Early Exercise Decision in American Options with Dividends, Stochastic Volatility and Jumps

One approach to cope with uncertain diffusion parameters when pricing options portfolios is to identify the parameters [Formula: see text] in a subset [Formula: see text] of the parameter space which form the worst-case for a particular portfolio. For the sell-side, this leads to a nonlinear algorithm that maximizes the expected liability under the risk-neutral measure. [Formula: see text] depends on the portfolio under consideration. Moreover, the algorithm must take into account that the exposure to [Formula: see text]-risk changes when non-vanilla components such as barrier or American options knock out or are exercised early. In this paper, we describe techniques to price portfolios with American options under worst-case scenarios based on uncertain volatility models. We also present heuristics which reduce the computational complexity that arises from the necessity to consider many early exercise combinations at a time. These heuristics reduce the compute time by almost one half.

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EXTENSION OF ASSET AND RISK MANAGEMENT IN THE PRESENCE OF AMERICAN OPTIONS: DIVIDENDS, EARLY EXERCISE, AND INFORMATION UNCERTAINTY

Derivatives, Risk Management & Value ◽

10.1142/9789812838636_0014 ◽

2009 ◽

pp. 615-666

Keyword(s):

Risk Management ◽

American Options ◽

Information Uncertainty ◽

Early Exercise

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COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024907004202 ◽

2007 ◽

Vol 10 (02) ◽

pp. 331-361 ◽

Cited By ~ 52

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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