Forward Volatility and Discrete Arithmetic Asian Options

Summary

The document asks whether a discretely sampled arithmetic Asian option depends on forward implied volatility. It compares the question with forward-starting and barrier options, whose values can be sensitive to the volatility smile at a future reset date, and notes that stochastic volatility models are often used to control forward volatility. It offers no answer, model, calculation, or market evidence, so the question remains open within the source.

An arithmetic Asian payoff depends on the distribution of the average of prices observed across multiple dates, not solely on volatility at one future date. The joint evolution of the underlying, including its volatility term structure, smile dynamics, and correlations across observation dates, can therefore affect valuation. This makes forward volatility relevant to modeling, but does not mean every path-dependent option has the same direct dependence on a single forward implied volatility. The post is a useful framing of that distinction, while leaving the precise sensitivity and model choice unresolved.

Key ideas

• A discrete arithmetic Asian option depends on prices sampled across its averaging schedule.
• Its value can be affected by the joint distribution of underlying prices over those dates.
• Forward volatility dynamics may matter, but the relevant sensitivity is not necessarily to one future smile alone.
• The source asks the question without providing an explanation or evidence.

Tags

# Does the Asian Option (average Option) depend on the forward implied vol


# Does the Asian Option (average Option) depend on the forward implied vol












I can easily understand that the forward starting Option and Barrier Option depend on the forward implied vol smile at resetting date, so we always choose the stochastic vol model for underlying to control the forward vol.

Does the Asian Option (discrete arithmetic araverage) also depend on the forward implied vol? And it seems each path dependent Option depends on the forward implied vol.

Can anyone give me a clear explaination?

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