R语言 fExoticOptions包 BinaryOptions()函数中文帮助文档(中英文对照)

loveR · 发表于 2012-9-17 20:23:48

BinaryOptions(fExoticOptions)
BinaryOptions()所属R语言包：fExoticOptions

 Valuation of Binary Options
 二元期权的估值

 译者：生物统计家园网机器人LoveR

描述----------Description----------

A collection and description of functions to valuate binary options. Binary options, also known as digital options, have discontinuous payoffs. They can be used as building blocks to develop options with more complicated payoffs. For example, a regular European call option is equivalent to a long position in an asset-or-nothing call and a short position in a cash-or-nothing call, where the both options have the same strike price and the cash payoff of the cash-or-nothing option equals the strike price. Unlike standard European style options, the payout for binary options does not depend on how much it is in-the-money but rather whether or not it is on the money. The option's payoff is fixed at the options inception and is based on the price of the underlying asset on the expiration date. Binary options may also incorporate barriers, as is the case with binary-barrier options. 
收集和功能说明到二元期权评价。二元期权，也被称为数字期权，有不连续的回报。它们可以被用来作为构建模块，以制定备选方案更复杂的回报。例如，一个普通的欧式看涨期权相当于术语的资产或没有检测和短仓的位置在两个选项具有相同的行使价及现金回报的现金或没有检测，现金或全无的选项等于行使价。二元期权的支出为标准的欧洲风格不同，不依赖于多少是在这方面的钱，而是它是否是在钱上。选项的回报是固定的选项以来，根据标的资产在到期日的价格。二进制选项也可能合并的障碍，与二进制障碍期权的情况一样。参考

The functions are:
这些功能是：

</table>
</ TABLE>

用法----------Usage----------

GapOption(TypeFlag, S, X1, X2, Time, r, b, sigma, title = NULL,
description = NULL)
CashOrNothingOption(TypeFlag, S, X, K, Time, r, b, sigma,
title = NULL, description = NULL)
TwoAssetCashOrNothingOption(TypeFlag, S1, S2, X1, X2, K, Time, r,
b1, b2, sigma1, sigma2, rho, title = NULL, description = NULL)
AssetOrNothingOption(TypeFlag, S, X, Time, r, b, sigma,
title = NULL, description = NULL)
SuperShareOption(S, XL, XH, Time, r, b, sigma, title = NULL,
description = NULL)
BinaryBarrierOption(TypeFlag, S, X, H, K, Time, r, b, sigma,
eta, phi, title = NULL, description = NULL)

参数----------Arguments----------

参数：b
the annualized cost-of-carry rate, a numeric value; e.g. 0.1 means 10% pa.
的年度成本进率，数值; 0.1是指每年10％。

参数：b1, b2
[TwoAssetCashOrNothing*] - the annualized cost-of-carry rate for the first and second asset, a numeric value.
[TwoAssetCashOrNothing *] - 的年度成本的携带率第一和第二的资产，一个数值。

参数：description
a character string which allows for a brief description.
一个字符串允许的简要说明。

