A building society issues a one-year bond that entitles the holder to the return on a weighted-average share index (ABC500) up to a maximum level of 30% growth over the year. The bond has a guaranteed minimum level of return so that investors will receive at least x% of their initial investment back. Investors cannot redeem their bonds prior to the end of the year.

The volatility of the ABC500

index is 30% pa

and the continuously compounded risk-free rate of return is 4% pa

. Assuming no dividends, use the Black-Scholes pricing formulae to

determine the value of x (to the nearest 1%)

that the building society should choose to make neither a profit nor a loss. [6

marks]