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| 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 option]]s.
| | The use of e-cigs is just a practice that's getting ever more popular, and several people took up the use of ecigs being a cleanser alternative to cigarette smoking. The reason being e-cigs don't result in ash, and they do not create a person’s residence, garments, and automobile smelling poor. Among the biggest areas of starting to employ ecigs entails investing in a beginner kit, and there are certainly a amount of issues someone should know about buying a beginner kit. Including investing in a slightly better beginner kit, and there are certainly a few factors a person must have a part of their starter kit.<br><br>Purchasing a marginally greater kit<br><br>Among the most frequent faults that people create when first just starting to smoke ecigs is that they tend to choose the cheapest ecig that's available to them. This could create a individual certainly not trying out the practice, and it also means that a person WOn't ever purchase a nice ecig when they do take up the practice. This is the reason it is a good idea to buy a better one, that appears the way in which someone want to buy to, which is even a good concept to purchase one which can be gradually replaced with time.<br><br>What should really be included in the kit<br><br>An excellent starter kit may have things such as a charger that is user friendly. The kit also needs to incorporate instructions on how to complete the e-cigarette with liquid, a rag to clean it with, plus it must also possess a some extra ejuice or tubes. More [http://ciglites.metroblog.com/ check out the post right here]. |
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| One advantage of Asian options is that these reduce the risk of [[market manipulation]] of the underlying instrument at maturity{{harv|Kemma|1990|1077}}.<ref>Kemna et al. 1990, p 1077</ref> 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. This can be an advantage for corporations that are subject to the [[Financial Accounting Standards Board]] {{harv|2004|FASB}} revised Statement No. 123, which required that corporations expense employee stock options.<ref name="FASB2004">{{cite report |publisher=Financial Accounting Standards Board|year=2004|number=123|title=Share-based payment|url=http://www.fasb.org/summary/stsum123r.shtml|author=FASB}}</ref>
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| == Etymology ==
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| In the 1980s Mark Standish was with the London-based Bankers Trust working on fixed income derivatives and proprietary arbitrage trading. David Spaughton, worked as systems analyst in the financial markets with Bankers Trust since 1984 when the Bank of England first gave licences for banks to do foreign exchange options in the London market. In 1987 Standish and Spaughton were in Tokyo on business when "they developed the first commercially used pricing formula for options linked to the average price of crude oil." They called this exotic option, the Asian option, because they were in Asia.<ref name="Falloon1999">{{cite book|editor1=William Falloon|editor2=David Turner|year=1999|chapter=The evolution of a market|title=Managing Energy Price Risk|location=London|publisher=Risk Books}}</ref><ref name="Wilmott2006">{{cite book|last=Wilmott|first=Paul|title=Paul Wilmott on Quantitative Finance|year=2006|publisher=John Wiley & Sons|page=427|url=http://books.google.co.uk/books?id=Y_R3Y4jkp_IC&pg=PA427&lpg=PA427&dq=Wilmott++%22david+Spaughton%22&source=bl&ots=5daJ7kpiq2&sig=qvAidjlVX7lZ1i38pwQSWLcSpTY&hl=en&sa=X&ei=WqpcUfPjH-SU0QXyj4GgDA&redir_esc=y#v=onepage&q=Wilmott%20%20%22david%20Spaughton%22&f=false|chapter=25}}</ref><ref>{{citation |url=http://www.slate.com/id/2260463/ |title = Why Do We Call Financial Instruments "Exotic"? Because some of them are from Japan. | first = Brian | last = Palmer | date = July 14, 2010 | publisher = Slate }}</ref><ref name="RiskEncyclopedia">{{cite web |year=2013 |publisher=Risk Encyclopedia |title=Asian Option (Average Option) |url=http://riskencyclopedia.com/articles/asian-option-average-option <!--|laysummary=This one page hypertext encyclopedia entry situates the Asian option (Average option) as document--> |quote="An Asian option (also called an average option) is an option whose payoff is linked to the average value of the underlier on a specific set of dates during the life of the option." "[I]n situations where the underlier is thinly traded or there is the potential for its price to be manipulated, an Asian option offers some protection. It is more difficult to manipulate the average value of an underlier over an extended period of time than it is to manipulate it just at the expiration of an option." |author=Glyn A. Holton}}</ref>
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| == Permutations of Asian option ==
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| There are numerous permutations of Asian option; the most basic are listed below:
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| Fixed strike (also known as an average rate) Asian call payout
