Forward Contract
Gives a table and graphical representation of the payoff of a forward contract, and calculates the forward price for the contract.
forward(S,t,r,position,div.structure="none",dividend=NA,df=1,D=NA,k=NA,plot=FALSE)
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 |
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}
A list of two components.
Payoff |
A data frame of different payoffs for given stock prices. |
Price |
The forward price of the contract. |
Leave an input variable as NA if it is not needed (ie. k=NA if div.structure="none").
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)
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