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]
ii. 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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The Akbarnama, which translates to Book of Akbar, the official chronicle of the reign of Akbar, the third Mughal Emperor, commissioned by Akbar himself by his court historian and biographer, Abu'l-Fazl ibn Mubarak, called one of the "nine jewels in Akbar's court" by Mughal writers.
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