Kategorien
Finance Research

Option valuation using Black-Scholes

Financial options have an intrinsic and a time value. The intrinsic value for a call option is simply the spot (S) minus the strike price (X). The time value of the call option can be derived using the Black-Scholes formula. The resulting price of the option minus the intrinsic value of the option results in the time value of the option.

The following graph illustrates the intrinsic value (red line), the price of the option (grey line) and the time value of the option (dark grey area).

Using the following code you can replicate the figure:

spot <- seq(1,100,by=1)
strike <- 50
riskfree <- 0
time <- 1
standarddev <- 0.2

d1 <- (log(spot/strike)+(0+standarddev^2/2)*1)/(standarddev*time)
d2 <- d1-standarddev*time^(1/2)

value.call <- pnorm(d1,0,1)*spot-pnorm(d2,0,1)*strike*exp(-riskfree*time)

inner.value <- spot-strike
inner.value <- pmax(inner.value,0)

require(ggplot2)

ggplot()+
geom_line(aes(spot,value.call))+
geom_line(aes(spot,inner.value),colour="red")+ geom_ribbon(aes(spot,ymin=value.call,ymax=inner.value),fill="darkgrey")

Schreibe einen Kommentar

Deine E-Mail-Adresse wird nicht veröffentlicht. Erforderliche Felder sind mit * markiert.