Internal Probability Seminars

1st Semester 2012/2013

• 17 Dec
  2012
  Swing Options in the Black & Scholes model: a free-boundary approach
  T. De Angelis
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  Swing options are particular financial derivatives that may be described as American options with multiple exercises. They are widely traded in the energy markets and the security underlying the option is often the price of a given commodity. In mathematical terms the price of an option of this kind is described by the value function of an optimal stopping problem with multiple stopping times. When the process describing the price's dynamics is a diffusion, the pricing and hedging of this options crucially rely on the geometry of the optimal exercise regions. We consider Black and Scholes model for the price process and study a Swing option on finite time horizon T > 0, with a PUT payoff with strike K > 0 and two exercise rights. We solve the free-boundary problem by characterising the value function and the free-boundary in terms of suitable integral equations that are evaluated numerically. Some insights about the general case of n exercise rights are also discussed.
  
  [1] BENDER, C. (2011). Dual pricing of multi-exercise options under volume con-straints. Finance and Stoch. 15 (1-26). [1] CARMONA, R. and DAYANIK, N. (2008). Optimal multiple stopping of linear diffusions. Math. of Operations Research 33 No. 2 (446-460). [2] CARMONA, R. and TOUZI, N. (2008). Optimal multiple stopping and valua-tion of Swing options. Math. Finance 18 No. 2 (239-268). [3] KOBYLANSKI, M., QUENEZ, M. and ROUY-MIRONESCU, E. (2011). Optimal multiple stopping time problem. Annals of Appl. Prob. 21 No. 4 (1365-1399).

• 10 Dec
  2012
  The ruin problem revisited
  R. Doney
  
  2pm - Alan Turing Building - Frank Adams Room References
  Abstract

  Abstract will appear here

• 26 Nov
  2012
  First passage times for Levy processes over a one-sided moving boundary
  T. Kramm
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  Abstract will appear here

• 19 Nov
  2012
  SDEs for sticky Brownian motion
  G. Peskir
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  Abstract will appear here

• 12 Nov
  2012
  Stochastic partial differential equations with two reflecting walls
  T. Zhang
  
  12pm - Alan Turing Building - Frank Adams Room *Note unusual time*
  Abstract

  Abstract will appear here

2nd Semester 2011/2012

• 21 May
  2012
  A stochastic solution to the Stroock-Williams equation - Part II
  G. Peskir
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA.

• 14 May
  2012
  A stochastic solution to the Stroock-Williams equation - Part I
  G. Peskir
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA.

• 30 April
  2011
  The ruin problem in the heavy-tail case
  R. Doney
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA

• 23 April
  2012
  The lookback option with fixed strike
  Y. Kitapbayev
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA

• 19 March
  2012
  Nonzero-sum games of optimal stopping
  N. Attard
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA/div>

• 12 March
  2012
  Spectral representations for affine processes
  R. Loeffen
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA

• 27 February
  2012
  Pricing American bond options under HJM: an infinite dimensional variational inequality
  T. de Angelis
  
  2pm - Alan Turing Building - Frank Adams Room
  Abstract

  TBA

Further information

For further information contact Dr John Moriarty