v2直播merton model教育frm二级培训知识点.pdfVIP

➢ Example ⚫ 假设某股东投资了一家公司，初始投资额为S0 = 100，同时公司向债权人 了面值为K=100、期限为1年的零息债券，到期 偿还本金，因 此会折价 。企业的初始价值（可以看成是总资产）V = B + S ，现 0 0 0 在 一年后债券到期日的情况： 一年后 企业价值 （V ） 债券价值 （B ） 股东权益 （S ） 1 1 1 情况1 V1 = 300 K B1 = K = 100 S1 = 200 = V1 – K 情况2 V1 = 200 K B1 = K = 100 S1 = 100 = V1 – K 情况3 V1 = 100 = K B1 = K = 100 S1 = 0 = V1 – K 情况4 V1 = 80 K B1 = V1 = 80 S1 = 0 B = Min (K, V ) 1 1 一般情况 V = B + S S = Max (V – K,0) 1 1 1 1 1 = K – Max (K – V ,0) 1 ➢ Infer Credit Risk from Equity Prices ⚫ Bondholder ✓ VT D, default occurs if the value of the firm is insufficient to repay the debt pr ipal. Bondholders have priority over shareholders and seize the entire value of the firm V . T ✓ VT ≥ D, bondholders receive what they are due: the pr ipal D. ✓ Payoff: Min (D, V ) = D – max (D – V , 0) T T ✓ D = Risk- debt – put option on firm ✓ The payoff received by corporate bondholders can be seen as the payoff of a riskless bond minus a put on the value of the firm. ➢ Infer Credit Risk from