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 1

Consider a European call option on a non-dividend-paying stock where thestock price is $52, the strike price $50, the risk-free rate is 5%, the volatilityis 30%, and the time to maturity is one year. Answer the following questionsassuming no recovery in the event of default, that the probability of defaultis independent of the option valuation, no collateral is posted, and no othertransactions 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 thatthe option seller will default at maturity?(c) Suppose that, instead of paying the option price up front, the option buyeragrees to pay the forward value of the option price at the end of option’slife. By how much does this reduce the cost of defaults to the option buyerin 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 ofthe life of the option, what is the default risk to the option seller? Discussthe two-sided nature of default risk in the case and the value of the optionto each side.

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