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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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13.
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@FUNCTION=OPT_RGW
@SYNTAX=OPT_RGW(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:
@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 expressed in currency.
@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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15.
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@FUNCTION=OPT_BJER_STENS
@SYNTAX=OPT_BJER_STENS(call_put_flag,spot,strike,time,rate,volatility[,cost_of_carry])
@DESCRIPTION=OPT_BJER_STENS models the theoretical price of American options according to the Bjerksund & Stensland approximation technique.
@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.
@time is the number of days to maturity of the option.
@rate is the annualized risk-free rate of interest.
@volatility is the annualized volatility in price of the underlying asset.
@cost_of_carry is the leakage in value of the underlying asset, 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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16.
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@FUNCTION=OPT_EXEC
@SYNTAX=OPT_EXEC(call_put_flag,spot,strike,time,rate,volatility,cost_of_carry,lambda)
@DESCRIPTION=OPT_EXEC models the theoretical price of executive stock options @call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
One would expect this to always be a call option.
@spot is the spot price of the underlying asset.
@strike is the strike price at which the option is struck.
@time is the number of days to maturity of the option.
@rate is the annualized risk-free rate of interest.
@volatility is the annualized volatility in price of the underlying asset.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
@lambda is the jump rate for executives. The model assumes executives forfeit their options if they leave the company.
@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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17.
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@FUNCTION=OPT_FORWARD_START
@SYNTAX=OPT_FORWARD_START(call_put_flag,spot,alpha,time1,time,rate,volatility,cost_of_carry)
@DESCRIPTION=OPT_FORWARD_START models the theoretical price of forward start options
@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.
@alpha is a fraction that set the strike price the future date @time1.
@time1 is the number of days until the option starts.
@time is the number of days to maturity of the option.
@rate is the annualized risk-free rate of interest.
@volatility is the annualized volatility in price of the underlying asset.
@cost_of_carry is the leakage in value of the underlying asset, 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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18.
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@FUNCTION=OPT_TIME_SWITCH
@SYNTAX=OPT_TIME_SWITCH(call_put_flag,spot,strike,a,time,m,dt,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_TIME_SWITCH models the theoretical price of time switch options. (Pechtl 1995)
The holder receives @a * @dt for each period dt that the asset price was greater than the strike price (for a call) or below it (for a put).
@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.
@a is the amount received for each time period as discussed above.
@time is the maturity of the option in years.
@m is the number of time units the option has already met the condition.
@dt is the agreed upon discrete time period (often a day) expressed as a fraction of a year.
@rate is the annualized risk-free rate of interest.
@cost_of_carry is the leakage in value of the underlying asset, 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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19.
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@FUNCTION=OPT_SIMPLE_CHOOSER
@SYNTAX=OPT_SIMPLE_CHOOSER(call_put_flag,spot,strike,time1,time2,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_SIMPLE_CHOOSER models the theoretical price of simple chooser options.
@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.
@time1 is the time in years until the holder chooses a put or a call option.
@time2 is the time in years until the chosen option expires.
@rate is the annualized risk-free rate of interest.
@cost_of_carry is the leakage in value of the underlying asset, 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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20.
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@FUNCTION=OPT_COMPLEX_CHOOSER
@SYNTAX=OPT_COMPLEX_CHOOSER(call_put_flag,spot,strike_call,strike_put,time,time_call,time_put,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_COMPLEX_CHOOSER models the theoretical price of complex chooser options.
@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_call is the strike price at which the option is struck, applicable if exercised as a call option.
@strike_put is the strike price at which the option is struck, applicable if exercised as a put option.
@time is the time in years until the holder chooses a put or a call option.
@time_call is the time in years to maturity of the call option if chosen.
@time_put is the time in years to maturity of the put option if chosen.
@rate is the annualized risk-free rate of interest.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
@volatility is the annualized volatility in price 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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21.
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@FUNCTION=OPT_ON_OPTIONS
@SYNTAX=OPT_ON_OPTIONS(type_flag,spot,strike1,strike2,time1,time2,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_ON_OPTIONS models the theoretical price of options on options.
@type_flag is 'cc' for calls on calls, 'cp' for calls on puts, and so on for 'pc', and 'pp'.
@spot is the spot price of the underlying asset.
@strike1 is the strike price at which the option being valued is struck.
@strike2 is the strike price at which the underlying option is struck.
@time1 is the time in years to maturity of the option.
@time2 is the time in years to the maturity of the underlying option.
(@time2 >= @time1).
@rate is the annualized risk-free rate of interest.
@cost_of_carry is the leakage in value of the underlying asset of the underlying option.for common stocks, this would be the dividend yield.
@volatility is the annualized volatility in price of the underlying asset of the underlying option.
@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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22.
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@FUNCTION=OPT_EXTENDIBLE_WRITER
@SYNTAX=OPT_EXTENDIBLE_WRITER(call_put_flag,spot,strike1,strike2,time1,time2,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_EXTENDIBLE_WRITER models the theoretical price of extendible writer options. These are options that can be exercised at an initial period, @time1, or their maturity extended to @time2 if the option is out of the money at @time1.
@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.
@strike1 is the strike price at which the option is struck.
@strike2 is the strike price at which the option is re-struck if out of the money at @time1.
@time1 is the initial maturity of the option in years.
@time2 is the is the extended maturity in years if chosen.
@rate is the annualized risk-free rate of interest.
@cost_of_carry is the leakage in value of the underlying asset, for common stocks, this would be the dividend yield.
@volatility is the annualized volatility in price 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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(no translation yet)
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