参数：eta, phi
[BinaryBarrier*] - a set of parameters to price 28 different types of Binary Barrier options: 01: eta=+1, phi=NA, [S>H] down-and-in cash-at-hit-or-nothing, 02: eta=-1, phi=NA, [S<H] up-and-in cash-at-hit-or-nothing, 03: eta=+1, phi=NA, [S>H] down-and-in asset-at-hit-or-nothing, 04: eta=-1, phi=NA, [S<H] up-and-in asset-at-hit-or-nothing, 05: eta=+1, phi=-1, [S>H] down-and-in cash-at-expiry-or-nothing, 06: eta=-1, phi=+1, [S<H] up-and-in cash-at-expiry-or-nothing, 07: eta=+1, phi=-1, [S>H] down-and-in asset-at-expiry-or-nothing, 08: eta=-1, phi=+1, [S<H] up-and-in asset-at-expiry-or-nothing, 09: eta=+1, phi=+1, [S>H] down-and-out cash-or-nothing, 10: eta=-1, phi=-1, [S<H] up-and-out cash-or-nothing, 11: eta=+1, phi=+1, [S>H] down-and-out asset-or-nothing, 12: eta=-1, phi=-1, [S<H] up-and-out asset-or-nothing, 13: eta=+1, phi=+1, [S>H] down-and-in cash-or-nothing call, 14: eta=-1, phi=+1, [S<H] up-and-in cash-or-nothing call, 15: eta=+1, phi=+1, [S>H] down-and-in asset-or-nothing call, 16: eta=-1, phi=+1, [S<H] up-and-in asset-or-nothing call, 17: eta=+1, phi=-1, [S>H] down-and-in cash-or-nothing put, 18: eta=-1, phi=-1, [S<H] up-and-in cash-or-nothing put, 19: eta=+1, phi=-1, [S>H] down-and-in asset-or-nothing put, 20: eta=-1, phi=-1, [S<H] up-and-in asset-or-nothing put, 21: eta=+1, phi=+1, [S>H] down-and-out cash-or-nothing call, 22: eta=-1, phi=+1, [S<H] up-and-out cash-or-nothing call, 23: eta=+1, phi=+1, [S>H] down-and-out asset-or-nothing call, 24: eta=-1, phi=-1, [S<H] up-and-out asset-or-nothing call, 25: eta=+1, phi=-1, [S>H] down-and-out cash-or-nothing put, 26: eta=-1, phi=-1, [S<H] up-and-out cash-or-nothing put, 27: eta=+1, phi=-1, [S>H] down-and-out asset-or-nothing put, 28: eta=-1, phi=-1, [S<H] up-and-out asset-or-nothing put.
[BinaryBarrier] - 的一组参数，定价28种不同类型的二元障碍期权：参考01：eta=+1, phi=NA, [S>H]命中现金或全无的，参考下02：eta=-1, phi=NA, [S<H]在命中现金或全无，参考03：eta=+1, phi=NA, [S>H]下的资产在灾区有或无，参考04：eta=-1, phi=NA, [S<H]和资产命中有或无，参考05：eta=+1, phi=-1, [S>H]下降和现金，在到期或没有，参考06：eta=-1, phi=+1, [S<H]的现金，到期或没有，参考07：eta=+1, phi=-1, [S>H]下的资产在到期或没有，参考08：eta=-1, phi=+1, [S<H]和资产到期或没有，参考09：eta=+1, phi=+1, [S>H]被击倒的现金或全无，参考10：eta=-1, phi=-1, [S<H]出的现金或无，参考11：eta=+1, phi=+1, [S>H]被击倒的资产或全无，参考12：eta=-1, phi=-1, [S<H]和出资产或什么都没有，参考13：eta=+1, phi=+1, [S>H]下的现金有或全无的调用，参考14：eta=-1, phi=+1, [S<H]，和现金或无通话，参考15：eta=+1, phi=+1, [S>H]下的资产或没有检测，参考16：eta=-1, phi=+1, [S<H]的资产或没有检测，参考17： eta=+1, phi=-1, [S>H]下以现金或没有认沽，参考18：eta=-1, phi=-1, [S<H]以现金或没有认沽，参考19：eta=+1, phi=-1, [S>H]下和资产或无的放，参考20：eta=-1, phi=-1, [S<H]的资产或没有认沽，参考21：eta=+1, phi=+1, [S>H]下的现金或没有检测，参考22：eta=-1, phi=+1, [S<H]以现金或全无的调用，参考23：eta=+1, phi=+1, [S>H]被击倒的资产或没有检测， H]的被击倒的现金或没有认沽，参考26：<X >，改以现金或没有认沽，参考27：eta=-1, phi=-1, [S<H]被击倒的资产或没有认沽，参考28：eta=+1, phi=-1, [S>H]和出资产或没有付诸表决。

