR |
| The static two price economy of conic finance is first employed to define capital, profit, and subsequently return and leverage. Examples illustrate how profits are negative on claims taking exposure to loss and positive on claims taking gain exposure. It is argued that though markets do not have preferences or objectives of their own, competitive pressures lead markets to become capital minimizers or leverage maximizers. Yet within a static context one observes that hedging strategies must then depart from delta hedging and incorporate gamma adjustments. Finally these ideas are generalized to a dynamic context where for dynamic conic finance, the bid and ask price sequences are seen as nonlinear expectation operators associated with the solution of particular backward stochastic difference equations (BSDE) solved in discrete time at particular tenors leading to tenor specific or equivalently liquidity contingent pricing. The drivers of the associated BSDEs are exhibited in complete detail. | |||
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Fri, 04/02/2011 14:15 |
Dr Anke Wiese (Heriot-Watt University) |
Nomura Seminar |
DH 1st floor SR |
| In the Heston stochastic volatility model, the variance process is given by a mean-reverting square-root process. It is known that its transition probability density can be represented by a non-central chi-square density. There are fundamental differences in the behaviour of the variance process depending on the number of degrees of freedom: if the number of degrees of freedom is larger or equal to 2, the zero boundary is unattainable; if it is smaller than 2, the zero boundary is attracting and attainable. We focus on the attainable zero boundary case and in particular the case when the number of degrees of freedom is smaller than 1, typical in foreign exchange markets. We prove a new representation for the density based on powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. Thus, we establish a new exact and efficient method for simulating the Cox-Ingersoll-Ross process for an attracting and attainable zero boundary, and thus establish a new simple method for simulating the Heston model. We demonstrate our method in the computation of option prices for parameter cases that are described in the literature as challenging and practically relevant. | |||
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Fri, 11/02/2011 14:15 |
Miklos Rasonyi (Edinburgh University) |
Nomura Seminar |
DH 1st floor SR |
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Wed, 16/02/2011 12:45 |
Prof. Dr. Ernst Eberlein (Universitaet Freiburg) |
Nomura Seminar |
Oxford-Man Institute |
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Fri, 18/02/2011 14:15 |
Mingyu Xu (Chinese Academy of Sciences, Beijing) |
Nomura Seminar |
DH 1st floor SR |
Non-linear backward stochastic differential equations (BSDEs inshort) were firstly introduced by Pardoux and Peng (\cite{PP1990},1990), who proved the existence and uniqueness of the adapted solution, under smooth square integrability assumptions on the coefficient and the terminal condition, and when the coefficient  is Lipschitz in  uniformly in  . From then on, the theory of backward stochastic differential equations (BSDE) has been widely and rapidly developed. And many problems in mathematical finance can be treated as BSDEs. The natural connection between BSDE and partial differential equations (PDE) of parabolic and elliptic types is also important applications. In this talk, we study a new developement of BSDE, BSDE with contraint and reflecting barrier.The existence and uniqueness results are presented and we will give some application of this kind of BSDE at last. |
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Fri, 25/02/2011 14:15 |
Prof Damiano Brigo (King's College London) |
Nomura Seminar |
Oxford-Man Institute |
| We present three examples of credit products whose valuation poses challenging modeling problems related to armageddon scenarios and extreme losses, analyzing their behaviour pre- and in-crisis. The products are Credit Index Options (CIOs), Collateralized Debt Obligations (CDOs), and Credit Valuation Adjustment (CVA) related products. We show that poor mathematical treatment of possibly vanishing numeraires in CIOs and lack of modes in the tail of the loss distribution in CDOs may lead to inaccurate valuation, both pre- and especially in crisis. We also consider the limits of copula models in trying to represent systemic risk in credit intensity models. We finally enlarge the picture and comment on a number of common biases in the public perception of modeling in relationship with the crisis. | |||
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Fri, 04/03/2011 14:15 |
Johannes Muhle-Karbe (ETH Zurich) |
Nomura Seminar |
L3 |
| We show how to solve optimization problems in the presence of proportional transaction costs by determining a shadow price, which is a solution to the dual problem. Put differently, this is a fictitious frictionless market evolving within the bid-ask spread, that leads to the same optimization problem as in the original market with transaction costs. In addition, we also discuss how to obtain asymptotic expansions of arbitrary order for small transaction costs. This is joint work with Stefan Gerhold, Paolo Guasoni, and Walter Schachermayer. | |||
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Fri, 11/03/2011 14:15 |
Yves Achdou (Universite Pierre et Marie Curie and Universite Paris-Diderot) |
Nomura Seminar |
DH 1st floor SR |
