Corrections in Heston Model Derivations for Bond Options

This paper proposes modified mean-variance risk measures for long-term investment portfolios. Two types of portfolios are considered: constant proportion portfolios and increasing amount portfolios. They are widely used in finance for investing assets and developing derivative securities. We compare the long-term behavior of a conventional mean-variance risk measure and a modified one of the two types of portfolios, and we discuss the benefits of the modified measure. Subsequently, an optimal long-term investment strategy is derived. We show that the modified risk measure reflects the investor’s risk aversion on the optimal long-term investment strategy; however, the conventional one does not. Several factor models are discussed as concrete examples: the Black–Scholes model, Kim–Omberg model, Heston model, and 3/2 stochastic volatility model.

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Removing the Correlation Term in Option Pricing Heston Model: Numerical Analysis and Computing

Abstract and Applied Analysis ◽

10.1155/2013/246724 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 5

Author(s):

R. Company ◽

L. Jódar ◽

M. Fakharany ◽

M.-C. Casabán

Keyword(s):

Option Pricing ◽

Stochastic Volatility Model ◽

Heston Model ◽

Diffusion Reaction ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Volatility Model ◽

Classical Technique ◽

Domain Consistency ◽

Positive Coefficients

This paper deals with the numerical solution of option pricing stochastic volatility model described by a time-dependent, two-dimensional convection-diffusion reaction equation. Firstly, the mixed spatial derivative of the partial differential equation (PDE) is removed by means of the classical technique for reduction of second-order linear partial differential equations to canonical form. An explicit difference scheme with positive coefficients and only five-point computational stencil is constructed. The boundary conditions are adapted to the boundaries of the rhomboid transformed numerical domain. Consistency of the scheme with the PDE is shown and stepsize discretization conditions in order to guarantee stability are established. Illustrative numerical examples are included.

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Escape problem under stochastic volatility: The Heston model

Physical Review E ◽

10.1103/physreve.78.056104 ◽

2008 ◽

Vol 78 (5) ◽

Cited By ~ 35

Author(s):

Jaume Masoliver ◽

Josep Perelló

Keyword(s):

Stochastic Volatility ◽

Heston Model ◽

Escape Problem

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