Asian option

Asian option ( English Asian option ) - a type of option in which the exercise price is determined based on the average value of the underlying asset for a certain period of time. An Asian option is also called an average price option or a mid-course option. As a rule, such options are for goods, stock indices , exchange rates and interest rates ^[1] . Asian options are popular in markets with high volatility of underlying assets (oil, non-ferrous metals, etc.) ^[2] .

Content

History

The first option of this type was sold in 1987 by the Tokyo branch of the American Bank ( English American Bank ) ^[3] .

Features

A distinctive feature of options of this type is that the strike price (strike) is unknown at the time of the conclusion of the contract. Only the method for determining the price by the spot price values for a certain period, including the future values, is indicated. The following options are possible:

The strike price is equal to the maximum value of the spot price for the duration of the option.
The strike price is equal to the minimum spot price for the time the option is valid.
The strike price is defined as the average value of the spot price at specified times. In this case, the dates involved in the formation of the average value are indicated, as well as the method for calculating the average value.

An option for which the strike price is indicated at the time of the conclusion of the contract, but instead of the spot price at the time of execution, the average spot price for a certain period is used, also called Asian ^[4] .

Basic options for Asian options

Fixed strike price (also known as “average rate”), sale:

P(T)={\text{max}}\left(A(0,T)-K,0\right),

{\ displaystyle P (T) = {\ text {max}} \ left (A (0, T) -K, 0 \ right),}

where A denotes the average, and K - strike. The equivalent of the put option is calculated by the formula:

P(T)={\text{max}}\left(K-A(0,T),0\right).

{\ displaystyle P (T) = {\ text {max}} \ left (KA (0, T), 0 \ right).}

The floating strike price (a floating rate) when selling an Asian option:

P(T)={\text{max}}\left(S(T)-kA(0,T),0\right),

{\ displaystyle P (T) = {\ text {max}} \ left (S (T) -kA (0, T), 0 \ right),}

,

where k is weighting, usually 1 is excluded from descriptions.

Receiving averages

The average can be obtained in various ways. This is usually the arithmetic average . With continuous monitoring, it is calculated as follows:

A(0,T)={\frac {1}{T}}\int _{0}^{T}S(t)dt.

{\ displaystyle A (0, T) = {\ frac {1} {T}} \ int _ {0} ^ {T} S (t) dt.}

With discrete monitoring (with monitoring during $t_{1},t_{2},\dots ,t_{n}$ ${\ displaystyle t_ {1}, t_ {2}, \ dots, t_ {n}}$ ):

A(0,T)={\frac {1}{N}}\sum _{i=1}^{N}S(t_{i}).

{\ displaystyle A (0, T) = {\ frac {1} {N}} \ sum _ {i = 1} ^ {N} S (t_ {i}).}

There are also Asian options, where the average value is calculated as the geometric average . With constant monitoring, it is calculated by the formula:

A(0,T)=\exp \left({\frac {1}{T}}\int _{0}^{T}\ln(S(t))dt\right).

{\ displaystyle A (0, T) = \ exp \ left ({\ frac {1} {T}} \ int _ {0} ^ {T} \ ln (S (t)) dt \ right).}

Benefits of Asian Options

Asian options are investment instruments with a moderate level of risk. Since the price of an option is based on data on the price of the underlying asset for a certain period, the investor has the opportunity to make a rational judgment about the appropriateness of investments ^[5] .

Another advantage of Asian options is that these options are usually cheaper than American or European options, because using the average cost of the underlying asset reduces the volatility of the derivative.

Notes

↑ Finam. Dictionaries
↑ Derivatives: Course for beginners, 2009 , p. 82
↑ Palmer, Brian (July 14, 2010), Why Do We Call Financial Instruments "Exotic"? Because some of them are from Japan. , Slate , < http://www.slate.com/id/2260463/ >
↑ Simon Vine, 2008 , p. 295.
↑ Financial investments - educational center

Literature

Simon Vine. Options. Full course for professionals. - M .: Alpina Publisher, 2008. - 466 p. - ISBN 978-5-9614-0855-3 .
Derivatives: Course for beginners = An Introduction to Derivatives. - M .: "Alpina Publisher", 2009. - 208 p. - (Series "Reuters for financiers"). - ISBN 978-5-9614-1092-1 .
Andrew M. Chisholm. = Derivatives Demystified: A Step-by-Step Guide to Forwards, Futures, Swaps and Options. - John Wiley & Sons, 2010. - 288 p. - (The Wiley Finance Series). - ISBN 978-0470749371 .

[1] Finam. Dictionaries

[_2863831602f50b20-2] Derivatives: Course for beginners, 2009 , p. 82

[3] Palmer, Brian (July 14, 2010), Why Do We Call Financial Instruments "Exotic"? Because some of them are from Japan. , Slate , < http://www.slate.com/id/2260463/ >

[_41aa2b982e3e323c-4] Simon Vine, 2008 , p. 295.

[5] Financial investments - educational center