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4.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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@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。
返り値は @市場価格 のユニット変更に対するδの変更率で表現されます。
@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
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Translated and reviewed by
Yukihiro Nakai
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5.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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(no translation yet)
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6.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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represents a space character.
Enter a space in the equivalent position in the translation.
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@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。
返り値は 100% ボラリティに対するオプション価格の変更率で表現されます。
@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
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Translated and reviewed by
Yukihiro Nakai
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7.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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(no translation yet)
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8.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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(no translation yet)
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9.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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represents a space character.
Enter a space in the equivalent position in the translation.
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(no translation yet)
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10.
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@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
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represents a line break.
Start a new line in the equivalent position in the translation.
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represents a space character.
Enter a space in the equivalent position in the translation.
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(no translation yet)
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11.
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@FUNCTION=OPT_JUMP_DIFF
@SYNTAX=OPT_JUMP_DIFF(call_put_flag,spot,strike,time,rate,volatility,lambda,gamma)
@DESCRIPTION=OPT_JUMP_DIFF models the theoretical price of an option according to the Jump Diffusion process (Merton).
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@spot is the spot price of the underlying asset.
@strike is the strike price of the option.
@time is the time to maturity of the option expressed in years.
@rate is the annualized rate of interest.
@volatility is the annualized volatility of the underlying asset.
@lambda is expected number of 'jumps' per year.
@gamma is proportion of volatility explained by the 'jumps.'
@EXAMPLES=
@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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represents a line break.
Start a new line in the equivalent position in the translation.
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(no translation yet)
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12.
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@FUNCTION=OPT_MILTERSEN_SCHWARTZ
@SYNTAX=OPT_MILTERSEN_SCHWARTZ(call_put_flag,p_t,f_t,x,t1,t2,v_s,v_e,v_f,rho_se,rho_sf,rho_ef,kappa_e,kappa_f)
@DESCRIPTION=OPT_MILTERSEN_SCHWARTZ models the theoretical price of options on commodities futures according to Miltersen & Schwartz.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@p_t is a zero coupon bond with expiry at option maturity.
@f_t is the futures price.
@x is the strike price.
@t1 is the time to maturity of the option.
@t2 is the time to maturity of the underlying commodity futures contract.
@v_s is the volatility of the spot commodity price.
@v_e is the volatility of the future convenience yield.
@v_f is the volatility of the forward rate of interest.
@rho_se is correlation between the spot commodity price and the convenience yield.
@rho_sf is correlation between the spot commodity price and the forward interest rate.
@rho_ef is correlation between the forward interest rate and the convenience yield.
@kappa_e is the speed of mean reversion of the convenience yield.
@kappa_f is the speed of mean reversion of the forward interest rate.
@EXAMPLES=
@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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represents a line break.
Start a new line in the equivalent position in the translation.
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represents a space character.
Enter a space in the equivalent position in the translation.
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(no translation yet)
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13.
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@FUNCTION=OPT_RGW
@SYNTAX=OPT_RGW(call_put_flag,spot,strike,t1,t2,rate,d,volatility)
@DESCRIPTION=OPT_RGW models the theoretical price of an american option according to the Roll-Geske-Whaley approximation where:
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@spot is the spot price of the underlying asset.
@strike is the strike price at which the option is struck.
@t1 is the time to the dividend payout.
@t2 is the time to option expiration.
@rate is the annualized rate of interest.
@d is the amount of the dividend to be paid.
@volatility is the annualized rate of volatility of the underlying asset.
@EXAMPLES=
@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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represents a line break.
Start a new line in the equivalent position in the translation.
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represents a space character.
Enter a space in the equivalent position in the translation.
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(no translation yet)
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Located in
../plugins/derivatives/options.c:1048
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