Consider a European call option on a non-dividend-paying stock

| November 9, 2018

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 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 option, 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.

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