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.

Explain how the building society can use a combination of call and put options to prevent making a loss on these bonds