参数：H
[BinaryBarrier*] - the barrier value, a numeric value.
[BinaryBarrier *] - 限制值，数值参考。

参数：K
[CashOrNothing*] - the cash amount at expiry if the option is in the money, a numerical value. [TwoAssetCashOrNothing*] - for the cash-or-nothing call the cash amount at expiry if asset S1 is above the strike X1 and asset S2 is above strike X2 at expiration, for the cash-or-nothing put the cash amount at expiry if asset S1 is below the strike X1 and asset S2 is below strike X2 at expiration, for the cash-or-nothing up-down the cash amount at expiry if asset S1 is above the strike X1 and asset S2 is below strike X2 at expiration, for the cash-or-nothing down-up the cash amount at expiry if asset S1 is below the strike X1 and asset S2 is above strike X2 at expiration. [BinaryBarrier*] - the prespecified cash amount, a numeric value.
[CashOrNothing *] - 于到期日的现金数额的钱如果该选项是数值。 - [TwoAssetCashOrNothing *] - 于到期时调用的现金金额的现金或无资产S1以上的罢工X1和资产的S2是上述罢工X2在合约到期时， 的现金或无于到期日的现金数额，如果是资产S1低于行使X1和资产S2低于罢工X2在合约到期时， 以现金或没有上下的现金金额到期如果资产S1高于行使X1和资产S2低于罢工X2在合约到期时， 以现金或倒没什么现金于到期日，如果资产S1是以下的罢工X1和资产S2是上述罢工X2到期时 - [BinaryBarrier *] - 参考预先设定的量现金款额，一个数值。

参数：r
the annualized rate of interest, a numeric value; e.g. 0.25 means 25% pa.
的年利息率，数值; 0.25是指每年25％。

参数：rho
[TwoAssetCashOrNothing*] - the correlation of the volatility between the first and second asset, a numeric value.
[TwoAssetCashOrNothing *] - 参考第一和第二的资产之间的波动，数值的相关性。

参数：S
the asset price, a numeric value.
资产价格的一个数值。

参数：S1, S2
[TwoAssetCashOrNothing*] - the price of the first and second asset, a numeric value.
[TwoAssetCashOrNothing *] - 参考第一和第二的资产的价格，一个数值。

参数：sigma
the annualized volatility of the underlying security, a numeric value; e.g. 0.3 means 30% volatility pa.
的年波幅率的基本安全，数字值; 0.3是指每年30％的波动。

参数：sigma1, sigma2
[TwoAssetCashOrNothing*] - the annualized volatility of the first and second underlying security, numeric values.
[TwoAssetCashOrNothing *] - 参考第一和第二的底层安全，数字值的年波幅率。

参数：Time
the time to maturity measured in years, a numeric value; e.g. 0.5 means 6 months.
至到期日的时间以年来衡量，数值; 0.5表示6个月。

参数：title
a character string which allows for a project title.
一个字符串，它允许一个项目的名称。

参数：TypeFlag
a character string either "c" for a call option or a "p" for a put option. [TwoAssetCashOrNothing*] - a character string either "c" for a call option, or a "p" for a put option, or a "ud" for an up-down option, or a "du" for a down-up option. [BinaryBarrier*] - an integer between 1 and 28, selecting one of the 28 types, for a definition lookup the arguments eta and phi.
一个字符串是"c"的看涨期权或"p"认沽期权。 - [TwoAssetCashOrNothing *] - 一个字符串是"c"认购期权，或"p"认沽期权，或"ud"上下选项或"du"向下-up选项。 - [BinaryBarrier *] - 参考1和28之间的一个整数，选择的28种中的一个，一个定义查询的参数eta 和phi。

参数：X
the exercise price, a numeric value.
行使价，一个数值。

参数：X1, X2
[GapOption][TwoAssetCashOrNothing*] - the first and the second exercise price, a numeric value.
[GapOption] [TwoAssetCashOrNothing *] - 第一个和第二个行权价格，一个数值。

