Stochastic Analysis and Stochastic Finance Seminar

The Emergence of Delta-Vega Hedging in the Black-Scholes Model

Speaker(s): 
Johannes Muhle-Karbe (ETH Zürich)
Date: 
Thursday, November 5, 2015 - 5:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

We study option pricing and hedging with uncertainty about a Black-Scholes reference model. For dynamic trading in the underlying asset and a liquidly traded vanilla option, delta-vega hedging is asymptotically optimal in the limit for small uncertainty aversion. The corresponding price corrections are determined by a number of second-order greeks, namely the option’s gamma, vanna, and volga.

(Joint work with Sebastian Herrmann)

Application of PPDEs to stochastic differential games

Speaker(s): 
Ibrahim Ekren (ETH Zürich)
Date: 
Thursday, July 9, 2015 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

In this talk, we define derivatives of functionals on the space of continuous paths and give an introduction to path-dependent partial differential equations (PPDEs). These equations extend the well-known Feynman-Kac Formula to a non-Markovian framework. Since the space of continuous paths is not locally compact, we cannot rely on the theory of viscosity solutions for PDEs and need to develop new approaches. We present new results on degenerate PPDEs and apply them to the study of non-Markovian stochastic differential games.

Robust pricing, hedging and investing in discrete time

Speaker(s): 
Ludovic Tangpi (HU Berlin)
Date: 
Thursday, July 9, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We provide a theoretical framework for pricing, hedging and investing in a model-independent financial market. Our method relies on representation results for convex increasing functionals and extends to hedging problems with given marginals. Based on joint works with P. Cheridito and M. Kupper.

Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes

Speaker(s): 
Laurent Denis (University of Le Mans, Frankreich)
Date: 
Thursday, June 25, 2015 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We present an approach to absolute continuity and regularity of laws of Poisson functionals based on the framework of local Dirichlet forms. The method mainly uses the chaos decomposition of the Poisson L^2 space which extends naturally to a chaos decomposition of the domain of the candidate closed form and gives rise to a new explicit calculus : it consists in adding a particle and taking it back after computing the gradient.

Benchmarked Risk Minimization

Speaker(s): 
Eckhard Platen (University of Technology Sydney)
Date: 
Thursday, June 25, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numeraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Föllmer, Sondermann and Schweizer. The latter relies on a quadratic criterion, requesting the square integrability of contingent claims and the existence of an equivalent risk neutral probability measure. The proposed concept of benchmarked risk minimization avoids these restrictive assumptions.

Incorporating parameter risk into derivatives prices - an approach to bid-ask spreads

Speaker(s): 
Karl F. Bannör (Deloitte & Touche GmbH)
Date: 
Thursday, June 11, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We present a new method based on convex risk measures to incorporate parameter risk (e.g. estimation and calibration risk) into derivative prices, generalizing the well-known conic finance approach. In this context, weak continuity properties of convex risk measures are discussed. As an application we calculate parameter risk-implied bid-ask spreads of exotics, enabling us to compare the parameter risk of different models and different exotics.

Chebyshev Interpolation for Parametric Option Pricing

Speaker(s): 
Kathrin Glau (Technische Universität München)
Date: 
Thursday, May 28, 2015 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

Function approximation with Chebyshev polynomials is a well-established and thoroughly investigated method within the field of numerical analysis. The method enjoys attractive convergence properties and its implementation is straightforward. We propose to apply tensorized Chebyshev interpolation to computing Parametric Option Prices (POP). This allows us to exploit the recurrent nature of the pricing problem in an efficient, reliable and general way.

Moral Hazard in Dynamic Risk Management

Speaker(s): 
Dylan Possamai (Université Paris Dauphine - CEREMADE)
Date: 
Thursday, April 30, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with respect to the risk choices of the agent. Using a very recent theory of singular changes of measures for Ito processes, we formulate the principal-agent problem in this context, and solve it in the case of CARA preferences.

Pricing under Rough Volatility

Speaker(s): 
Christian Bayer (WIAS Berlin)
Date: 
Thursday, April 16, 2015 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum [SSRN 2509457, 2014] showed that log-volatility behaves

Sensitivity of Optimal Comsumption Streams

Speaker(s): 
Martin Herdegen (ETH Zürich)
Date: 
Thursday, April 16, 2015 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. We show that to the leading order, any consumption correction for the perturbed endowment is still optimal as long as the budget constraint is binding. More importantly, we also establish the optimal correction at the next-to-leading order. This can be computed in two steps. First, one has to find the optimal correction for a deterministic perturbation. This only involves the risk-tolerance process of the unperturbed problem and yields a "risk-tolerance martingale".

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