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21.
@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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22.
@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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23.
@FUNCTION=OPT_2_ASSET_CORRELATION
@SYNTAX=OPT_2_ASSET_CORRELATION(call_put_flag,spot1,spot2,strike1,strike2,time,cost_of_carry1,cost_of_carry2,rate,volatility1,volatility2,rho)
@DESCRIPTION=OPT_2_ASSET_CORRELATION models the theoretical price of options on 2 assets with correlation @rho.
The payoff for a call is max(@spot2 - @strike2,0) if @spot1 > @strike1 or 0 otherwise.
The payoff for a put is max (@strike2 - @spot2, 0) if @spot1 < @strike1 or 0 otherwise.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@spot1 & @spot2 are the spot prices of the underlying assets.
@strike1 & @strike2 are the strike prices at which the option is struck.
@time is the initial maturity of the option in years.
@rate is the annualized risk-free rate of interest.
@cost_of_carry1 & @cost_of_carry2 are the leakage in value of the underlying assets, for common stocks, this would be the dividend yield.
@volatility1 & @volatility2 are the annualized volatility in price of the underlying assets.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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24.
@FUNCTION=OPT_EURO_EXCHANGE
@SYNTAX=OPT_EURO_EXCHANGE(spot1,spot2,qty1,qty2,time,rate,cost_of_carry1,cost_of_carry2,volatility1,volatility2,rho)
@DESCRIPTION=OPT_EURO_EXCHANGE models the theoretical price of a European option to exchange one asset with quantity @qty2 and spot price @spot2 for another, with quantity @qty1 and spot price @spot1.
@time is the initial maturity of the option in years.
@rate is the annualized risk-free rate of interest.
@cost_of_carry1 & @cost_of_carry2 are the leakage in value of the underlying assets, for common stocks, this would be the dividend yield.
@volatility1 & @volatility2 are the annualized volatility in price of the underlying assets.
@rho is the correlation between the two assets.

@EXAMPLES=

@SEEALSO=OPT_AMER_EXCHANGE, OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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25.
@FUNCTION=OPT_AMER_EXCHANGE
@SYNTAX=OPT_AMER_EXCHANGE(spot1,spot2,qty1,qty2,time,rate,cost_of_carry1,cost_of_carry2,volatility1, volatility2, rho)
@DESCRIPTION=OPT_AMER_EXCHANGE models the theoretical price of an American option to exchange one asset with quantity @qty2 and spot price @spot2 for another, with quantity @qty1 and spot price @spot1.
@time is the initial maturity of the option in years.
@rate is the annualized risk-free rate of interest.
@cost_of_carry1 & @cost_of_carry2 are the leakage in value of the underlying assets, for common stocks, this would be the dividend yield.
@volatility1 & @volatility2 are the annualized volatility in price of the underlying assets.
@rho is the correlation between the two assets.

@EXAMPLES=

@SEEALSO=OPT_EURO_EXCHANGE, OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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26.
@FUNCTION=OPT_SPREAD_APPROX
@SYNTAX=OPT_SPREAD_APPROX(call_put_flag,fut_price1,fut_price2,strike,time, rate,volatility1,volatility2,rho)
@DESCRIPTION=OPT_SPREAD_APPROX models the theoretical price of a European option on the spread between two futures contracts.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@fut_price1 & @fut_price2 are the prices of the two futures contracts.
@strike is the strike price at which the option is struck
@time is the initial maturity of the option in years.
@rate is the annualized risk-free rate of interest.
@volatility1 & @volatility2 are the annualized volatility in price of the underlying futures contracts.
@rho is the correlation between the two futures contracts.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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27.
@FUNCTION=OPT_FLOAT_STRK_LKBK
@SYNTAX=OPT_FLOAT_STRK_LKBK(call_put_flag,spot,spot_min,spot_max,time,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_FLOAT_STRK_LKBK models the theoretical price of an option where the holder of the option may exercise on expiry at the most favourable price observed during the options life of the underlying asset.
@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.
@spot_min is the minimum spot price of the underlying asset so far observed.
@spot_max is the maximum spot price of the underlying asset so far observed.
@time is the initial maturity of the option in years.
@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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28.
@FUNCTION=OPT_FIXED_STRK_LKBK
@SYNTAX=OPT_FIXED_STRK_LKBK(call_put_flag,spot,spot_min,spot_max,strike,time,rate,cost_of_carry,volatility)
@DESCRIPTION=OPT_FIXED_STRK_LKBK models the theoretical price of an option where the holder of the option may exercise on expiry at the most favourable price observed during the options life of the underlying asset.
@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.
@spot_min is the minimum spot price of the underlying asset so far observed.
@spot_max is the maximum spot price of the underlying asset so far observed.
@strike is the strike prices at which the option is struck.
@time is the initial maturity of the option in years.
@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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29.
@FUNCTION=OPT_BINOMIAL
@SYNTAX=OPT_BINOMIAL(amer_euro_flag,call_put_flag,num_time_steps, spot, strike, time, rate, volatility, cost_of_carry)
@DESCRIPTION=OPT_ models the theoretical price of either an American or European style option using a binomial tree.
@amer_euro_flag is either 'a' or 'e' to indicate whether the option being valued is an American or European style option respectively.
@call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
@num_time_steps is the number of time steps used in the valuation, a greater number of time steps yields greater accuracy however is slower to calculate.
@spot is the spot price of the underlying asset.
@strike is the strike price at which the option is struck.
@time is the initial maturity of the option in years.
@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.

@EXAMPLES=

@SEEALSO=OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA
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30.
@FUNCTION=COMPLEX
@SYNTAX=COMPLEX(real,im[,suffix])
@DESCRIPTION=COMPLEX returns a complex number of the form x + yi.

@real is the real and @im is the imaginary part of the complex number. @suffix is the suffix for the imaginary part. If it is omitted, COMPLEX uses 'i' by default.

* If @suffix is neither 'i' nor 'j', COMPLEX returns #VALUE! error.
* This function is Excel compatible.

@EXAMPLES=
COMPLEX(1,-1) equals 1-i.

@SEEALSO=
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Contributors to this translation: Hasbullah Bin Pit.