To fund an expansion in its operations Company X has just issued 12-year zero coupon bonds with a total face value of 135 million, taking its total asset value to 395 million.

1. a)Explain how the value of the bonds can be expressed in terms of a European put option and in terms of European call option. [4]
2. b)Calculate the fair price of a holding of company bonds with face value of 100 using Black-Scholes model, given that the price of a 8-year zero-coupon government bond is 80.57353. Assume that the annualized volatility of thecompany's asset's over 8-year period is 27%. [8]
3. c)Estimate the risk-neutral probability of default on the company's bond.[2]