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SkipperLin · 2020年04月07日

问一道题：NO.PZ2020021203000078

  1. FRM I
  2. Financial Markets And Products

问题如下：

Use the results in Chapter 9 to determine put-call parity for a currency options on the GBP/USD exchange rate. Express your answer in terms of the USD risk-free rate, RUSD, the GBP risk-free rate, RGBP, and the time to maturity, T.

选项：

解释：

with equation F=S(1+RUSD)(1+RGBP)F=S\frac{(1+R_{USD})}{(1+R_{GBP})}

Substituting this into Equation Price + PV(K) = European Put Price + PV(F) and noting that:

PV(K)=K(1+RUSD)TPV(K)=\frac K{{(1+R_{USD})}^T}

PV(F)=S(1+RUSD)T(1+RGBP)T1(1+RUSD)T=S(1+RGBP)TPV(F)=S\frac{{(1+R_{USD})}^T}{{(1+R_{GBP})}^T}\frac1{{(1+R_{USD})}^T}=\frac S{{(1+R_{GBP})}^T}

European Call Price + K(1+RUSD)T\frac K{{(1+R_{USD})}^T} = European Put Price + K(1+RGBP)T\frac K{{(1+R_{GBP})}^T}

请问solution一开始的这个equation怎么来的呀

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袁园_品职助教 · 2020年04月07日

同学你好！

这里是先求一下 forward rate, 用的是 interest parity 公式，如下图：

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NO.PZ2020021203000078问题如下 Use the results in Chapter 9 to termine put-call parity for a currenoptions on the GBP/USexchange rate. Express your answer in terms of the USrisk-free rate, RUS the Grisk-free rate, RGBP, anthe time to maturity, T. with equation F=S(1+RUS(1+RGBP)F=S\frac{(1+R_{US)}{(1+R_{GBP})}F=S(1+RGBP​)(1+RUS)​ Substituting this into Equation Pri+ PV(K) = EuropePut Pri+ PV(F) annoting that:PV(K)=K(1+RUSTPV(K)=\frK{{(1+R_{US)}^T}PV(K)=(1+RUS)TK​PV(F)=S(1+RUST(1+RGBP)T1(1+RUST=S(1+RGBP)TPV(F)=S\frac{{(1+R_{US)}^T}{{(1+R_{GBP})}^T}\frac1{{(1+R_{US)}^T}=\frS{{(1+R_{GBP})}^T}PV(F)=S(1+RGBP​)T(1+RUS)T​(1+RUS)T1​=(1+RGBP​)TS​EuropeCall Pri+ K(1+RUST\frK{{(1+R_{US)}^T}(1+RUS)TK​ = EuropePut Pri+ S(1+RGBP)T\frS{{(1+R_{GBP})}^T}(1+RGBP​)TS​ 这是哪块的知识点。。。。

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