The Moderne healthcare company has issue one and two-year annual coupon bonds with par value of $100. Both have coupon rates of 9% per year. The yields to maturity of the first and the second bond are 6.2% and 6.5% (continuous compounding), respectively. The risk-free rate is 4.5%. The recovery rate is 35%. Defaults can only take place halfway through each year.

Estimate the risk-neutral default probability in year one.

Estimate the risk-neutral default probability in year two.