NO.PZ2022071105000009
问题如下：
Company PQR has an outstanding zero-coupon bond with 1 year remaining to maturity. The bond, the
company’s only debt, has a face value of USD 2,000,000 and a recovery rate of 0% in the event of default. The
bond is currently trading at 75% of face value. Assuming the excess spread only captures credit risk and that
the continuously-compounded risk-free rate is 3% per year, and using risk-neutral binomial tree methodology,
what is the approximate risk-neutral 1-year probability of default of Company PQR?
选项：
A.13.3%
B.16.5%
C.19.2%
D.22.7%
解释：
中文解析：
债券的价格是0.75*2=1.5M USD.
根据下列等式可以求出风险中性概率：
1.5 * exp(0.03*1) = 0 * PD + 2 * (1 - PD)，
其中PD（风险中性概率）= 0.227.
因此，1,500,000 = [(1-λ)*2,000,000 + λ*0]*exp(-3%*1)，
λ = 22.72%
As the bond is trading at 75% of the current value, the bond price for face value USD 2M
is 0.75*2 = USD 1.5M. The risk-neutral argument equates the risk-free investment payoff
in 1 year to the expected risk-neutral payoff, i.e.,
1.5 * exp(0.03*1) = 0 * PD + 2 * (1 - PD)
where PD is the risk-neutral probability of default. Thus,
PD = 1- [1.5 * exp(0.03) /2] = 0.227
Easier explanation:
Risk-neutral probability of default (λ)
1,500,000 = [(1-λ)*2,000,000 + λ*0]*exp(-3%*1)
and thus λ = 22.72%
如题
