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Asian options explained

Asian options are options where the payout is determined by the average of prices at a set interval over a certain maturity. The affect is generally they are cheaper at inception than a regular call/put. 

Asian Option Example

Lets look at an Equity example (the results would be the same for other underlyings such as commodities or foreign exchange)

• Stock Price: 100
• Strike: 100
• Expiry: 1 year
• Averaging: Monthly (12 periods)
• Volatility: 20%
• Risk Free Rate: 1.5%

Using a Turnball-Wakeman approximation we calculate the price and delta, and for comparison using Black-Scholes to show the result for a regular European call. Not how much less the Asian call is to a regular call option.

Now, let's move forward 6 months. At the start of each month we note the current stock price and calculate the average to date.

Now let's calculate the price at the 6 month mark. We use the average of all 6 months as our underlying in our Turnball Wakeman Approximation model, 101.917. For the Black Scholes we use the current stock price, 102.250. Once again our Asian call is considerably less than a regular call option.

Since the Asian has been set for 6 out of the 12 averages, the valuation is already fairly close to it's intrinsic value (ie Current Average - Stike). Now lets look at the rest of the year.

At year end, the Asian option would pay $3.875, as our average for the year was 103.875, while the regular call would pay $10 because the price at expiry was 110. Of course if the average was closer to the price at maturity the payoff would have been close to the regular call option. 

Asian options are often used in commodities for hedging since the underlying contracts will often have averaging components to them (for example Natural Gas deliveries over a month) 

Resolution provides tools for the valuation of Asian options as well as other exotic options. A free trial is available.

For more information see our pricing plans.