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| : <math> P(T) = \text{max}\left( A(0,T) - K, 0 \right),</math>
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| where A denotes the average, and K the strike. The equivalent put option is given by
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| : <math> P(T) = \text{max}\left( K - A(0,T), 0 \right).</math>
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| The floating strike (or floating rate) Asian call option has the payout
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| : <math> P(T) = \text{max}\left( S(T) - k A(0,T), 0 \right),</math>
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| where k is a weighting, usually 1 so often omitted from descriptions. The equivalent put option payoff is given by
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| : <math> P(T) = \text{max}\left( k A(0,T) - S(T), 0 \right).</math>
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| == Types of averaging ==
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| The Average <math>A</math> may be obtained in many ways. Conventionally, this means an [[arithmetic average]]. In the ''continuous'' case, this is obtained by
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| : <math>A(0,T) = \frac{1}{T} \int_{0}^{T} S(t) dt.</math>
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| For the case of ''discrete monitoring'' (with monitoring at the times <math> t_1, t_2, \dots, t_n </math>) we have the average given by
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| : <math>A(0,T) = \frac{1}{N} \sum_{i=1}^{N} S(t_i).</math>
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| There also exist Asian options with [[geometric average]]; in the continuous case, this is given by
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| : <math>A(0,T) = \exp \left( \frac{1}{T} \int_{0}^{T} \ln( S(t)) dt \right).</math>
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| == Pricing of Asian options ==
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| A discussion of the problem of pricing Asian options with [[Monte Carlo method]]s is given in a paper by Kemna and Vorst.<ref name=Kemna1990>{{Citation
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| | last1 = Kemna | first1 = A.G.Z.
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| | last2 = Vorst | first2 = A.C.F.
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| | last3 = Rotterdam | first3 = E.U.
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| | last4 = Instituut | first4 = Econometrisch
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| | year = 1990
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| | title = A Pricing Method for Options Based on Average Asset Values
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| |url=http://ideas.repec.org/a/eee/jbfina/v14y1990i1p113-129.html
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| }}</ref>
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| In the path integral approach to option pricing
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| ,<ref name=Kleinert2009>{{Citation
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| | last = [[Hagen Kleinert|Kleinert]] | first = H.
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| | year = 2009
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| | title = Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets
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| |url=http://www.worldscibooks.com/physics/7305.html
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| }}</ref> the problem for geometric average can be solved via the Effective Classical
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| potential
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| <ref>
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| {{Citation
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| | title = Effective classical partition functions
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| | author = [[Richard P. Feynman|Feynman R.P.]], [[Hagen Kleinert|Kleinert H.]]
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| | journal = [[Physical Review]]
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| | volume = A 34
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| | issue =
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| | pages = 5080–5084
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| | year = 1986
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| | doi = 10.1103/PhysRevA.34.5080
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| |url=http://www.physik.fu-berlin.de/~kleinert/159/159.pdf
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| | pmid=9897894
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| | bibcode=1986PhRvA..34.5080F}}</ref> of [[R.P. Feynman|Feynman]] and [[Hagen Kleinert|Kleinert]].<ref>
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| {{Citation
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| | title = Path integral approach to Asianoptions in the Black-Scholes model
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| | author = Devreese J.P.A., Lemmens D., Tempere J.