参数：XL, XH
[SuperShare*] - the lower and upper boundary strike, a numeric value.
[SuperShare *] - 上，下边界罢工，该数值。

Details

详细信息----------Details----------

Gap Options: The payoff on a gap option depends on the usual factors of a plain option, but is also affected by a "gap" amount of exercise prices, which may be positive or negative. Note, that a gap call (put) option is equivalent to being long (short) an asset-or-nothing call (put) and short (long) a cash-or-nothing call (put). The option price is calculated analytically according to Reiner and Rubinstein (1991). [Haug's Book, Chapter 2.11.1] 
间隙选项：参考参考收益上的差距选项依赖于一个简单的选项通常的因素，但也行使价量的“差距”，这可能是积极或消极的影响。请注意，差距认购（售）选项相当于长（短）的资产或没有认购（售）和短（长）以现金或无认购（售）。期权价格的计算分析，根据Reiner和鲁宾斯坦（1991）。 - [豪格的书，第2.11.1]参考

Cash-or-Nothing Options: For this option a predetermined amount is paid at expiration if the asset is above for a call or below for a put some strike level. The amount independent of the path taken. These options require no payment of an exercise price. The exercise price determines whether or not the option returns a payoff. The value of a cash-or-nothing call (put) option is the present value of the fixed cash payoff multiplied by the probability that the terminal price will be greater than (less than) the exercise price. The option price is calculated analytically according to Reiner and Rubinstein (1991). [Haug's Book, Chapter 2.11.2] 
现金或什么选项：此选项 对于预定量在到期时支付，则该资产以上的呼叫或以下的放一些行使水平。独立的量的所采取的路径。这些选项不需要支付行使价。行使价确定是否选择返回一个回报。值的现金有或全无的呼叫（放）选项终端价格的概率将大于（小于），行使价乘以固定现金收益的现值。期权价格的计算分析，根据Reiner和鲁宾斯坦（1991）。 - [豪格的书，第2.11.2]参考

Two-Asset-Cash-Or-Nothing Options: These options are building blocks for constructing more complex exotic options. There are four types of two-asset cash-or-nothing options, the first two situationsa are: A two-asset-cash-or-nothing call pays out a fixed cash amount if the price of the first asset is above (below) the strike price of the first asset and the price of the second asset is also above (below) the strike price of the second asset at expiration. The other two situations arise under the following conditions: A two-asset cash-or-nothing down-up pays out a fixed cash amount if the price of the first asset is is below (above) the strike price of the first asset and the price of the second asset is above (below) the strike price of the second asset at expiration. The option price is calculated analytically according to Heynen and Kat (1996). [Haug's Book, Chapter 2.11.3] 
两资产以现金或全无选项： 的 这些选项的积木构建更复杂的奇异期权。有四种类型的两个资产现金或全无的选项，前两个situationsa是：一个两资产为现金或无检测支付固定现金金额的第一个资产的价格高于（低于）的第一个资产价格的第二个资产行使价高于（低于）的第二个资产在到期日行使价。在下列情况下，会出现两种情况：两资产的现金或倒没什么支付固定现金金额的第一个资产的价格是低于（高于）行权价格的第一个资产和第二资产价格高于（低于）的第二个资产在到期日行使价。期权价格的计算分析根据Heynen和吉（1996）。 - [豪格的书，第2.11.3]参考

