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12.

@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

19.

@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

35.

@FUNCTION=IMINV
@SYNTAX=IMINV(inumber)
@DESCRIPTION=IMINV returns the inverse, or reciprocal, of the complex number z (@inumber), where

[tab]1/z = (x - i y)/(x^2 + y^2).

* If @inumber is not a valid complex number, IMINV returns #VALUE! error.

@EXAMPLES=
IMINV("1-j") equals 0.5+0.5j.

@SEEALSO=

158.

@FUNCTION=RATE
@SYNTAX=RATE(nper,pmt,pv[,fv,type,guess])
@DESCRIPTION=RATE calculates the rate of an investment.

* If @pmt is ommitted it defaults to 0
* If @nper <= 0, RATE returns #NUM! error.
* If @type != 0 and @type != 1, RATE returns #VALUE! error.

@EXAMPLES=

@SEEALSO=PV,FV

231.

COLUMN:vector of column numbers.

232.

[reference].

233.

COLUMN function returns a Nx1 array containing the series of integers from the first column to the last column of @reference.
* @reference defaults to the position of the current expression.

* If @reference is neither an array nor a reference nor a range, returns #VALUE! error.

234.

COLUMN(A1:C4) equals {1,2,3}

235.

COLUMN(A:C) equals {1,2,3}

236.

COLUMN() in G13 equals 7.