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论文题目：金融数学
论文语种：英文
您的研究方向：金融数学
是否有数据处理要求：是
您的国家：英国
您的学校背景：
要求字数：2道题目
论文用途：硕士课程论文
是否需要盲审（博士或硕士生有这个需要）：否

补充要求和说明：看附件

1.第一个投资组合是长期在同一个股票资产是个看涨期权和短期看跌期权，与两个选项是出了钱的。对于这第一个图集利率可以被认为是确定的，因此，它们被假定不是代表一个危险因素。第一组合：ONE CALL OPTION减去一个认沽期权在同一股票。物理标准下公平：;μ= 0:08 DST = STDT + SStdW T，S0 = 100; S = 0：DST = rStdt + SStdWt; R = 0：定价措施下2股权01认购期权行使：=的Kc 120看涨期权期限：5年将期权行权：=的Kp选项80.Put期限：5年。风险价值的持有期：1Y刀豆置信水平：99％2.A第二组合与在同一股票资产S和以零息债券，2年期与大型名义相比，该选项的钱看涨期权。债券将在利率风险驱动。在这第二个组合中的学生最初可能会认为驾驶短期利率RT布朗运动是独立驱动股票资产圣布朗运动的建议在thestudent使用Vasicek利率模型。我们建议该模型的参数是特定下面编。对于第二个组合中的学生应该在谨慎，一致性，股权选项必须与具有由用于债券相同的随机RT给予利率模型进行估值。最后，学生应该尽量去除独立的假设，并讨论何时加息和股权股票是相关的投资组合第二次会发生什么：ONE认购期权的股票PLUS ONE零息债券。物理措施下短期利率：DRT = KR（RT）DT + RDZ吨; R0 = 0：01; KR = 0：1;θ= 0：1; R = 0：004定价措施下，短期利率：DRT = KR（θRT）DT + rdZt;θ= 0：05零息债券，期限2年，物理措施名义下的股票1000：DST = STDT + SStdW T，S0 = 100;μ= 0:09; S = 0：DST = rStdt + SStdWt;上述rtthe短期随机过程：定价措施下2股权。认购期权行使：的Kc = 100看涨期权期限：2年的VaR持有期：1Y刀豆
置信水平：99％的相关性dZtdWt = DT，
首先尝试ρ= 0.A可能的分析，让ρ= 0:99或ρ= ..0：99和讨论results.The学生需要在1小心
该相关性都在风险地平线的危险因素高达风险地平线和在期权定价的模拟部分包括这样的情况下

最终到期日在地平线上的每个股权/利率的情况。 

1. A  first portfolio which is long a call option and short a put option on the same equity asset S, with both option being out of the money. For this firs portfolio interest rates can be considered to be deterministic, and hence they are assumed not to represent a risk factor. FIRST PORTFOLIO: ONE CALL OPTION MINUS ONE PUT OPTION ON THE SAME STOCK. Equity under the physical measure:dSt =  Stdt +  SStdW t, S0 = 100;μ = 0:08; S =0:2 Equity under the pricing measure:dSt = rStdt +  SStdWt;r =0:01 Call option strike:Kc = 120. Call option maturity: 5 years Put option strike:Kp = 80.Put option maturity: 5 years. VaR holding period: 1y Con 
dence level: 99 percent 

2.A second portfolio with an at the money call option on the same equity asset S and with a zero coupon bond with 2 years maturity with large notional compared to the option. The bond will be driven by interest rate risk. In this second portfolio the student may initially assume that the brownian motion driving the short term interest rate rt is independent of the brownian motion driving the equity asset St. It is suggested that thestudent uses the Vasicek interest rate model. The model parameters we suggest are speci 
ed below. For this second portfolio the student should be careful in that, for consistency, the equity option must be valued with a model having interest rates given by the same stochastic rt used for the bond.Finally, the student should try to remove the independence assumption and discuss what may happen when interest rates and the equity stock are correlated SECOND PORTFOLIO: ONE CALL OPTION ON THE STOCK PLUS ONE ZERO COUPON BOND. Short term interest rate under the physical measure:drt = kr(  . rt)dt +   rdZ t;r0 =0:01;kr =0:1;θ =0:1; r =0:004 Short term interest rate under the pricing measure:drt = kr(θ . rt)dt +  rdZt;θ =0:05 Zero coupon bond with Maturity 2 years and notional 1000. Equity under the physical measure:dSt =  Stdt +  SStdW t, S0 = 100;μ = 0:09; S =0:2 Equity under the pricing measure:dSt = rStdt +  SStdWt;rtthe short term stochastic process given above. Call option strike:Kc = 100. Call option maturity: 2 years VaR holding period: 1y Con 
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