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| | journal = Physica A
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| | volume = 389
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| | pages = 780–788
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| | year = 2010
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| | doi = 10.1016/j.physa.2009.10.020 |bibcode = 2010PhyA..389..780D |arxiv = 0906.4456 }}
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| </ref>
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| Rogers and Shi solve the pricing problem with a PDE approach
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| .<ref name=Rogers1995>{{citation | |
| | last1 = Rogers | first1 = L.C.G.
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| | last2 = Shi | first2 = Z.
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| | year = 1995
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| | journal = Journal of Applied Probability
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| | title = The value of an Asian option
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| | volume = 32
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| | pages = 1077–1088
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| |url=http://www.institut.math.jussieu.fr/~boka/enseignement/isifar/refs/Ref_Asiatiques_Rogers_Shi_95.pdf
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| | doi = 10.2307/3215221
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| | issue = 4
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| | publisher = Applied Probability Trust
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| | jstor = 3215221
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| }}</ref>
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| Variance Gamma model can be efficiently implemented when pricing Asian style options. Then using the Bondesson series representation for generating the [[variance gamma process]] shows to increase performance when pricing this type of option.<ref>Mattias Sander. Bondesson's Representation of the Variance Gamma Model and Monte Carlo Option Pricing. Lunds Tekniska Högskola 2008</ref>
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| Within Lévy models the pricing problem for geometrically Asian options can still be solved.<ref name=Fusai2008>{{citation
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| | last1 = Fusai | first1 = Gianluca.
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| | last2 = Meucci | first2 = Attilio
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| | year = 2008
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| | journal = J. Bank. Finan.
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| | title = Pricing discretely monitored Asian options under Lévy processes
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| | volume = 32
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| | pages = 2076–2088
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| | issue = 10
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| }}</ref> For the arithmetic Asian option in Lévy models one can rely on numerical methods<ref name=Fusai2008 /> or on analytic bounds
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| .<ref name=Lemmens2010>{{citation
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| | last1 = Lemmens | first1 = Damiaan
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| | last2 = Liang | first2 = Ling Zhi
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| | last3 = Tempere | first3 = Jacques
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| | last4 = De Schepper | first4 = Ann
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| | year = 2010
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| | journal = Physica A: Statistical Mechanics and its Applications
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| | title = Pricing bounds for discrete arithmetic Asian options under Lévy models
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| | volume = 389
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| | pages = 5193–5207
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| |url=http://www.sciencedirect.com/science/article/B6TVG-50MN7J2-1/2/263630a943781cf0132d87b1e2b2cca6
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| | doi = 10.1016/j.physa.2010.07.026
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| | issue = 22
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| |bibcode = 2010PhyA..389.5193L }}</ref>
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| == References ==
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| <references/>
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| {{Derivatives market}}
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| {{DEFAULTSORT:Asian Option}}
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| [[Category:Options (finance)]]
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| [[Category:Investment]]
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| [[Category:Derivatives (finance)]]
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The use of e-cigs is just a practice that's getting ever more popular, and several people took up the use of ecigs being a cleanser alternative to cigarette smoking. The reason being e-cigs don't result in ash, and they do not create a person’s residence, garments, and automobile smelling poor. Among the biggest areas of starting to employ ecigs entails investing in a beginner kit, and there are certainly a amount of issues someone should know about buying a beginner kit. Including investing in a slightly better beginner kit, and there are certainly a few factors a person must have a part of their starter kit.
Purchasing a marginally greater kit
Among the most frequent faults that people create when first just starting to smoke ecigs is that they tend to choose the cheapest ecig that's available to them. This could create a individual certainly not trying out the practice, and it also means that a person WOn't ever purchase a nice ecig when they do take up the practice. This is the reason it is a good idea to buy a better one, that appears the way in which someone want to buy to, which is even a good concept to purchase one which can be gradually replaced with time.
What should really be included in the kit
An excellent starter kit may have things such as a charger that is user friendly. The kit also needs to incorporate instructions on how to complete the e-cigarette with liquid, a rag to clean it with, plus it must also possess a some extra ejuice or tubes. More check out the post right here.