Analysis of the stability of the linear boundary condition for the Black–Scholes equation

By H. Windcliff, Peter A. Forsyth, Kenneth R. Vetzal. 2004

117 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Condensed Matter Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/06c5b000ac99733fdb9420d5d90d703eab748261

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Peter A. Forsyth
2. George Labahn
3. Kenneth R. Vetzal
4. S. Clift

In Condensed Matter Physics

1. Peter A. Forsyth

In Numerical Analysis

1. Peter A. Forsyth
2. Ronald E. Mickens
3. Matthias Ehrhardt
4. S. Clift
5. Qamar Din

Citations in the corpus

• Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals (2009, background): “0 (Windcliff et al., 2004), which implies V HðB;D; ÞS þ FðB;D; Þ; (D:1) where HðB;D; Þ and FðB;D; Þ are independent of S.”
• Pricing methods and hedging strategies for volatility derivatives (2006, background): “However, the lower boundary is an outflow boundary [22] and using the approximation VSS = 0 at S = S1 will not affect the solution near S = S(0), t = 0, assuming that the computational domain is sufficiently wide [14].”
• Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance (2007, background): “…θ sup Qn∈Q̂ { (LQ n h φ n+1)n+1i + d n i } ] ∣∣∣∣∣ ≤ ∣∣∣∣∣(φτ )n+1i − φn+1i − φni∆τ ∣∣∣∣∣ + sup Q∈Q̂ ∣∣∣∣∣{LQφ + d}n+1i − (1− θ) { (LQh φ n+1)n+1i + d n+1 i } − θ { (LQh φ n)ni + d n i }∣∣∣∣∣ = O(∆τ) + O((∆S)max) + θ sup Q∈Q̂ ∣∣∣∣∣{LQφ + d}n+1i − { (LQh φ n)ni + d n i }∣∣∣∣∣ = O(∆τ) +…”
• Numerical solution of two asset jump diffusion models for option valuation (2008, background): “The outer region then acts as a buffer zone, so that the integral terms in the inner region have enough information for a sufficiently accurate evaluation.”
• A FAST, STABLE AND ACCURATE NUMERICAL METHOD FOR THE BLACK–SCHOLES EQUATION OF AMERICAN OPTIONS (2008, background): “Windcliff, Forsyth and Vetzal [40] derived necessary stability conditions for a finite difference discretization of the Black–Scholes equation for European options with the common linear asymptotic boundary condition , i.e. assuming that the second derivative of the option value vanishes as the mark”