forward.prepaid {FinancialMath}

Prepaid Forward Contract

Description

Gives a table and graphical representation of the payoff of a prepaid forward contract, and calculates the prepaid forward price for the contract.

Usage

forward.prepaid(S,t,r,position,div.structure="none",dividend=NA,df=1,D=NA,
k=NA,plot=FALSE)

Arguments

S

spot price at time 0

t

time of expiration (in years)

r

continuously compounded yearly risk free rate

position

either buyer or seller of the contract ("long" or "short")

div.structure

the structure of the dividends for the underlying ("none", "continuous", or "discrete")

dividend

amount of each dividend, or amount of first dividend if k is not NA

df

dividend frequency- number of dividends per year

D

continuous dividend yield

k

dividend growth rate per df

plot

tells whether or not to plot the payoff

Details

Stock price at time t =S_t

Long Position: payoff = S_t - prepaid forward price

Short Position: payoff = prepaid forward price - S_t

If div.structure = "none"

forward price=S

If div.structure = "discrete"

eff.i=e^r-1

j=(1+eff.i)^{\frac{1}{df}}-1

Number of dividends: t^*=t*df

if k = NA: prepaid forward price =S-dividend*{a_{\left. {\overline {\, t^* \,}}\! \right |j}}

if k != j: prepaid forward price =S-dividend*\frac{1-(\frac{1+k}{1+j})^{t^*}}{j-k}

if k = j: prepaid forward price =S-dividend*\frac{t^*}{1+j}

If div.structure = "continuous"

prepaid forward price=S*e^{-D*t}

Value

A list of two components.

Payoff

A data frame of different payoffs for given stock prices.

Price

The prepaid forward price of the contract.

Note

Leave an input variable as NA if it is not needed (ie. k=NA if div.structure="none").

See Also

forward

Examples

forward.prepaid(S=100,t=2,r=.04,position="short",div.structure="none")

forward.prepaid(S=100,t=2,r=.03,position="long",div.structure="discrete",
dividend=3,k=.02,df=2)

forward.prepaid(S=100,t=1,r=.05,position="long",div.structure="continuous",D=.06)