An integral equation representation approach for valuing Russian options with a finite time horizon

Jeon, Junkee; Han, Heejae; Kim, Hyeonuk; Kang, Myungjoo

doi:10.1016/j.cnsns.2015.12.019

Cited by 20 publications

(16 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the BSM model there are several quantitative studies, e.g. Duistermaat et al (2005) by the method referred to as nth-order randomization, based on a method proposed by Carr (1998) for American options, Kimura (2008) applying the Laplace-Carlson transform and Jeon et al (2016) defining an equivalent PDE problem with mixed boundary conditions and solving it using Mellin transform. These methods rely on the possibility of explicit solving the respective transformed problems and hence are restricted to the BSM model.…”

Section: The Russian Optionmentioning

confidence: 99%

“…Additionally to these two natural constrains we considered the following one: we asked the free boundary to be a concave function, such form of the boundary can be see in Kimura (2008), Jeon et al (2016). That is, in terms for our approximate boundary we posed additionally In Figure 4 the typical absolute errors that we obtain for the boundary conditions ( 40) and (41) are presented.…”

Section: Minimization Processmentioning

confidence: 99%

“…Even though there are several quantitative studies on the FHRO, e.g. Duistermaat et al (2005), Kimura (2008) and Jeon et al (2016), it seems that there is no agreement on the exact value for the option. We contribute to this discussion confirming the values from Jeon et al (2016) and providing possible explanation of the discrepancy with Kimura (2008).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing

Kravchenko¹,

Kravchenko²,

Torba³

et al. 2018

Preprint

View full text Add to dashboard Cite

This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of solutions for the heat equation, transmutation operators and recently discovered Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations to construct a complete system of solutions for the considered partial differential equations. The conceptual algorithm for the application of the method is presented. The valuation of Russian options with finite horizon is used as a numerical illustration. The solution under different horizons is computed and compared to the results that appear in the literature.

show abstract

Section: The Russian Optionmentioning

confidence: 99%

Section: Minimization Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing

Kravchenko¹,

Kravchenko²,

Torba³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…In recent years, the diverse options have been studied with Mellin transforms by many researchers (cf. [5][6][7][8][9]). In particular, pricing formulas for vulnerable options under the structural model have been derived using the double Mellin transforms (cf.…”

Section: Introductionmentioning

confidence: 99%

An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon

Jeon

Kim

2020

Mathematics

Self Cite

View full text Add to dashboard Cite

This paper studies an irreversible investment problem under a finite horizon. The firm expands its production capacity in irreversible investments by purchasing capital to increase productivity. This problem is a singular stochastic control problem and its associated Hamilton–Jacobi–Bellman equation is derived. By using a Mellin transform, we obtain the integral equation satisfied by the free boundary of this investment problem. Furthermore, we solve the integral equation numerically using the recursive integration method and present the graph for the free boundary.

show abstract

“…Mixed boundary condition usually arises in the option pricing problem related to maximum process of underlying asset. Jeon et al [5] derived an integral equation satisfying the Russian option using the Mellin transform. The Russian option satisfies (1+1)-dimensional Black-Scholes equations with mixed boudnary conditions.…”

mentioning

confidence: 99%

(1+2)-dimensional Black-Scholes equations with mixed boundary conditions

Jeon¹,

Oh²

2020

Communications on Pure &Amp; Applied Analysis

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate (1+2)-dimensional Black-Scholes partial differential equations(PDE) with mixed boundary conditions. The main idea of our method is to transform the given PDE into the relatively simple ordinary differential equations(ODE) using double Mellin transforms. By using inverse double Mellin transforms, we derive the analytic representation of the solutions for the (1+2)-dimensional Black-Scholes equation with a mixed boundary condition. Moreover, we apply our method to European maximumquanto lookback options and derive the pricing formula of this options. 2000 Mathematics Subject Classification. 35K20. Key words and phrases. (1+2)-dimensional Black-Scholes equations, parabolic partial differential equations, double-Mellin transform, mixed boundary condition, option pricing.

show abstract

An integral equation representation approach for valuing Russian options with a finite time horizon

Cited by 20 publications

References 20 publications

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing

An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon

(1+2)-dimensional Black-Scholes equations with mixed boundary conditions

Contact Info

Product

Resources

About