Choosing Volatility for Pricing Discrete-Average Asian Options

Summary

The document discusses how to select an implied volatility for a fixed-strike Asian put with discrete averaging in a Black–Scholes setting. A simple practical choice is the volatility at the option’s expiry from the vanilla volatility surface; this can provide a rough valuation or vega estimate. For greater accuracy, it points to local volatility calibrated to the full surface through expiry, as well as semi-analytical approximations that weight volatility over time.

It also gives a short-maturity approximation: use the vanilla implied volatility at the same maturity but at a modified strike, defined as spot multiplied by the strike-to-spot ratio raised to the six-fifths power. This rule assumes a flat forward curve, such as for a futures contract, and is linked to an expansion for continuously averaged Asian options in a local volatility model. The recommendations are approximations; the simple surface lookup is described as adequate for rough assessment, while more involved methods may be warranted for competitive quoting. The cited rule’s assumptions limit its generality, particularly for discrete averaging or non-flat forwards.

Key ideas

• A vanilla volatility surface value at the Asian option’s expiry offers a simple rough volatility input.
• A local volatility model using the surface through expiry can provide a more detailed approach.
• Semi-analytical methods may approximate Asian option values using weighted volatilities over time.
• A short-maturity approximation uses the same expiry’s vanilla volatility at a modified strike.
• The modified-strike rule assumes a flat forward curve and is based on continuous averaging.

Tags

# Implied Volatility for Asian option


# Implied Volatility for Asian option












I am new to the topic of Asian options. Assume I want to price an Asian put (fixed strike, discrete average) in the Black Scholes world. I know implementations to calculate the value but what is the best way to find the implied volatility parameter? Is there a usual way to derive it from the option market of plain vanilla products, e.g. European calls or puts of a certain range of maturities?

## Answer by Strange (score 3, accepted)

https://quant.stackexchange.com/a/4445

The easiest way is to use single-expiry volatility that you would get from your volatility surface. It is usually good enough for government work (e.g. to get a sense if you are getting fleeced by a dealer or to understand your vega risk).

A better way is to use local volatility model and the whole volatility surface up to the date of expiry. There is also a bunch of semi-analytical approximations that use weighted volatilities up to there expiry date. Unless you are a dealer and trying to quote these in competition, you don't need to bother with these.

## Answer by danp (score 2)

https://quant.stackexchange.com/a/55744

The approximation I mentioned earlier is that in order to price an Asian option with strike K and maturity T on an asset with spot price S0, one should use the implied volatility at the modified strike K'=S0*(K/S0)^(6/5) and the same maturity T. This assumes an asset with a flat forward curve, like a futures contract.

The derivation of this result is presented in this Risk magazine article What is the volatility of an Asian option?

The approach is based on a short maturity expansion for Asian options in the local volatility model (continuous time averaging) presented in an earlier paper with Lingjiong Zhu.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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