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1.
@FUNCTION=CUM_BIV_NORM_DIST
@SYNTAX=CUM_BIV_NORM_DIST(a,b,rho)
@DESCRIPTION=CUM_BIV_NORM_DIST calculates the cumulative bivariate normal distribution from parameters a, b & rho.
The return value is the probability that two random variables with correlation @rho are respectively each less than @a and @b.

@EXAMPLES=

@SEEALSO=NORMDIST,NORMSDIST,NORMSINV
represents a line break. Start a new line in the equivalent position in the translation.
@FUNCTION=CUM_BIV_NORM_DIST
@SYNTAX=CUM_BIV_NORM_DIST(a,b,rho)
@DESCRIPTION=CUM_BIV_NORM_DISTはパラメータa, b, rhoから累積二変量正規分布を求めます。返り値は@rhoと相関関係にある2つの乱数値がそれぞれ@aと@bよりも小さくなる確率です。

@EXAMPLES=

@SEEALSO=NORMDIST,NORMSDIST,NORMSINV
Translated and reviewed by Yukihiro Nakai on 2007-03-23
2.
@FUNCTION=OPT_BS
@SYNTAX=OPT_BS(call_put_flag,spot,strike,time,rate,volatility [,cost_of_carry])
@DESCRIPTION=OPT_BS uses the Black-Scholes model to calculate the price of a European option using call_put_flag, @call_put_flag, 'c' or 'p' struck at @strike on an asset with spot price @spot.
@time is the time to maturity of the option expressed in years.
@rate is the risk-free interest rate.
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
* The returned value will be expressed in the same units as @strike and @spot.

@EXAMPLES=

@SEEALSO=OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_VEGA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
represents a space character. Enter a space in the equivalent position in the translation.
@FUNCTION=OPT_BS
@SYNTAX=OPT_BS(コールプットフラグ,市場価格,行使価格,満期,レート,ボラティリティ [,持越費用])
@DESCRIPTION=OPT_BSは'c'または'p'の@コールプットフラグ、@市場価格の資産を行使する@行使価格から、ブラックショールズモデルを使ってヨーロピアンオプションの価格を計算します。
@満期 はオプションの満期の年数です。
@レート は、安全金利です。
@ボラティリティ は年間のボラティリティで、取り引きを行った期間に対する資産の百分率で表現します。
@持越費用 は原資産の流出で、普通株の場合にはこれは配当利回りなどになります。
* 返り値は、@行使価格と@市場価格と同じ単位で表現されます。

@EXAMPLES=

@SEEALSO=OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_VEGA, OPT_BS_GAMMA
Translated and reviewed by Yukihiro Nakai on 2007-03-23
3.
@FUNCTION=OPT_BS_DELTA
@SYNTAX=OPT_BS_DELTA(call_put_flag,spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BS_DELTA uses the Black-Scholes model to calculate the 'delta' of a European option with call_put_flag, @call_put_flag, 'c' or 'p' struck at @strike on an asset with spot price @spot.
Where @time is the time to maturity of the option expressed in years.
@rate is the risk-free interest rate.
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
* The returned value will be expressed in the same units as @strike and @spot.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_VEGA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
represents a space character. Enter a space in the equivalent position in the translation.
(no translation yet)
4.
@FUNCTION=OPT_BS_GAMMA
@SYNTAX=OPT_BS_GAMMA(spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BS_GAMMA uses the Black-Scholes model to calculate the 'gamma' of a European option struck at @strike on an asset with spot price @spot.

(The gamma of an option is the second derivative of its price with respect to the price of the underlying asset, and is the same for calls and puts.)

@time is the time to maturity of the option expressed in years.
@rate is the risk-free interest rate to the exercise date, in percent.
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
* The returned value will be expressed as the rate of change of delta per unit change in @spot.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_VEGA
represents a line break. Start a new line in the equivalent position in the translation.
@FUNCTION=OPT_BS_GAMMA
@SYNTAX=OPT_BS_GAMMA(危険証券の価格,市場価格,ボラティリティ,満期,収益率)
@DESCRIPTION=@市場価格 で @危険証券の価格 をオプションとしてヨーロピアンプットの "γ" を計算するためにブラック=ショールズ方式を使用します。
(あるオプションのγは基本資産の価格に関連する二番目の配当で、コールとプットと同じです。)
@ボラティリティ は可変はボラティリティで、取り引きを行った期間に対する資産の百分率で表現します。@満期 は取り引きが完了するまでの期間で、@収益率 は市場取り引きの期間に対する安全証券の利率で、百分率で表現します。

@EXAMPLES=

@SEEALSO=opt_bs_call, opt_bs_put, opt_bs_call_delta opt_bs_put_delta, opt_bs_call_rho, opt_bs_put_rho, opt_bs_call_theta, opt_bs_put_rho, opt_bs_vega
Translated and reviewed by Yukihiro Nakai on 2007-03-23
5.
@FUNCTION=OPT_BS_THETA
@SYNTAX=OPT_BS_THETA(call_put_flag,spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BS_THETA uses the Black-Scholes model to calculate the 'theta' of a European option with call_put_flag, @call_put_flag struck at @strike on an asset with spot price @spot.

