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论文作者:www.51lunwen.org论文属性:作业 Assignment登出时间:2016-05-27编辑:anne点击率:5350
论文字数:200论文编号:org201605221504037526语种:英语 English地区:英国价格:$ 22
摘要:英国金融数学要计算两个Portfolio的 Delta-Normal VaR 跟 Delta-Gamma VaR.
补充要求和说明:看附件
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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