Consider a European call option on a non-dividend-paying stock where the stock price is $52, the strike price $50, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is one year. Answer the following questions assuming no recovery in the event of default that the probability of default is independent of the option valuation, no collateral is posted, and no other transactions between the parties are outstanding
(a) What is the value of the option assuming no possibility of a default?
(b) What is the value of the option to the buyer if there is a 2% chance that the option seller will default at maturity?
(c) Suppose that, instead of paying the option price up front, the option buyer agrees to pay the forward value of the option price at the end of the option’s life. By how much does this reduce the cost of defaults to the option buyer in the case where there is a 2% chance of the option seller defaulting?
(d) If in case (c) the option buyer has a 1% chance of defaulting at the end of the life of the options, what is the default risk to the option seller? Discuss the two-sided nature of default risk in the case and the value of the option to each side.