3 Presentations

• 
  04:00 PM - 04:30 PM

  A Dynamic Programming Approach Using Tchebychev Interpolation for Pricing Bonds with Embedded Options under a Two Factor Gaussian Model

  • Yaovi Gassesse Siliadin, presenter, HEC Montréal
  • Michèle Breton, GERAD, HEC Montréal

  Multifactor interest rate models are necessary for realistic replications of bond markets. However, traditional reliable pricing methods of bonds with embedded options were developed under one-factor interest rate model assumptions, and their complexity did not allow for their application to multifactor models. Ben Ameur et al. (2006) were the …first to propose a fast and accurate dynamic programming approach, under one-factor interest rate models, which has exhibited a real potential of extension to multifactor models. The only obstacle to the extension is the large number of interpolating points that their method requires. The aim of this project has been to tackle that extension issue and attempt to solve it by means of Tchebychev interpolation. As the project is ambitious, we have divided it into two phases and broken each of the phases down into small steps.
  The first phase has consisted of performing the extension to the most analytically tractable multifactor model: the two-factor Vasicek model. To complete this phase we have successively designed, implemented and tested numerical DP approaches based on Tchebychev interpolation for pricing increasingly complex bonds : zero coupon bonds under the one-factor Vasicek model, zero coupon bonds under the two-factor Vasicek model, vanillas under the two-factor Vasicek model, and bonds with embedded options under the two-factor Vasicek model. The main problem we have faced is that there is no closed-form solution for the transition parameters. Computing these parameters by numerical integration would be too time-consuming. Hence, we have …first developed a recurrence algorithm for the computation of the transition parameters. The recurrence works for the zero coupons but fails to give stable and sufficiently precise price for vanillas. Then we have proposed another dynamic programming approach which reduces the number of numerical integration needed from O(n2m2) to O(nm). The second phase has consisted of extending our DP approach to the two-factor Gaussian model. We have started by formulating the exact DP approach and provided an approximation algorithm based on Tchebychev interpolation. The approach has then been implemented in C++. The new classes have been declared as child classes of the already existing C++ class developed in the first phase. Finally, we have performed successfully real market applications and tests on the Government of Canada Bonds and Treasury bill market. This last step was perhaps the most interesting one as we had to look for a market, decide which variables will actually be used as interest rate factors, collect the data, estimate the model parameters and compare prices given by our approach to those of the market.

• 
  04:30 PM - 05:00 PM

  American Options in a Jump-Diffusion Framework: Estimation and Evaluation

  • Rim Cherif, presenter, HEC Montréal
  • Hatem Ben Ameur, GERAD, HEC Montréal
  • Bruno Rémillard, HEC Montréal

  In this paper, we propose a quasi-explicit formula for pricing
  American options in jump-diffusion models. Our procedure is based
  on dynamic programming coupled with piecewise linear approximations. The
  proposed methodology is numerically tested and compared to other
  evaluation methods when the jumps are lognormal. We also address the
  estimation and calibration problems, and report a few results on
  real data.

• 
  05:00 PM - 05:30 PM

  EU ETS Futures Spread Analysis and Pricing Contingent Claims Under Different Market Schemes

  • Matt Davison, presenter, Departments of Applied Mathematics and Statistical & Actuarial Sciences, Richard Ivey School of Business, The University of Western Ontario
  • Walid Mnif, University of Western Ontario

  The European Union Emission Trading Scheme is the largest market mechanism yet implemented to spur emissions reduction. In the scheme emissions certificates are traded within annual periods to compensate for the total emissions of given companies. The rules for how certificates can be passed from one annual period to another arephase dependent. During phase II of the EU ETS, emissions can be borrowed between years falling within phase II, but not from phase III years. We are interested in investigating the way in which this structural change affects the impact of unexpected release of information on futures returns. We propose a continuous-time model that depicts the relationship assimilated into the spread. We assume that two futures that mature at subsequent dates are traded. Their dynamic is driven by Brownian motions augmented by two jump processes. The discontinuous component reflects the impact of any unexpected release of information. We estimate the model parameters and draw economic conclusions. Furthermore our empirical results supports the stance that the market is mature and efficient enough to be comparable to other many futures markets. We present a pricing solution based on the Follmer-Schweizer decomposition. The optimal hedging strategy depends on all traded futures and minimizes the mean conditional square error of the cumulative process. We show how the fair price of any contingent claim can theoretically be computed in this context. Pricing examples under different market schemes are investigated.