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.
i. Explain how the building society can use a combination of call and put options to prevent making a loss on these
bonds. (4 marks]
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]
Answers
Explanation:
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.
i. Explain how the building society can use a combination of call and put options to prevent making a loss on these
bonds. (4 marks]
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]
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