Ques: A very highly geared company, Risky plc, has issued zero coupon bonds payable in three year time for a nominal amount of £3,200m. A Black-Scholes model for the value of the company is adopted. The current gross value of the company is £6,979m. The continuously compounded risk-free interest rate is 2% p.a. and the price of £100 nominal of the bond is £92.603. An insurance company is offering default insurance on Risky plc. They will charge a premium of £55,000 for a contract which pays £1m at the end of three years if Risky plc defaults. (iii) Discuss whether there is an arbitrage opportunity. Doubt: in the solution it is given the probability of default is 1-PHI(d2). How ? Is there some standard way to decide the probability in case of options ?
