MSMoD53
Challenges in Financial Modelling: Numerics, Statistics, and Calibration.
Date: August 10
Time: 13:3015:30
Room: 311B
(Note: Click title to show the abstract.)
Organizer:
Zubelli, Jorge (IMPA)
Abstract: Modeling of financial markets leads to a plethora of challenging problems that range from analytic to numerical ones. They are characterized by massive quantities of data and unobservable variables that are fundamental in the model interpretation.
This minisymposium concerns largescale and illposed problems arising or motivated by financial applications. Typical examples appear in risk management and volatility calibration. We shall start with an overview of the relevant problems such as volatility calibration and correlation.
Then, we will discuss discretization and iterative techniques that have impact on risk management and volatility modeling. In particular, we focus on discrepancy principles and on the issue of stopping criteria for iterative algorithms. Another highly used group of techniques is associated to state space methods and Kalman filtering. Finally, we present specific examples coming from commodity markets and multifactor stochastic volatility models.
MSMoD531
13:3014:00
Robust timeconsistent dynamic utility maximization under stochastic volatility
Li, Bin (Univ. of Waterloo)
Abstract: We consider a financial market with a riskfree asset and a risky asset, with the latterĄ¯s price following a diffusion with stochastic volatility. Under the robust timeconsistent dynamic utility introduced by BionNadal and Delbaen, utilizing timeconsistency and gexpectation, a closedform optimal strategy is obtained for the incomplete market with either full uncertainty or partial uncertainty. The convergence of the associated optimal strategy is also proved when the market is approaching from partial uncertainty to full uncertainty.
MSMoD532
14:0014:30
Local Volatility Calibration in Commodity Markets and Practical Simplifications
Albani, Vinicius (Univ. of Vienna)
Abstract: We adapt Dupire's local volatility model to price European options on commodity Futures, applying Tikhonov regularization to the corresponding calibration problem, under a discrete setting. We also present two simplifications. The first one is a parametric local volatility surface. In the second one, we make use of the Bayes theorem to find a simplified pricing technique, reducing the dimension of the inverse problem. We perform numerical tests with synthetic as well as market data.
MSMoD533
14:3015:00
Calibration Problems in Finance: From State Space Models to Iterative Algorithms
Zubelli, Jorge (IMPA)
Yang, Xu (Instituto Nacional de Matematica Pura e Aplicada)
Abstract: We shall start with a brief overview of the importance of calibration methods in mathematical finance in general and risk management in particular. After that we shall focus on the problem of recovering the local volatility (not the implied one) from observed market prices.Here we shall compare competing approaches to handle such problem, including iterative methods and state space methods. This will set the stage for the other talks in this minisymposium.
MSMoD534
15:0015:30
Data Completion
Ascher, Uri (Univ. of BC)
Abstract: We consider inverse problems whose forward operator involves the solution of a partial differential equation (PDE). The PDE depends on some material property  a distributed parameter that forms a surface over the PDE domain, and the purpose of the inverse problem is to calibrate the PDE model by estimating the distributed parameter function. This is done by requiring a given function of the field (i.e., the PDE solution) to match a set of given noisy measured data. Often in applications the data is available only at a restricted set of locations, or situations, while existence and uniqueness theory, or other considerations, demand that a fuller set (e.g., ``data everywhere'') be given. There may also be uncertainty in data locations. It is then tempting to ``complete the data'', e.g. by interpolation, before starting the inverse problem solution process. Such data completion, however, has its wellknown perils as well.
This talk describes our various techniques for handling (or avoidance) of data completion in the context of practical applications that include local volatility surface calibration for commodity markets; data inversion in geophysical exploration; and plant motion tracking and calibration in computer graphics.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