(The theta of an option is the rate of change of its price with respect to time to expiry.)

@time is the time to maturity of the option expressed in years
and @rate is the risk-free interest rate to the exercise date, in percent.
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
* The returned value will be expressed as minus the rate of change of option value, per 365.25 days.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_VEGA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
(no translation yet)
6.
@FUNCTION=OPT_BS_VEGA
@SYNTAX=OPT_BS_VEGA(spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BS_VEGA uses the Black-Scholes model to calculate the 'vega' of a European option struck at @strike on an asset with spot price @spot.
(The vega of an option is the rate of change of its price with respect to volatility, and is the same for calls and puts.)
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@time is the time to maturity of the option expressed in years.
@rate is the risk-free interest rate to the exercise date, in percent.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.

* The returned value will be expressed as the rate of change of option value, per 100% volatility.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
represents a space character. Enter a space in the equivalent position in the translation.
@FUNCTION=opt_bs_vega
@SYNTAX=opt_bs_bega(危険証券の価格,市場価格,ボラティリティ,満期,収益率)
@DESCRIPTION=@市場価格 で @危険証券の価格 をオプションとしてヨーロピアンオプションの "γ" を計算するためにブラック=ショールズ方式を使用します。
(あるオプションのγは基本資産の価格に関連する二番目の配当で、コールとプットと同じです。)
@ボラティリティ は可変はボラティリティで、取り引きを行った期間に対する資産の百分率で表現します。@満期 は取り引きが完了するまでの期間で、@収益率 は市場取り引きの期間に対する安全証券の利率で、百分率で表現します。

@EXAMPLES=

@SEEALSO=opt_bs_call, opt_bs_put, opt_bs_call_delta opt_bs_put_delta, opt_bs_call_rho, opt_bs_put_rho, opt_bs_call_theta, opt_bs_put_rho, opt_bs_gamma
Translated and reviewed by Yukihiro Nakai on 2007-03-23
7.
@FUNCTION=OPT_BS_RHO
@SYNTAX=OPT_BS_RHO(call_put_flag,spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BS_RHO uses the Black-Scholes model to calculate the 'rho' of a European option with call_put_flag, @call_put_flag struck at @strike on an asset with spot price @spot.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.

(The rho of an option is the rate of change of its price with respect to the risk free interest rate.)
@time is the time to maturity of the option expressed in years.
@rate is the risk-free interest rate to the exercise date, in percent.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
* The returned value will be expressed as the rate of change of option value, per 100% change in @rate.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_THETA, OPT_BS_VEGA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
(no translation yet)
8.
@FUNCTION=OPT_BS_CARRYCOST
@SYNTAX=OPT_BS_CARRYCOST(call_put_flag,spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BS_CARRYCOST uses the Black-Scholes model to calculate the 'elasticity' of a European option struck at @strike on an asset with spot price @spot.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.

(The elasticity of an option is the rate of change of its price with respect to its cost of carry.)

@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date. @time is the time to maturity of the option expressed in years.
@rate is the risk-free interest rate to the exercise date, in percent.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.

* The returned value will be expressed as the rate of change of option value, per 100% volatility.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
(no translation yet)
9.
@FUNCTION=OPT_GARMAN_KOHLHAGEN
@SYNTAX=OPT_GARMAN_KOHLHAGEN(call_put_flag,spot,strike,time,domestic_rate,foreign_rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_GARMAN_KOHLHAGEN values the theoretical price of a European currency option struck at @strike on an asset with spot price @spot.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@time the number of days to exercise.
@domestic_rate is the domestic risk-free interest rate to the exercise date.
@foreign_rate is the foreign risk-free interest rate to the exercise date, in percent.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
* The returned value will be expressed as the rate of change of option value, per 100% volatility.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
represents a space character. Enter a space in the equivalent position in the translation.
(no translation yet)
10.
@FUNCTION=OPT_FRENCH
@SYNTAX=OPT_FRENCH(call_put_flag,spot,strike,time,t2,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_FRENCH values the theoretical price of a European option adjusted for trading day volatility, struck at @strike on an asset with spot price @spot.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date.
@time the number of calendar days to exercise divided by calendar days in the year.
@t2 is the number of trading days to exercise divided by trading days in the year.
@rate is the risk-free interest rate.
@cost_of_carry is the leakage in value of the underlying asset, to the exercise date, in percent.
For common stocks, this would be the dividend yield.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
represents a line break. Start a new line in the equivalent position in the translation.
represents a space character. Enter a space in the equivalent position in the translation.
(no translation yet)
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