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Gordon
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Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then, \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}, \end{align*} where $r_d$ and $r_f$ are the respective USD and GBP interest rates. Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}, \end{align*} where $r_d$ and $r_f$ are the respective USD and GBP interest rates. Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then, \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}, \end{align*} where $r_d$ and $r_f$ are the respective USD and GBP interest rates. Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

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Gordon
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Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}. \end{align*}\begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}, \end{align*} where $r_d$ and $r_f$ are the respective USD and GBP interest rates. Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}. \end{align*} Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}, \end{align*} where $r_d$ and $r_f$ are the respective USD and GBP interest rates. Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

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Gordon
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Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}. \end{align*} Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

Let $\{X_t \mid t \ge 0\}$ be the foreign exchange rate rate from $£$ to $\\\$$. Moreover, let $C(X_0, K, T)$ and $P(X_0, K, T)$ be the prices of the respective call and put options with strike $K$ and maturity $T$. Then \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} Based on the given condition, we have \begin{align*} P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right) = 0.03. \end{align*} Then \begin{align*} C\left(\frac{1}{1.5} £/\\\$, \, \frac{1}{1.5} £/\\\$,\, 0.5 \right) &= \frac{1}{1.5\times 1.5}\times P\left(1.5 \\\$/£, \, 1.5 \\\$/£,\, 0.5 \right)\\ &\approx 0.01333. \end{align*}

$$ $$ The above duality formula can be derived as follows. Note that, for the put option payoff at maturity $T$, \begin{align*} (K-X_T)^+ = KX_T\left(\frac{1}{X_T} - \frac{1}{K} \right)^+. \end{align*} Let $P_d$ and $P_f$ denote, respectively, the USD and GBP risk-neutral measures. Moreover, let $E_d$ and $E_f$ denote the expectation operators corresponding to $P_d$ and $P_f$. Note that, \begin{align*} \frac{dP_d}{dP_f}\big|_T=\frac{X_0 e^{r_d T}}{X_T e^{r_f T}}. \end{align*} Then, \begin{align*} P(X_0, K, T) &= E_d\left(\frac{1}{e^{r_d T}} (K-X_T)^+\right)\\ &=E_d\left(\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= E_f\left(\frac{dP_d}{dP_f}\big|_T\frac{KX_T}{e^{r_d T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K E_f\left(\frac{1}{e^{r_f T}} \left(\frac{1}{X_T} - \frac{1}{K} \right)^+\right)\\ &= X_0 K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*} That is, \begin{align*} \frac{1}{X_0}P(X_0,\, K,\, T) = K C\left(\frac{1}{X_0},\, \frac{1}{K},\, T \right). \end{align*}

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