scholarly journals Dynkin's Games and Israeli Options

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Yuri Kifer
Keyword(s):  
Transaction Costs ◽  
Error Estimates ◽  
Optimal Stopping ◽  
Derivative Securities ◽  
Discrete Approximations ◽  
Game Options ◽  
Related Derivative ◽  
Stopping Games

We start by briefly surveying a research on optimal stopping games since their introduction by Dynkin more than 40 years ago. Recent renewed interest to Dynkin’s games is due, in particular, to the study of Israeli (game) options introduced in 2000. We discuss the work on these options and related derivative securities for the last decade. Among various results on game options we consider error estimates for their discrete approximations, swing game options, game options in markets with transaction costs, and other questions.

Optimal Stopping Games for Markov Processes

2008 ◽  
Vol 47 (2) ◽  
pp. 684-702 ◽  
Author(s):  
Erik Ekström ◽  
Goran Peskir
Keyword(s):  
Markov Processes ◽  
Optimal Stopping ◽  
Stopping Games

scholarly journals On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile

2005 ◽  
Vol 2005 (3) ◽  
pp. 235-258 ◽  
Author(s):  
Martin Jandačka ◽  
Daniel Ševčovič
Keyword(s):  
Transaction Costs ◽  
Real Option ◽  
Time Lag ◽  
Derivative Securities ◽  
Volatility Smile ◽  
Market Data ◽  
Nonlinear Parabolic ◽  
Black Scholes ◽  
Parabolic Pde ◽  
Option Market

We analyse a model for pricing derivative securities in the presence of both transaction costs as well as the risk from a volatile portfolio. The model is based on the Black-Scholes parabolic PDE in which transaction costs are described following the Hoggard, Whalley, and Wilmott approach. The risk from a volatile portfolio is described by the variance of the synthesized portfolio. Transaction costs as well as the volatile portfolio risk depend on the time lag between two consecutive transactions. Minimizing their sum yields the optimal length of the hedge interval. In this model, prices of vanilla options can be computed from a solution to a fully nonlinear parabolic equation in which a diffusion coefficient representing volatility nonlinearly depends on the solution itself giving rise to explaining the volatility smile analytically. We derive a robust numerical scheme for solving the governing equation and perform extensive numerical testing of the model and compare the results to real option market data. Implied risk and volatility are introduced and computed for large option datasets. We discuss how they can be used in qualitative and quantitative analysis of option market data.

Optimal stopping rules for directionally reinforced processes

2001 ◽  
Vol 33 (2) ◽  
pp. 483-504 ◽  
Author(s):  
Pieter Allaart ◽  
Michael Monticino
Keyword(s):  
Transaction Costs ◽  
Optimal Stopping ◽  
Optimal Strategies ◽  
Stopping Rules ◽  
Elementary Model ◽  
Numerical Examples ◽  
Special Cases ◽  
Correlated Random Walks ◽  
Multiple Stopping ◽  
Optimal Stopping Rules

This paper analyzes optimal single and multiple stopping rules for a class of correlated random walks that provides an elementary model for processes exhibiting momentum or directional reinforcement behavior. Explicit descriptions of optimal stopping rules are given in several interesting special cases with and without transaction costs. Numerical examples are presented comparing optimal strategies to simpler buy and hold strategies.

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