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PDE Schemes for Pricing Discrete Barrier Options

Article Quant Q&A · Author: VAR
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Summary

The note identifies finite-difference methods as a classical approach to pricing discrete barrier options. For a local-volatility model, it points to a PDE solved with Crank–Nicolson time stepping and Rannacher startup steps. For a stochastic local-volatility model, it names an alternating direction implicit (ADI) scheme.

The answer is a brief recommendation, not a worked derivation or comparison. It provides no implementation details, numerical tests, accuracy estimates, or model-specific boundary and monitoring treatments. The suggested methods therefore serve as a starting point; choosing and validating a scheme for a particular barrier contract still requires attention to its dynamics and discrete observation schedule.

Key ideas

  • Finite-difference PDE methods are presented as a classical approach to discrete barrier pricing.
  • Crank–Nicolson with Rannacher time stepping is suggested for local-volatility models.
  • An ADI scheme is suggested for stochastic local-volatility models.
  • The brief answer does not compare methods or give validation evidence.

Tags

OptionsDerivatives pricingVolatility
Full text
# What is the go-to method for numerical pricing of discrete barriers?


# What is the go-to method for numerical pricing of discrete barriers?












There are tons of methods for pricing discrete barrier options in various models?

What is the go-to "classical" method that is most popular?

Hopefully not Monte Carlo (significant accuracy would take ages even with variance reduction since it's path-dependent)....

## Answer by Magic is in the chain (score 2)

https://quant.stackexchange.com/a/50405

The ‘classical’ would be PDE based, say Crank Nicolson with Rannacher time marching for local vol based approach, and ADI scheme for Stochastic local vol.

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