SC²S Colloquium - September 6, 2011

Date:	September 6, 2011
Room:	02.07.023
Time:	15:00 am, s.t.

Donglin Wang: Sparse Grid Combination Technique for Regression Problems in Finance (MA)

The risk management of portfolios containing multiple financial derivatives (such as options) requires periodical valuation of the portfolios. The pricing framework is usually implemented such that it involves a nested Monte-Carlo simulation. That means, on each simulated market scenario path, at each time step, thousands of Monte-Carlo paths are generated again. This makes it highly computational intensive. In order to avoid nested Monte-Carlo simulations, previous work suggested to apply the regression technique at each time step to obtain the price of the financial derivatives and thus the portfolio value as a function of the underlying factors as stock prices, volatilities, interest rate.

Meanwhile the currently applied framework for pricing early-exercisable options is the so-called least squares Monte Carlo simulation. It involves regression as a subtask at each early exercisable time step to construct a conditional expectation function, based on which the optimal exercisable decisions can be made.

This work focuses on implementation of the sparse grid combination technique and the dimensionally adaptive sparse grid combination technique as an alternative technique on the regression problems embedded in the above mentioned two pricing frameworks. This work compares the accuracy of the sparse grid combination technique and the dimensionally adaptive sparse grid combination technique with direct regression on sparse grids as well as regression on thin-plate spline basis for several financial problems.