Asset-Or-Nothing Options: In this option a predetermined asset value is paid if the asset is, at expiration, above for a call or below for a put some strike level, independent of the path taken. For a call (put) the terminal price is greater than (less than) the exercise price, the call (put) expires worthless. The exercise price is never paid. Instead, the value of the asset relative to the exercise price determines whether or not the option returns a payoff. The value of an asset-or-nothing call (put) option is the present value of the asset multiplied by the probability that the terminal price will be greater than (less than) the exercise price. The option price is calculated analytically according to Cox and Rubinstein (1985). [Haug's Book, Chapter 2.11.4] 
资产有或全无的选项：此选项 在预定的资产价值，则该资产支付，在到期日，上述通话或以下的把一些独立行使水平，所采取的路径。就认购（售）的终端价格大于（小于）行使价，认购（售）作废。从来没有支付行使价。相反，该值的资产相对的行使价确定是否选择返回了回报。值的资产有或全无的呼叫（放）选项是终端价格的概率将大于（小于），行使价乘以该资产的现值。期权价格的计算分析，根据Cox和鲁宾斯坦（1985年）。 - [豪格的书，第2.11.4]参考

Supershare Options: These options represents a contingent claim on a fraction of the underlying portfolio. The contingency is that the value of the portfolio must lie between a lower and an upper bound at expiration. If the value lies within these boundaries, the supershare is worth a proportion of the assets underlying the portfolio, else the supershare expires worthless. A supershare has a payoff that is basically like a spread of two asset-or-nothing calls, in which the owner of a supershare purchases an asset-or-nothing call with an strike price of the lower strike and sells an asset-or-nothing call with an strike price of the upper strike. The option price is calculated analytically according to Hakansson (1976). [Haug's Book, Chapter 2.11.5] 
Supershare的选项： 这些选项代表一种未定的相关投资组合的一小部分。的应变是投资组合的价值必须位于一个上限和下限约束在到期日之间。如果这些边界内的价值在于，supershare相关投资组合的资产价值的比例，其他的supershare的作废。一个supershare有回报，基本上是想传播两种资产有或全无的呼叫，在其所有者的的一个supershare购买的资产或没有通知的行使价较低的行使和销售的资产或没有检测上罢工的行使价。购股权价格计算，，分析性根据，以哈坎森（1976年）。 - [豪格的书，第2.11.5]参考

Binary Barrier Options: These options combine characteristics of both binary and barrier options. They are path dependent with a discontinuous payoff. Similar to barrier options, the payoff depends on whether or not the asset price crosses a predetermined barrier. There are 28 different types of binary barrier options, which can be divided into two main categories: Cash-or-nothing and Asset-or-nothing barrier options. Cash-or-nothing barrier options pay out a predetermined cash amount or nothing, depending on whether the asset price has hit the barrier. Asset-or-nothing barrier options pay out the value of the asset or nothing, depending on whether the asset price has crossed the barrier. The barrier monitoring frequency can be adjusted to account for discrete monitoring using an approximation developed by Broadie, Glasserman, and Kou (1995). Binary-barrier options can be priced analytically using a model introduced by Reiner and Rubinstein (1991). [Haug's Book, Chapter 2.11.6]
二元障碍期权： 这些选项的二进制和障碍期权相结合的特点。他们是路径依赖的，不连续的回报。障碍期权，收益取决于资产价格是否跨越了预定的障碍。有28种不同类型的二进制障碍期权，它可分为两大类：以现金或无资产或无障碍期权。现金或没有障碍期权支付现金金额，或没有预定，具体取决于资产价格是否击中了障碍。资产或没有障碍期权支付的资产或没有价值的，这取决于资产价格是否已经越过了障碍。栅障监视频率可以调整到账户离散监测使用Broadie，格拉瑟曼，和蔻（1995）开发的一个近似。二进制障碍期权的定价可以解析使用Reiner和鲁宾斯坦（1991）模型中引入。 - [豪格的书，第一章2.11.6]

值----------Value----------

The option price, a numeric value.
购股权行使价，一个数值。

注意----------Note----------

The functions implement the algorithms to valuate plain vanilla options as described in Chapter 2.11 of Haug's Book (1997).
函数实现的算法，，普通期权评价豪格的书（1997）第2.11章中所描述的。

（作者）----------Author(s)----------

Diethelm Wuertz for the Rmetrics R-port.

