3 Presentations

• 
  04:00 PM - 04:30 PM

  Time-Consistent Equilibria in a Portfolio and Life Insurance Model With Time-Inconsistent Preferences

  • Jesus Marin-Solano, presenter, Universitat de Barcelona
  • Jorge Navas, Universitat de Barcelona
  • Carmen Ribas, Universitat de Barcelona
  • Oriol Roch, Universitat de Barcelona

  The effects of introducing time-inconsistent preferences in investment-consumption models in a continuous time setting are analyzed. Time-consistent equilibria for a consumption and portfolio rules model with a general discount function are described. Results are derived for these problems in the case of nonconstant time-distance (hyperbolic) discounting. Some numerical illustrations are presented for the cases of CARA and CRRA utility functions. These results are compared with those obtained for problems with heterogeneous discounting (instantaneous utilities enjoyed from consumption and the final/bequest function are discounted by using different discount rates of time preference). Next, the model is extended by introducing, first, a life insurance and, next, life settlements. Some numerical illustrations are presented for these models. Finally, attention is addressed to the computational difficulties arising in the search of time-consistent equilibria for problems with time-inconsistent preferences.

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  04:30 PM - 05:00 PM

  Multi-Fold Compound Options and Principal Protected Notes Valuation

  • Mbaye Ndoye, presenter, HEC Montréal
  • Michèle Breton, GERAD, HEC Montréal

  We discuss two valuation methods for multi-fold compound options and principal protected notes. The first method is an analytical formula proposed in financial literature, where we propose an extension to a regime switching log-normal model. The second method is a dynamic-programming-based numerical approach, which is very general and can accommodate any dynamics for the underlying asset, such as for instance stochastic volatility models. We show that this approach is more efficient than both Monte Carlo simulation and analytical valuation. Numerical illustrations are provided for compound and 3-fold compound options, and for principal protected notes issued by the National Bank of Canada under geometric Brownian motion, GARCH and regime switching log-normal models assumptions
  

• 
  05:00 PM - 05:30 PM

  Solvency Capital Requirement for Insurance Products via Dynamic Cash Flow Matching under Lattice Models

  • Alfred Ka Chun Ma, presenter, Chinese University of Hong Kong
  • Yuen Ki Cheung, JP Morgan

  We propose a framework based on cash flow matching for computing the Solvency Capital Requirement under Solvency II. The time horizon of the insurance liabilities is typically longer than the maturities of bonds available in the market. With the assumption that a collection of bonds will be available for purchase in the future, we study the cash flow matching program under interest rate lattice models. The solution can be interpreted as the worst-case cost and the economic capital can be found accordingly.