forward: Forward Contract

In FinancialMath: Financial Mathematics for Actuaries

Description

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

Usage

forward(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 - forward price

Short Position: payoff = forward price - S_t

If div.structure = "none"

forward price=S*e^{r*t}

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: forward price =S*e^{r*t}-dividend*{s_{≤ft. {\overline {\, t^* \,}}\! \right |j}}

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

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

If div.structure = "continuous"

forward price=S*e^{(r-D)*t}

Value

A list of two components.

Payoff	A data frame of different payoffs for given stock prices.
Price	The 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.prepaid

Examples

forward(S=100,t=2,r=.03,position="short",div.structure="none")

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

forward(S=100,t=1,r=.03,position="long",div.structure="continuous",D=.01)

FinancialMath documentation built on May 1, 2019, 11:16 p.m.