Asian Options
This page demonstrates pricing of Asian Options by solving corresponding partial differencial equations using finite difference method.
An Asian option (or average value option) is a special type of option contract. For Asian options the payoff is determined by the average
underlying price over some pre-set period of time. This is different from the case of the usual European option and American option,
where the payoff of the option contract depends on the price of the underlying instrument at exercise; Asian options are thus one of the
basic forms of exotic options. Here we constder Asian Average Rate (Fixed Strike) call and put options.
One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity
Another advantage of Asian options involves the relative cost of Asian options compared to European or American options.
Because of the averaging feature, Asian options reduce the volatility inherent in the option; therefore, Asian options are typically
cheaper than European or American options.
The underlying asset is assumed to follow a geometric Brownian motion with process \[ dS_t = (r - \delta) S_t dt + \sigma S_t dW_t, \]
where \(r\) is the riskless rate of return, \(\delta\) is a continuously paid dividend, \(\sigma\) is the standard deviation and \(W_t\)
is the Brownian motion and \(S\) is the underlying asset price. For an Average Rate Asian call, the payout is \[ C(T)=\max(A(0,T)-K,0) \]
where \(K\) is the strike and \(A\) is the average. Similarly for a put the payout is \[ C(T)=\max(K-A(0,T),0) \]
For a discretely monitored Asian option, the standard arithmetic average over the monitoring times
\(t_1, . . . , t_n\) is defined as \[ A(t_n)=\frac{1}{n} \sum_{i=1}^n{S(t_i)} \]
| Call/Put |
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| Spot |
\( S = \) |
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Please enter a value in range [0.01, 99999]
The input cannot be empty
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| Maturity (years) |
\( T = \) |
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Please enter a value in range [0.001, 150]
The input cannot be empty
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| Strike |
\( K = \) |
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Please enter a value in range [0.01, 99999]
The input cannot be empty
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| Interest rate |
\( r = \) |
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Please enter a value in range [0.0, 1.0]
The input cannot be empty
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| Volatility |
\( \sigma = \) |
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Please enter a value in range [0.0, 1.0]
The input cannot be empty
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| Dividend |
\( \delta = \) |
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Please enter a value in range [0.0, 1.0]
The input cannot be empty
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| Mesh size in asset S |
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Please enter an integer in range [10, 1,000]
The input cannot be empty
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| Number of time steps |
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Please enter an integer in range [10, 5,000]
The input cannot be empty
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| Mesh size in average A |
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Please enter an integer in range [10, 500]
The input cannot be empty
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| Number of monitoring dates |
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Please enter an integer in range [10, 500]
The input cannot be empty
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Important! This model is for online demonstration purposes only. Calculations can take a long time if the number of monitoring dates, times steps and mesh size are high. The time-out for calculations has been set to 1 hour, after which the webpage will return an error. We suggest you start with low values and then increase them if better accuracy is needed.