# Asian option

Asian option |
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An **Asian option** is a type of exotic option that is based on the average price of the underlying asset over a predetermined period of time. This allows the option to be based on more than one price point, unlike a traditional option which is based on a single price point. This type of option is more often used for hedging purposes, as it provides a more accurate representation of the asset's performance. It also provides investors with more flexibility in terms of how to approach their hedging strategy.

## Example of asian option

- An Asian option is a type of exotic option that is based on the average price of the underlying asset over a predetermined period of time. This type of option is commonly used by investors to hedge their positions. For example, an investor might purchase an Asian option to protect themselves against potential losses in the event that the underlying asset’s price falls. The investor could then choose an option that pays out if the average price of the asset over the predetermined period falls below a certain level.
- Another example of an Asian option is a digital Asian option. This type of option pays out a predetermined amount if the average price of the underlying asset over the predetermined period is equal to or greater than a certain level. This type of option is often used by investors to hedge against potential losses if the underlying asset’s price rises.
- A third example of an Asian option is a barrier Asian option. This type of option pays out if the average price of the underlying asset over the predetermined period either falls below or rises above a certain level. This type of option is often used by investors to hedge against potential losses if the underlying asset’s price moves in either direction.

## Formula of asian option

The value of an Asian option is determined by taking the average price of the underlying asset over a predetermined period of time and multiplying it by the option’s strike price. The formula for calculating the value of an Asian option is as follows:

$$V = \frac{1}{T} \sum_{t=1}^{T} S_t \cdot e^{-rT} - K \cdot e^{-rT} $$

Where:

V = Value of the Asian option

$$S_t$$ = Price of the underlying asset at time t

T = Number of time periods

K = Strike price

This formula takes the average price of the underlying asset over the predetermined period of time and multiplies it by the option’s strike price. The discounted factor $$e^{-rT}$$ is used to account for the time value of money. The result is then subtracted from the strike price to reach the final value of the option.

The advantage of using an Asian option is that it is more accurate than a traditional option. This is because it takes into account more than one price point, so it more accurately reflects the true performance of the underlying asset. This can be especially beneficial for investors who are looking to hedge their positions with more precision.

## When to use asian option

An Asian option is an exotic option that is based on the average price of an underlying asset over a predetermined period of time. It is often used in hedging strategies, as it provides more flexibility and accuracy in pricing than traditional options. Asian options can be used in a variety of situations, such as:

- To mitigate the risk of price fluctuations in volatile markets;
- To limit losses when trading commodities;
- To protect against sudden changes in currency exchange rates;
- To hedge against shifts in the value of assets;
- To provide protection against the expiration of traditional options;
- To reduce the cost of hedging strategies.

## Types of asian option

Asian options are a type of exotic option that are based on the average price of the underlying asset over a predetermined period of time. The main types of Asian options are:

- Average Price Option – This option is based on the average price of the underlying asset over the predetermined period.
- Capped Average Price Option – This option is similar to an average price option, but it is capped at a certain price level.
- Range Average Option – This option is based on the average price of the underlying asset within a certain range.
- Lookback Average Option – This option is based on the average price of the underlying asset over the entire predetermined period, not just a single point.
- Asian Barrier Option – This option is based on the average price of the underlying asset over the predetermined period and is triggered when the price reaches a certain level.
- Asian Digitals Option – This option is based on the average price of the underlying asset over the predetermined period and is either triggered or not triggered based on whether it reaches a certain level.

## Advantages of asian option

An Asian option is an exotic option based on the average price of the underlying asset over a predetermined period of time. It provides investors with more flexibility in terms of how to approach their hedging strategy, and offers several advantages:

- It provides a more realistic assessment of the asset's performance, as it takes into account the fluctuations in the asset's price over the predetermined period.
- It gives investors the ability to hedge their positions over time, as the option is based on the average price of the asset over the predetermined period.
- It can provide a more stable return, since it is not tied to a single price point.
- It is often cheaper than traditional options, as the pricing is based on a range of prices rather than just one.
- It can be used to hedge against volatility, as the option allows investors to take advantage of the average price of the underlying asset.

## Limitations of asian option

Asian options have certain limitations that should be taken into account when considering them as a hedging strategy. These include:

- The cost of the option can be higher than that of a European option due to the added complexity of the contract.
- The option may be less liquid than a European option and therefore not as easily traded.
- The option may be more difficult to price accurately due to the complexity of the contract.
- The option may be more difficult to hedge due to the multiple price points being considered.
- The option may be difficult to exercise as the underlying asset may not be available for delivery at the time of expiration.

An introduction to the other approaches related to Asian options is that they involve more complex strategies and are often used to reduce risk or increase returns in a portfolio. Some of these approaches include:

**Options Arbitrage**: This involves taking advantage of the price differences between two or more options on the same asset. By buying the cheaper option and selling the more expensive one, the investor can gain a risk-free profit.**Delta Hedging**: This involves taking a position in the underlying asset in order to offset the risk associated with the option. By taking a long or short position in the underlying asset, the investor can reduce their exposure to the option's price fluctuations.**Options Spreads**: This involves taking a position in two or more options on the same asset in order to reduce the risk associated with the option. By buying one option and selling another, the investor can reduce the risk of the option while still receiving the potential for gains.

In summary, other approaches related to Asian options involve complex strategies and are often used to reduce risk or increase returns in a portfolio. These strategies include options arbitrage, delta hedging, and options spreads.

## Suggested literature

- Rogers, L. C. G., & Shi, Z. (1995).
*The value of an Asian option*. Journal of Applied Probability, 32(4), 1077-1088. - Vecer, J. (2001).
*A new Pde approach for pricing arithmetic average Asian options*. Journal of computational finance, 4(4), 105-113. - Sun, J., & Chen, X. (2015).
*Asian option pricing formula for uncertain financial market*. Journal of Uncertainty Analysis and Applications, 3(1), 1-11.