Comparing Asian Strike and Asian Rate Option Values

Summary

The document raises a pricing question about arithmetic-average Asian options with discrete sampling. The author describes simulating asset paths with the Euler method and estimating expected payoffs by Monte Carlo, then observes that at-the-money Asian strike options appear more valuable than Asian rate options in their calculations.

The proposed intuition is that averaging the underlying price smooths its volatility for an Asian rate option, while the strike option retains more of the underlying’s variation despite its random average strike. The author notes that this result conflicts with online explanations but provides no resolution, model parameters, numerical results, or answer. It is therefore a useful statement of a payoff-comparison problem and a simulation setup, but not a validated pricing conclusion. The observed ordering may depend on precise payoff conventions and implementation details.

Key ideas

• The question concerns arithmetic-average Asian options with discrete monitoring.
• The author estimates payoffs using Euler-simulated paths and Monte Carlo.
• The reported simulations place at-the-money Asian strike options above Asian rate options in value.
• The proposed explanation focuses on how averaging affects exposure to underlying price variation.
• The document offers no answer or validation, so the reported ordering is not established generally.

Tags

# Asian Strike vs Asian Rate option: difference in value


# Asian Strike vs Asian Rate option: difference in value












I wrote a few lines of python code to price Asian options. I simulated asset prices with Euler method and run a Monte Carlo to calculate the expected payoffs. I use arithmetic average, discrete sampling.

When pricing ATM options, the Asian Strike price is always higher than the Asian Rate price. My reasoning would be that in the case of the Asian Strike, the volatility of the underlying asset would remain in full (though the strike is uncertain), whereas in the case of the Asian Rate the volatility of the underlying asset is smoothened by taking the average of S.

I can't quite get my head around it, as I found online resources saying that it should be the opposite. Any help would be really appreciated.

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