参考文献----------References----------

Cox J.C., Rubinstein M. (1985); Innovations in Option Markets, Prentice-Hall, New Jersey.
Hakkansson N.H. (1976); The Purchasing Power Fund: A New Kind of Financial Intermediary, Financial Analysts Journal 32, 49–59.
Haug E.G. (1997); The complete Guide to Option Pricing Formulas, Chapter 2.11, McGraw-Hill, New York.
Heinen R.C., Kat H.M. (1996); Brick by Brick, Risk Magazine 9, 6.
Reiner E., Rubinstein M. (1991); Unscrambling the Binary Code; Risk Magazine 4, 9.

实例----------Examples----------

## Examples from Chapter 2.11 in E.G. Haug's Option Guide (1997)[＃示例在例如第2.11章豪格的选件指南“（1997年）]

## Gap Option [2.11.1]:[[2.9.1]＃缺口期权：]
GapOption(TypeFlag = "c", S = 50, X1 = 50, X2 = 57, Time = 0.5,
 r = 0.09, b = 0.09, sigma = 0.20)

## Cash Or Nothing Option [2.11.2]:[＃现金或没有选择[2.11.2]：]
CashOrNothingOption(TypeFlag = "p", S = 100, X = 80, K = 10,
 Time = 9/12, r = 0.06, b = 0, sigma = 0.35)

## Two Asset Cash Or Nothing Option [2.11.3]:[＃两个资产现金或任何选项[2.11.3。]：]
# Type 1 - call:[1型 - 呼叫：]
TwoAssetCashOrNothingOption(TypeFlag = "c", S1 = 100, S2 = 100,
 X1 = 110, X2 = 90, K = 10, Time = 0.5, r = 0.10, b1 = 0.05,
 b2 = 0.06, sigma1 = 0.20, sigma2 = 0.25, rho = 0.5)
# Type 2 - put:[第2类 - 地说：]
TwoAssetCashOrNothingOption(TypeFlag = "p", S1 = 100, S2 = 100,
 X1 = 110, X2 = 90, K = 10, Time = 0.5, r = 0.10, b1 = 0.05,
 b2 = 0.06, sigma1 = 0.20, sigma2 = 0.25, rho = -0.5)
# Type 3 - down-up:[类型3 - 下：]
TwoAssetCashOrNothingOption(TypeFlag = "ud", S1 = 100, S2 = 100,
 X1 = 110, X2 = 90, K = 10, Time = 1, r = 0.10, b1 = 0.05,
 b2 = 0.06, sigma1 = 0.20, sigma2 = 0.25, rho = 0)
# Type 4 - up-down:[第4类 - 上下：]
TwoAssetCashOrNothingOption(TypeFlag = "du", S1 = 100, S2 = 100,
 X1 = 110, X2 = 90, K = 10, Time = 1, r = 0.10, b1 = 0.05,
 b2 = 0.06, sigma1 = 0.20, sigma2 = 0.25, rho = 0)

## Asset Or Nothing Option [2.11.4]: [＃资产或没有选项[2.11.4]：]
AssetOrNothingOption(TypeFlag = "p", S = 70, X = 65, Time = 0.5,
 r = 0.07, b = 0.07 - 0.05, sigma = 0.27)

## Super Share Option [2.11.5]: [[2.11.5]＃超购股权：]
SuperShareOption(S = 100, XL = 90, XH = 110, Time = 0.25, r = 0.10,
 b = 0, sigma = 0.20)

## Binary Barrier Option [2.11.6]: [[2.11.6]＃二进制障碍期权：]
BinaryBarrierOption(TypeFlag = "6", S = 95, X=102, H = 100,
 K = 15, Time = 0.5, r = 0.1, b = 0.1, sigma = 0.20)
BinaryBarrierOption(TypeFlag = "12", S = 95, X = 98, H = 100,
 K = 15, Time = 0.5, r = 0.1, b = 0.1, sigma = 0.20)


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