Workshop in Computational and Mathematical Finance
On October 8 we are organizing a workshop in Computational and Mathematical Finance. The workshop will be held in room 4307 in house 4, apart from the keynote presentation that will take place in 2446 in house 2 at Polacksbacken. You find directions how to get there here. Note that since a keycard is required for 4307, entrance is only possible 9.30-10.00, 13.00-13.20 and 15.00-15.30. If you arrive at any other time you need to send an email to firstname.lastname@example.org or an sms to 0706-242438.
The workshop including coffee, lunch and dinner is free of charge and everybody that is interested in this vibrant field of research is welcome to join us on this occasion.
The workshop is now closed for registrations.
This workshop is jointly organized by the Centre for Interdisciplinary Mathematics (CIM) and the Division of Scientific Computing (TDB), Dept. of Information Technology
Program (may be subject to changes)
|Coffee and registration
Jonas Persson, Sungard Front Arena
Some practical aspects of implementing financial software for pricing, risk and position keeping - Jonas will present his view on demands on numerical methods used in SunGard Front Arena´s software PRIME. PRIME is used by banks and other financial institutions for trading, risk and position keeping across many different asset classes. He will also talk about what different valuation methods that have been implemented in PRIME to price different contracts.
Johan Tysk, Department of Mathematics, Uppsala University
Feynman-Kac theorems for generalized diffusions - We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measured valued coefficients. This talk is based on a joint work with Erik Ekström and Svante Janson.
Jari Toivanen, The Institute for Computational and Mathematical Engineering, Stanford University
A front-tracking method for pricing American options under jump-diffusion models - Under finite activity jump-diffusion models the price function of an American put/call option satisfies a smooth-pasting principle at the optimal exercise boundary. Due to this a free boundary problem with Dirichlet and Neumann boundary conditions at this boundary can be formulated for the price. After an implicit finite difference discretization the location of the boundary at each time step is found iteratively by solving PIDEs in varying domains. This formulation leads to a more accurate approximation for the optimal exercise boundary than a more traditional linear complementarity formulation.
Erik Lindström, Mathematical Statistics, Lund University
Simultaneous Calibration and Hedging - Hedging derivatives is typically done by applying simple delta, delta-gamma or delta-vega strategies. These may work satisfactory for equity but is highly unsuitable for many commondities, in particular for electricity. It is well known that the electricity spot price is very volatile, and spikes are frequent, making these simple strategies suboptimal.
We derive a sequential algorithm for simultaneous calibration and quadratic hedging of options. It can be applied to any model from which we can simulate paths and price options. The quadratic hedging comes at no extra cost! We have calibrated the Bates and NIG-CIR model to S&P 500 index options in order to evaluate various hedging strategies (delta, quadratic), clearly indicating the advantage of quadratic hedging over delta hedging.
Johan Waldén, Haas School of Business, University of California Berkeley
Keynote presentation and CIM Seminar, lunch is served during presentation
Investor Networks - A financial market may be modeled by a network of investors, through which heterogeneous information diffuses. Such an approach can potentially explain several stylized facts, such as rich dynamics of returns, return volatility, and trading volume in such markets, heterogeneous portfolio holdings and performance of investors, and large market movements without public news. I introduce an information network model, and discuss its theoretical and computational challenges.
Elisabeth Larsson, Department of Information Technology, Uppsala University
Radial basis function methods in computational finance - Radial basis function (RBF) based approximation methods for numerical solution of partial differential equations are interesting due to their potentially spectral accuracy and due to being meshfree. This could be especially beneficial for high dimensional problems, where meshing is non- trivial. In this work, we present different RBF approaches and evaluate them for multi-asset option pricing problem.
Victor Shcherbakov, Department of Information Technology, Uppsala University
An RBF penalty method for the pricing of American call options - The pricing of American options is a challenge due to the free boundary. Penalty method allows the free boundary to be removed by adding a small term to the Black-Scholes equation. Particularly, we focus on solving the problem for call options. The space discretization is done by radial basis functions.
Erik Ekström, Department of Mathematics, Uppsala University
Bayesian sequential testing of drift coefficients - We consider a problem of deciding the sign of the unknown drift as quickly as possible by sequential observations of a drifted Brownian motion. Both some closed form solutions will be presented, as well as natural examples for which no simple solutions are to be expected.
Marta Leniec, Department of Mathematics, Uppsala University
Credit Risk Modelling - The talk is devoted to the so-called structural approach in modelling credit risk. Within this framework, the default time is defined as the first crossing time of the value process through a default triggering barrier. We specify the basic tools needed in pricing default-sensitive contingent claims.
Love Lindholm, Department of Mathematics, Royal Institute of Technology
Local volatility calibration as an optimal control problem - We pose the calibration of a local volatility to market data on European options as an optimal control problem which is numerically solved via the Hamiltonian system of the corresponding Hamilton-Jacobi-Bellman equation. The method is tested on option price data on the equity index Euro STOXX 50 from the first three months of 2013.
Santtu Salmi, Department of Mathematical Information Technology, Jyväskylä University
Robust and efficient IMEX schemes for option pricing under jump-diffusion models - Partial-integro differential equation (PIDE) formulations are often used to solve option pricing problems where the underlying asset follows a jump-diffusion process. The main challenge lies in the effcient treatment of the jump term resulting in a full matrix. We discuss some robust and efficient implicit-explicit (IMEX) time discretization methods where the jump term is treated explicitly.
Ron Chan, Royal Docks Business School, University of East London
An RBF scheme for option pricing in exponential Lévy models - We use Radial Basis Function (RBF) interpolation to price options in exponential Lévy models by numerically solving the fundamental pricing PIDE. Our RBF scheme can handle arbitrary singularities of the Lévy measure in 0 without introducing further approximations, making it simpler to implement than competing methods. In numerical experiments using processes from the CGMY-KoBoL class, the scheme is found to be second order convergent in the number of interpolation points, including for processes of unbounded variation.
Lina von Sydow, Department of Information Technology, Uppsala University
On Discontinuous Galerkin for Time Integration in Option Pricing Problems with Adaptive Finite Differences in Space - The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. The results show that the dG method are in most cases at least comparable to standard timeintegrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.