compute the Rho of a European-style option with given payoff

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
- テンソル解析
- パッケージ
- ファンクションアドバイザ
- ベキ級数
- ベクトル解析
- 不活性関数
- 代数
- 因数分解と方程式解法
- 基本数学
- 基本的な注意事項
- 変分法
- 変換
- 幾何
- 微分代数方程式
- 微分幾何学
- 微分方程式
- 微積分
- 数
- 数値計算
- 数学関数
- 数論
- 最適化
- 特殊関数
- 統計
- 線形代数
- 群論
- 評価
- 論理
- 過去のパッケージ
- 金融
  - はじめに
  - キャッシュフロー分析
  - パーソナルファイナンス
  - ラティス法
  - 日付計算
  - 短期料率モデル
  - 確率過程
  - 金利
  - 金融商品
  - 概要
- 離散数学
- piecewise examples
- グラフ電卓
- 区分関数
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
エラーメッセージガイド
マニュアル
数学アプリ

Finance[BlackScholesRho] - compute the Rho of a European-style option with given payoff

	Calling Sequence
	BlackScholesRho(, K, T, sigma, r, d, optiontype) BlackScholesRho(, P, T, sigma, r, d)

Parameters

	-	algebraic expression; initial (current) value of the underlying asset
K	-	algebraic expression; strike price
T	-	algebraic expression; time to maturity
sigma	-	algebraic expression; volatility
r	-	algebraic expression; continuously compounded risk-free rate
d	-	algebraic expression; continuously compounded dividend yield
P	-	operator or procedure; payoff function
optiontype	-	call or put; option type

Description

•	The Rho of an option or a portfolio of options is the sensitivity of the option or portfolio to changes in the risk-free rate

•	The BlackScholesRho command computes the Rho of a European-style option with the specified payoff function.

•	The parameter is the initial (current) value of the underlying asset. The parameter T is the time to maturity in years.

•

The parameter K specifies the strike price if this is a vanilla put or call option. Any payoff function can be specified using the second calling sequence. In this case the parameter P must be given in the form of an operator, which accepts one parameter (spot price at maturity) and returns the corresponding payoff.

•	The sigma, r, and d parameters are the volatility, the risk-free rate, and the dividend yield of the underlying asset. These parameters can be given in either the algebraic form or the operator form. The parameter d is optional. By default, the dividend yield is taken to be 0.

Compatibility

•	The Finance[BlackScholesRho] command was introduced in Maple 15.

•	For more information on Maple 15 changes, see Updates in Maple 15.

Examples

First you compute the Rho of a European call option with strike price 100, which matures in 1 year. This will define the Rho as a function of the risk-free rate, the dividend yield, and the volatility.

-50*exp(-r)*(-1+erf((1/4)*(-2*r+2*d+sigma^2)*2^(1/2)/sigma))

(1)

In this example you will use numeric values for the risk-free rate, the dividend yield, and the volatility.

(2)

We can also use the generic method in which the option is defined through its payoff function.

-50*exp(-r)*(-1+erf((1/4)*(-2*r+2*d+sigma^2)*2^(1/2)/sigma))

(3)

(4)

Rho := 0.1000000000e-9*(0.3871517540e12*exp(-0.1999999999e-17*(2312585093.+500000000.*ln(1/K)+250000000.*sigma^2)^2/sigma^2)+4756147122.*K*sigma+4756147122.*K*sigma*erf(0.5000000000e-9*(6540978404.+1414213562.*ln(1/K)-707106781.*sigma^2)/sigma)-3794856357.*K*exp(-0.2500000000e-18*(6540978404.+1414213562.*ln(1/K)-707106781.*sigma^2)^2/sigma^2))/sigma

(5)

Here are similar examples for the European put option.

-25*(2*exp(-r)*Pi^(1/2)*sigma+2*exp(-r)*erf((1/4)*(2*ln(2)-2*r+2*d+sigma^2)*2^(1/2)/sigma)*Pi^(1/2)*sigma+2*2^(1/2)*exp(-(1/8)*(4*r*sigma^2+4*ln(2)^2-8*ln(2)*r+8*ln(2)*d+4*ln(2)*sigma^2+4*r^2-8*r*d+4*d^2+4*d*sigma^2+sigma^4)/sigma^2)-exp(-(1/8)*(4*d*sigma^2+4*ln(2)^2-8*ln(2)*r+8*ln(2)*d-4*ln(2)*sigma^2+4*r^2-8*r*d+4*r*sigma^2+4*d^2+sigma^4)/sigma^2)*2^(1/2))/(Pi^(1/2)*sigma)

(6)

(7)

25*exp(-r-d)*(-2*Pi^(1/2)*sigma*erf((1/4)*(2*ln(2)-2*r+2*d+sigma^2)*2^(1/2)/sigma)*exp(d)-2*Pi^(1/2)*sigma*exp(d)-2*2^(1/2)*exp(-(1/8)*(4*ln(2)^2-8*ln(2)*r+8*ln(2)*d+4*ln(2)*sigma^2+4*r^2-8*r*d-4*r*sigma^2+4*d^2-4*d*sigma^2+sigma^4)/sigma^2)+exp(-(1/8)*(-4*r*sigma^2+4*ln(2)^2-8*ln(2)*r+8*ln(2)*d-4*ln(2)*sigma^2+4*r^2-8*r*d+4*d^2-4*d*sigma^2+sigma^4)/sigma^2)*2^(1/2))/(Pi^(1/2)*sigma)

(8)

(9)

In this example, you will compute the Rho of a strangle.

(10)

C := -50*exp(-r)*(-1+erf((1/4)*(-2*r+2*d+sigma^2)*2^(1/2)/sigma))

(11)

P := 25*(-exp(-r)*Pi^(1/2)*sigma+exp(-r)*erf((1/4)*2^(1/2)*(-sigma^2+2*ln(2)+2*r-2*d)/sigma)*Pi^(1/2)*sigma-exp(-(1/8)*(4*r*sigma^2+sigma^4-4*ln(2)*sigma^2+4*d*sigma^2+4*ln(2)^2+8*ln(2)*r-8*ln(2)*d+4*r^2-8*r*d+4*d^2)/sigma^2)*2^(1/2)+2*2^(1/2)*exp(-(1/8)*(4*d*sigma^2+4*r^2+8*ln(2)*r+4*r*sigma^2-8*r*d+4*ln(2)^2+4*ln(2)*sigma^2-8*ln(2)*d+sigma^4+4*d^2)/sigma^2))/(Pi^(1/2)*sigma)

(12)

Check:

(13)

	See Also
	Finance[AmericanOption], Finance[BermudanOption], Finance[BlackScholesDelta], Finance[BlackScholesGamma], Finance[BlackScholesPrice], Finance[BlackScholesTheta], Finance[BlackScholesVega], Finance[EuropeanOption], Finance[ImpliedVolatility], Finance[LatticePrice]