Question $4$

The current price of a non $-$ dividend $-$ paying share is R$140$ and its volatility is thought to

be $40\%$ per annum. The continuously compounded risk $-$ free interest rate is $5\%$ per

annum.

A European call option on this share has a strike price of R$130$ and term to maturity

of one year.

$($i$)$ Calculate the price of this call option, assuming that the Black $-$ Scholes model

applies. $[5]$

The market price for the option is actually R$40.$

$($ii$)$ Show that the volatility of the share implied by the true market price of the

option is $60\%$ per annum, to the nearest $1\%$ per annum. $[15]$