问题如下图：
选项：
A. 
B. 
C. 
解释：老师 求exposure时,为啥不用下面表里的spot rate
发亮_品职助教 · 2019年03月12日
其实是用了的，除了最后一年，求每一年的Expected exposure都要涉及到折现问题。
每一年的Exposure包括两部分：当年的Coupon，和以后现金流的折现值。
这道题这个Bond 1是一个零息债券，所以不存在Coupon，那除了最后一期，每一年的Exposure就是以后现金流的折现值：
第四年债券到期，Exposures是1000；
第三年的Expected exposure是：1000/(1+3%)=970.87
第二年的Exposure是： 970.87/(1+3%) = 942.60
第一年的Exposure是： 942.59 / (1+3%) = 915.15
NO.PZ201812310200000101 问题如下 The market priof bonis€875. The bonis: fairly value overvalue unrvalue B is correct. The following table shows ththe cret valuation austment (CVfor the bonis €36.49, the sum of the present values of expecteloss. The steps taken to complete the table are follows. Step 1: Exposure te T is 1000 (1+r) 4−T , where r is 3%. This, exposure is computescounting the favalue of the bonusing the risk-free rate anthe number of years until maturity. Step 2: Recovery = Exposure × Recovery rate Step 3: Loss given fault (LG = Exposure – Recovery Step 4: Probability of fault (PO on te 1 is 1.50%, the assumehazarrate. The probability of surviv(POS) on te 1 is 98.50%. For subsequent tes, POis calculatethe hazarrate multipliethe previous te’s POS. For example, to termine the te 2 PO(1.4775%), the hazarrate of (1.50%) is multipliethe te 1 POS (98.50%). Step 5: POS in tes 2–4 = POS in the previous ye– POD (This, POS in YeT= POS in ye[ T– 1] – POin YeT.) POS calso be terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 6: Expecteloss = LG× POD Step 7: scount factor () for te T is 1 (1+r) T , where r is 3%. Step 8: PV of expecteloss = Expecteloss × Value of the bonif the bonwere fault free woul1,000 × for te 4 = €888.49. Fair value of the bonconsiring CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market priof the bon(€875) is greater ththe fair value of €852, B is correct. A is incorrect because the market priof the bonffers from its fair value. C is incorrebecause although the bons value if the bonwere fault free is greater ththe market price, the bond ha risk of fault, anCVA lowers its fair value to below the market price. RT
NO.PZ201812310200000101 问题如下 The market priof bonis€875. The bonis: fairly value overvalue unrvalue B is correct. The following table shows ththe cret valuation austment (CVfor the bonis €36.49, the sum of the present values of expecteloss. The steps taken to complete the table are follows. Step 1: Exposure te T is 1000 (1+r) 4−T , where r is 3%. This, exposure is computescounting the favalue of the bonusing the risk-free rate anthe number of years until maturity. Step 2: Recovery = Exposure × Recovery rate Step 3: Loss given fault (LG = Exposure – Recovery Step 4: Probability of fault (PO on te 1 is 1.50%, the assumehazarrate. The probability of surviv(POS) on te 1 is 98.50%. For subsequent tes, POis calculatethe hazarrate multipliethe previous te’s POS. For example, to termine the te 2 PO(1.4775%), the hazarrate of (1.50%) is multipliethe te 1 POS (98.50%). Step 5: POS in tes 2–4 = POS in the previous ye– POD (This, POS in YeT= POS in ye[ T– 1] – POin YeT.) POS calso be terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 6: Expecteloss = LG× POD Step 7: scount factor () for te T is 1 (1+r) T , where r is 3%. Step 8: PV of expecteloss = Expecteloss × Value of the bonif the bonwere fault free woul1,000 × for te 4 = €888.49. Fair value of the bonconsiring CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market priof the bon(€875) is greater ththe fair value of €852, B is correct. A is incorrect because the market priof the bonffers from its fair value. C is incorrebecause although the bons value if the bonwere fault free is greater ththe market price, the bond ha risk of fault, anCVA lowers its fair value to below the market price. 如题
NO.PZ201812310200000101问题如下 The market priof bonis€875. The bonis: fairly value overvalue unrvalue B is correct. The following table shows ththe cret valuation austment (CVfor the bonis €36.49, the sum of the present values of expecteloss. The steps taken to complete the table are follows. Step 1: Exposure te T is 1000 (1+r) 4−T , where r is 3%. This, exposure is computescounting the favalue of the bonusing the risk-free rate anthe number of years until maturity. Step 2: Recovery = Exposure × Recovery rate Step 3: Loss given fault (LG = Exposure – Recovery Step 4: Probability of fault (PO on te 1 is 1.50%, the assumehazarrate. The probability of surviv(POS) on te 1 is 98.50%. For subsequent tes, POis calculatethe