scholarly journals American Options Under Stochastic Volatility: Control Variates, Maturity Randomization & Multiscale Asymptotics

2014 ◽  
Author(s):  
Ankush Agarwal ◽  
Sandeep Juneja ◽  
Ronnie Sircar
Keyword(s):  
Stochastic Volatility ◽  
American Options ◽  
Control Variates ◽  
Multiscale Asymptotics

scholarly journals COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY

2007 ◽  
Vol 10 (02) ◽  
pp. 331-361 ◽  
Author(s):  
SAMULI IKONEN ◽  
JARI TOIVANEN
Keyword(s):  
Stochastic Volatility ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
American Options ◽  
Splitting Method ◽  
Linear Complementarity ◽  
Splitting Methods ◽  
Time Step ◽  
Operator Splitting Methods ◽  
Volatility Model

Efficient numerical methods for pricing American options using Heston's stochastic volatility model are proposed. Based on this model the price of a European option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option. This price can be computed by solving a linear complementarity problem. The idea of operator splitting methods is to divide each time step into fractional time steps with simpler operators. This paper proposes componentwise splitting methods for solving the linear complementarity problem. The basic componentwise splitting decomposes the discretized problem into three linear complementarity problems with tridiagonal matrices. These problems can be efficiently solved using the Brennan and Schwartz algorithm, which was originally introduced for American options under the Black and Scholes model. The accuracy of the componentwise splitting method is increased by applying the Strang symmetrization. The good accuracy and the computational efficiency of the proposed symmetrized splitting method are demonstrated by numerical experiments.

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