Monte Carlo Bias in Lévy-Driven Barrier Option Pricing

Summary

The document raises a pricing question about a down-and-out call when the underlying follows a jump process, with the Kou double-exponential and normal inverse Gaussian models suggested to represent asymmetric jumps. It considers raw Monte Carlo simulation as an alternative to mathematically complex semi-analytical methods and asks whether a large simulation can still produce a biased estimate.

No answer, calculation, or empirical comparison is included, so the document does not establish the source or size of any bias. It frames an important limitation to investigate: a large number of simulated paths can reduce sampling error, but it does not by itself resolve errors from how paths are simulated or how barrier crossings between observation times are handled. The question is therefore a starting point for studying jump-process simulation and barrier monitoring, rather than a complete pricing method.

Key ideas

• The document asks whether Monte Carlo estimates of down-and-out calls can be biased under Lévy jump models.
• It identifies the Kou double-exponential and NIG processes as candidate models for asymmetric jumps.
• It contrasts simulation with more mathematically demanding semi-analytical pricing methods.
• The text provides no answer or evidence about bias, so the pricing question remains unresolved.

Tags

# Pricing barrier option under Levy process: Biased estimate?


# Pricing barrier option under Levy process: Biased estimate?












I want to price a down and out call, barrier option, with the underlying asset following a Levy process. I am interest on the Kou double exponential model or the NIG process, to capture asymmetric behavior of jumps. Due to high mathematical complexity of semi-analytical approaches provided in the literature, I am leaning towards a raw monte carlo simulation. However, would the estimate of the price be biased, even after a large number of Iterations (e.g N=100.000)?

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