hazarrate multipliethe previous te’s POS. For example, to termine the te 2 PO(1.4775%), the hazarrate of (1.50%) is multipliethe te 1 POS (98.50%). Step 5: POS in tes 2–4 = POS in the previous ye– POD (This, POS in YeT= POS in ye[ T– 1] – POin YeT.) POS calso be terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 6: Expecteloss = LG× POD Step 7: scount factor () for te T is 1 (1+r) T , where r is 3%. Step 8: PV of expecteloss = Expecteloss × Value of the bonif the bonwere fault free woul1,000 × for te 4 = €888.49. Fair value of the bonconsiring CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market priof the bon(€875) is greater ththe fair value of €852, B is correct. A is incorrect because the market priof the bonffers from its fair value. C is incorrebecause although the bons value if the bonwere fault free is greater ththe market price, the bond ha risk of fault, anCVA lowers its fair value to below the market price. 为什么不用下面二叉树利率折线呢
NO.PZ201812310200000101 问题如下 The market priof bonis€875. The bonis: fairly value overvalue unrvalue B is correct. The following table shows ththe cret valuation austment (CVfor the bonis €36.49, the sum of the present values of expecteloss. The steps taken to complete the table are follows. Step 1: Exposure te T is 1000 (1+r) 4−T , where r is 3%. This, exposure is computescounting the favalue of the bonusing the risk-free rate anthe number of years until maturity. Step 2: Recovery = Exposure × Recovery rate Step 3: Loss given fault (LG = Exposure – Recovery Step 4: Probability of fault (PO on te 1 is 1.50%, the assumehazarrate. The probability of surviv(POS) on te 1 is 98.50%. For subsequent tes, POis calculatethe hazarrate multipliethe previous te’s POS. For example, to termine the te 2 PO(1.4775%), the hazarrate of (1.50%) is multipliethe te 1 POS (98.50%). Step 5: POS in tes 2–4 = POS in the previous ye– POD (This, POS in YeT= POS in ye[ T– 1] – POin YeT.) POS calso be terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 6: Expecteloss = LG× POD Step 7: scount factor () for te T is 1 (1+r) T , where r is 3%. Step 8: PV of expecteloss = Expecteloss × Value of the bonif the bonwere fault free woul1,000 × for te 4 = €888.49. Fair value of the bonconsiring CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market priof the bon(€875) is greater ththe fair value of €852, B is correct. A is incorrect because the market priof the bonffers from its fair value. C is incorrebecause although the bons value if the bonwere fault free is greater ththe market price, the bond ha risk of fault, anCVA lowers its fair value to below the market price. 是因为利率没有波动才用的无风险收益吗？如果利率有波动就要用表格里的？
NO.PZ201812310200000101 问题如下 The market priof bonis€875. The bonis: fairly value overvalue unrvalue B is correct. The following table shows ththe cret valuation austment (CVfor the bonis €36.49, the sum of the present values of expecteloss. The steps taken to complete the table are follows. Step 1: Exposure te T is 1000 (1+r) 4−T , where r is 3%. This, exposure is computescounting the favalue of the bonusing the risk-free rate anthe number of years until maturity. Step 2: Recovery = Exposure × Recovery rate Step 3: Loss given fault (LG = Exposure – Recovery Step 4: Probability of fault (PO on te 1 is 1.50%, the assumehazarrate. The probability of surviv(POS) on te 1 is 98.50%. For subsequent tes, POis calculatethe hazarrate multipliethe previous te’s POS. For example, to termine the te 2 PO(1.4775%), the hazarrate of (1.50%) is multipliethe te 1 POS (98.50%). Step 5: POS in tes 2–4 = POS in the previous ye– POD (This, POS in YeT= POS in ye[ T– 1] – POin YeT.) POS calso be terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 6: Expecteloss = LG× POD Step 7: scount factor () for te T is 1 (1+r) T , where r is 3%. Step 8: PV of expecteloss = Expecteloss × Value of the bonif the bonwere fault free woul1,000 × for te 4 = €888.49. Fair value of the bonconsiring CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market priof the bon(€875) is greater ththe fair value of €852, B is correct. A is incorrect because the market priof the bonffers from its fair value. C is incorrebecause although the bons value if the bonwere fault free is greater ththe market price, the bond ha risk of fault, anCVA lowers its fair value to below the market price. bon的hazarrate是1.5%。而bon本身是个零息债券，其他时刻没有现金流。因此我认为只有在4年到期的时候才会违约，那么我们按违约概率1.5%，即0.985的不违约概率代入有什么问题呢？题目为什么用 0.985^4算不违约概率呢？