Asian Options – Tutorial and Excel Spreadsheet

This articles explores Asian options, and offers an Excel spreadsheet based on geometric and arithmetic averages.

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 have several advantages

  • 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.

Payoff Equations 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)

Asian Option Excel

Feel free to leave a comment, or let me know if you have any questions.

Download Excel Spreadsheet to Price Asian Options (locked spreadsheet, only change parameters and view results)

Buy Unlocked Spreadsheet for $5 (unlocked, all formulas exposed)


13 thoughts on “Asian Options – Tutorial and Excel Spreadsheet”

  3. 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

    Reply

    • 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)

      Reply

      • 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

        Reply

      • Hi Samir,
        First sorry if the qestion apears in two sections. I just can’t see my question anywhere.
        I bought the sheet hope that helps a bit :-).

        I have a similar question as duderino.
        I both want to value the option before the averaging period start and in the averaging period before maturity. I thought this formula was for valuing before averaging period started?
        “Time to maturity” is obvious but “remaining time” I’m not totally sure. I thought that was the time until the averaging period starts?
        An then also about the “averaging price”. The averaging price is first known at maturity so it must be something different? You wrote average price sampled over time so is that the future prices for each time in the averaging period? I’m unsure about this input.
        And last I’m trying to link the excel formula to the Levy formula which I can find on google, but I’m having a hard time. Do you have the formula expressed in non excel format so i can try to link them?
        Thanks alot in advance and appreciated the work done.

        cheers

        Reply

  4. 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

    Reply

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