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| {{Unreferenced|date=November 2006}}
| | Nice to satisfy you, my title is Ling and I completely dig that name. The preferred hobby for my children and me is dancing and now I'm trying to earn money with it. I am a production and distribution officer. Delaware has always been my living location and will by no means move.<br><br>my weblog - [http://www.schwaben-gaming.de/index.php?mod=users&action=view&id=9562 auto warranty] |
| '''Mountain ranges''' are [[exotic option]]s originally marketed by [[Société Générale]] in 1998. The options combine the characteristics of [[basket option]]s and [[range option]]s by basing the value of the option on several underlying assets, and by setting a time frame for the option.
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| The mountain range options are further subdivided into further types, depending on the specific terms of the options. Examples include: | |
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| * ''Altiplano'' - in which a [[vanilla option]] is combined with a compensatory coupon payment if the underlying security never reaches its strike price during a given period.
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| * ''Annapurna'' - in which the option holder is rewarded if all securities in the basket never fall below a certain price during the relevant time period
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| * ''Atlas'' - in which the best and worst-performing securities are removed from the basket prior to execution of the option
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| * ''Everest'' - a long-term option in which the option holder gets a payoff based on the worst-performing securities in the basket
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| * ''Himalayan'' - based on the performance of the best asset in the portfolio
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| Most mountain ranges cannot be priced using closed form formulae, and are instead valued through the use of [[Monte Carlo methods for option pricing| Monte Carlo simulation methods]].
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| == Everest Options ==
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| Although Mount Everest is the highest point on earth, the Everest option payoff is on the worst performer in a basket of 10-25 stocks, with 10-15 year maturity. (Richard Quessette 2002).
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| Given ''n'' stocks, <math>S_1, S_2,..., S_n</math> in a basket, the payoff for an Everest option is: <math> \min_{i=1...n}(\frac{S_i^T}{S_i^0}). </math>
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| == Atlas Options ==
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| [[Atlas (mythology)|Atlas]] was a Titan who supported the Earth on his back. The Atlas option is a call on the mean (or average) of a basket of stocks, with some of the best and worst performers removed. (Quessette 2002). Given ''n'' stocks <math>S_1, S_2,..., S_n</math> in a basket, define:
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| :<math>R_{(1)}^t=\min{\{\frac{S_1^t}{S_1^0},\frac{S_2^t}{S_2^0},...,\frac{S_n^t}{S_1^n}\}}, </math>
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| :<math>R_{(n)}^t=\max{\{\frac{S_1^t}{S_1^0},\frac{S_2^t}{S_2^0},...,\frac{S_n^t}{S_n^0}\}}, </math>
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| where <math>R_{(i)}^t </math> is the ''i''-th smallest return, so that:
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| :<math>R_{(1)}^t \leq R_{(2)}^t \leq \dots \leq R_{(i)}^t \leq \dots \leq R_{(n)}^t. </math>
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| The Atlas removes a fixed number (<math>n_1</math>) of stocks from the minimum ordering of the basket and a fixed number (<math>n_2</math>) of stocks from the maximum ordering of the basket. In a basket of ''n'' stocks, notice that (<math>n_1+n_2 < n</math>), to leave at least one stock in the basket on which to compute the option payoff. With a strike price <math>K</math>, the payoff for the Atlas option is:
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| :<math>\sum_{j=1+n_1}^{n-n_2}{\frac{R_{(j)}^T}{n-(n_1+n_2)}-K})^{+}.</math>
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| ==Himalayan Options==
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| A Himalayan option with [[notional amount| notional <math>N</math>]], and maturity <math>T</math> starts with a '''basket''' of <math>m</math> equities. The terms of the contract will specify <math>m</math> payoff times: <math>t_0 = 0 < t_1 < t_2 < \dots < t_m = T</math>. At payoff time <math>t_i, \ i=1:m</math>, the percentage returns since inception of all equities currently in the basket are computed, and the equity with the largest return is noted; denote this equity by <math>S_{k_i}, \ 1\leq k_i \leq m</math>. The derivative then makes the payoff: <math>N \max \left(\frac{S_{k_i, t_i} - S_{k_i, t_0}}{S_{k_i, t_0}}, \ 0\right)</math>, and <math>S_{k_i}</math> is removed from the basket. The procedure is repeated until maturity, at which time the final payoff occurs and the basket is emptied.
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| {{Derivatives market}}
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| {{DEFAULTSORT:Mountain Range (Options)}}
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| [[Category:Options (finance)]]
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Nice to satisfy you, my title is Ling and I completely dig that name. The preferred hobby for my children and me is dancing and now I'm trying to earn money with it. I am a production and distribution officer. Delaware has always been my living location and will by no means move.
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