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# Asian Options – Tutorial and Excel Spreadsheet

Of the many types of exotic options that are available for investors, Average Rate Options or, as they are better known, Asian Options are some of the most practical. Asian options are priced based on the average price of the underlying instrument. Both the strike value and expiration value can be calculated from the average value over a period of time.

Asian options are no more difficult to understand than their vanilla counterparts. Consider a call on oil for a month, assuming a strike of \$100 per barrel. The average price over the month would determine  if a payout is due.  If the average is \$104 per barrel, then the investor would receive \$4 per barrel. However, the option is worthless if  the average price of a barrel of oil is is \$96

• Asian options reduce the impact of any market manipulation.
• The averaging tends to lower volatility (with a greater averaging period resulting in a lower volatility).  Hence Asian options are cheaper than their European or American counterparts

Asian options are, however, difficult to price.  Unlike their European counterparts which have an analytical solution in the form of the Black Scholes equation, no closed form solution exists for Asian Options when the asset is lognormally distrubuted.
Asian options are largely used for derivatives based on commodities (such as crude oil) and currencies.  Their history dates from 1987, when they were used to price crude oil derivatives in Tokyo.

Asian options are averaged arithmetically or geometrically, and either of these approaches can be weighted.  The following equations give the payoffs for Asian options.

Kemna & Vorst (1990) proposed a closed form solution for pricing asian options with an geometric average.

However, there no closed form solutions for pricing Asian options with an arithmetic average. Some authors have proposed approximations for this problem, including Turbull and Wakeman (1991) and Levy (1991).  Numerical approaches, such as binomial lattices or monte carlo simulation, are also used.

## Price Asian Options in Excel

This Excel spreadsheet gives the price of an Asian Option based on geometric averages (Kemna & Vorst, 1990) and arithmetic averages (Levy, 1991)

### 8 Responses to "Asian Options – Tutorial and Excel Spreadsheet"

1. Samir says:

Email sent!

Hi,
Does anyone can help to find vba for building excel trinomial tree, please ?

3. duderino says:

Hi Samir,

Thanks for the calculator. Can I clarify what the ‘Average price’ is in your spreadsheet – is the forward price at the averaging start time?

Cheers

• Samir says:

It’s the average price sampled over time (not the price at the average start time)

Arithmetic Avg Price = (sum of 1 to n (S1 + S2 + S3 + … Sn)) / n
Geometric Avg Price = nth root of (S1 * S2 * S3 * … Sn)

• duderino says:

Thanks. This only really works for valuation of options where we are already in the averaging period, yes?

I’m looking to value an option valued today with averaging start time in 6 months and expiry in 1 year. If the spreadsheet worked for this I would put Time to Maturity = 1y and Remaining Time = 0.5y and Average Price as spot escalated by the risk free rate.

Thanks

4. Bill O'Keefe says:

Samir,

Any idea’s on how to replicate Asian Options using listed option…The CBOE has a flexible customized system that can trade out to 15 years and you can define exipies and have non-standard strikes…i.e S&P 500 1362.54 call with any ex-date

5. Samir says:

Hi Julien