Compounded Risk


A building society issues a one year bond that entities the holder to the return of weighted average share index (NSE 20) up to a maximum level of 30% growth over the year. The bond has guaranteed minimum level of return so that the investor will receive at least x% of their initial investment back. Investors cannot redeem their bonds prior to the end of the year.

  1. Explain how the building society can use a combination of call and put option to prevent making a loss on these bonds. [4 marks]
  2. The volatility of the NSE 20 index is 30% p.a and continuously compounded risk free rate of return is 4% p.a. 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 break even. [6 marks]


A company share price is to be modelled using a 5-step recombining binomial tree, with each step in the tree representing one day. Each day, its assumed that the share price:

  •  Increase by 2%, or
  •  Decrease by 1%

Assume that the force of interest is 5.5% p.a and that there are 365 days in a year. No dividends are to be paid over the next five days.


  1. Calculate the risk-neutral probability of an up-step on any given day. [3 marks]
  2. Calculate the fair price of a 5-day at-the-money call option on Ksh 10,000 worth of shares in this company. [7 marks]

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