Consider a $100M (face value), one-year, non-recourse, zero-coupon, risky, collateralized loan (i.e., the borrower promises to pay $100M in one year but may default on the loan). The YTM for this risky loan is 5.0% per year whereas the risk-free rate of return is 1.0% per year. What is the implied present value (price) of the default option?
Hint: You don’t need to know the option payoff in the next year for this question. The YTM for a one-year zero-coupon loan equals [the promised payment in one year]/[the current market price of the loan] – 1.