State Equidistant and Time Non-Equidistant Valuation of American Call Options on Stocks With Known Dividends
Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
In computational finance, finite differences are a widely used tool in the valuation of standard derivative contracts. In a lower-dimensional setting, high accuracy and speed often characterize such methods, which gives them a competitive advantage against Monte Carlo methods. For option contracts with discontinuous payoff functions, however, finite differences encounter problems to maintain the order of convergence of the employed finite difference scheme. Therefore the timesteps are often computed in a conservative manner, which might increase the total execution time of the solver more than necessary.
It can be shown that for American call options written on dividend paying stocks, it may be optimal to exercise the option right before a dividend is paid out. The result is that yet another discontinuity is introduced in the solution and the timestep is often reduced to preserve the intrinsic convergence order. However, it is thought that at least in theory the optimal length of the timestep is an increasing function of the time elapsed since the last discontinuity occured. The objective thus becomes that of finding an explicit method for adjusting the timestep both at the dividend instants and between dividend instants. Keeping the discretization in space constant leads to a time non-equidistant finite difference problem.
The aim of this thesis is to propose a time non-equidistant numerical finite difference algorithm for valuation of American call options on stocks with dividends known in advance. In particular, an explicit formula is proposed for computing timesteps at the dividend instants and between dividend payments given a user-specified error tolerance. A portion of the report is also devoted to numerical stabilization techniques that are applied to maintain the convergence order, including Rannacher time-marching and mollification.
Place, publisher, year, edition, pages
2014. , 68 p.
UPTEC F, ISSN 1401-5757 ; 14018
Computational Finance, American Call Options, Escrowed Dividend Model, Finite Differences, Time Non-Equidistant Methods
Engineering and Technology
IdentifiersURN: urn:nbn:se:uu:diva-226518OAI: oai:DiVA.org:uu-226518DiVA: diva2:726226
Sungard Front Arena
Master Programme in Engineering Physics
2014-06-05, Rum 2001, Ångströmlaboratoriet, Lägerhyddsv. 1, Uppsala, 15:15 (English)
Nyberg, Tomas, ForskareLötstedt, Per, Professor