Dmitrii Silvestrov: American-Type Options. Stochastic Approximation Methods

The lecture presents the second volume of the comprehensive two-volume monograph. The first volume, [1], was devoted to stochastic approximation methods for American-type options with general pay-off functions, for discrete time modulated Markov log-price processes. The second volume, [2], gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions, for continuous time Markov log-price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic time-space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov log-price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov log-price processes and general pay-off functions, which can depend not only on log-price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also presents results of experimental studies and contains an extended bibliography of works in the area.

 

References
[1] Silvestrov, D.S. American-Type Options. Stochastic Approximation Methods. Vol. 1. De Gruyter Studies in Mathematics, 56, De Gruyter, Berlin, 2014, x+509 pp.
[2] Silvestrov, D.S. American-Type Options. Stochastic Approximation Methods. Vol. 2. De Gruyter Studies in Mathematics, 57, De Gruyter, Berlin, 2015, xi+558 pp.