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 TurnballWakeman approximation we calculate the price and delta, and for comparison using BlackScholes to show the result for a regular European call. Not how much less the Asian call is to a regular call option.

Asian Call

Regular Call

Value

4.55 
8.68 
Delta

0.52 
&.57 
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.
Month

Stock Price

Average

1

100.000

100.000

2

102.000

101.000

3

102.500

101.500

4

103.000

101.875

5

101.750

101.850

6

102.250

101.917

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.

Asian Call

Regular Call

Value

2.28 
7.83 
Delta

0.49 
0.61 
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.
Month

Stock Price

Average

7

103.000

102.071

8

104.000

102.313

9

105.500

102.611

10

106.000

102.950

11

107.000

103.318

12

110.000

103.875

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.
