Internal Probability Seminars
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17 DecSwing Options in the Black & Scholes model: a free-boundary approach
2012
T. De Angelis
2pm - Alan Turing Building - Frank Adams RoomAbstractSwing 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 DecThe ruin problem revisited
2012
R. Doney
2pm - Alan Turing Building - Frank Adams Room ReferencesAbstractAbstract will appear here
- 26 NovFirst passage times for Levy processes over a one-sided moving boundary
2012
T. Kramm
2pm - Alan Turing Building - Frank Adams RoomAbstractAbstract will appear here
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19 NovSDEs for sticky Brownian motion
2012
G. Peskir
2pm - Alan Turing Building - Frank Adams RoomAbstractAbstract will appear here
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12 NovStochastic partial differential equations with two reflecting walls
2012
T. Zhang
12pm - Alan Turing Building - Frank Adams Room *Note unusual time*AbstractAbstract will appear here
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21 MayA stochastic solution to the Stroock-Williams equation - Part II
2012
G. Peskir
2pm - Alan Turing Building - Frank Adams RoomAbstractTBA.
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14 MayA stochastic solution to the Stroock-Williams equation - Part I
2012
G. Peskir
2pm - Alan Turing Building - Frank Adams RoomAbstractTBA.
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30 AprilThe ruin problem in the heavy-tail case
2011
R. Doney
2pm - Alan Turing Building - Frank Adams RoomAbstractTBA
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23 AprilThe lookback option with fixed strike
2012
Y. Kitapbayev
2pm - Alan Turing Building - Frank Adams RoomAbstractTBA
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19 MarchNonzero-sum games of optimal stopping
2012
N. Attard
2pm - Alan Turing Building - Frank Adams RoomBack to Probability and Statistics Research SeminarsAbstractTBA/div>
12 MarchSpectral representations for affine processes
2012
R. Loeffen
2pm - Alan Turing Building - Frank Adams RoomAbstractTBA
27 FebruaryPricing American bond options under HJM: an infinite dimensional variational inequality
2012
T. de Angelis
2pm - Alan Turing Building - Frank Adams RoomAbstractTBA
Further information
For further information contact Dr John Moriarty
