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Oscillating Errors in Explicit Finite-Difference Black–Scholes Pricing

Article Quant Q&A · Author: Chris
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Summary

The document describes a numerical experiment comparing an explicit finite-difference solution for a European call option with the analytical Black–Scholes price. The author fixes the time step and plots pricing error against the price-grid spacing, expecting the spatial error to follow the method’s second-order behavior.

The reported curve appears broadly consistent with that expectation but contains unexplained oscillations. The document provides no plot details, parameter values, boundary conditions, stability analysis, or resolution, and it does not establish the source of the oscillations. It is best read as a numerical-methods question about diagnosing discretization error in option pricing. Interpretation would require more information about the grid, payoff treatment, time-step relation to spatial spacing, and the error metric.

Key ideas

  • The experiment compares explicit finite-difference call prices with the analytical Black–Scholes value.
  • The author examines error as spatial grid spacing changes while holding the time step fixed.
  • The observed error trend is accompanied by unexplained oscillations.
  • Diagnosing the oscillations requires details about the grid, boundaries, stability, and error measurement.

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OptionsDerivatives pricingStatistics
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# Oscillating errors in finite difference Black Scholes


# Oscillating errors in finite difference Black Scholes












I am writing an implementation of the explicit finite difference method to price a standard european call option, and comparing the results to the corresponding analytical value to gauge the error both in time and space/price. This is the error curve I get for fixed dt = 1.0e-5 and plotting as a function of ds:

Recalling that the finite difference for BS is of order ds^2, the behaviour of the curve seems appropriate, except for those strange oscillations. Has anyone seen anything like it? What could be the reason for such strange behaviour?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.