$\mathbb{P}$ vs. $\mathbb{Q}$ measure in FX options

Background I want to look at this FX rate with the risk-neutral measure. I read that we strip away the real-world historical trend ( $\mu=−2.88\%$ ). In the risk-neutral world, my assumption is that investors do not demand a risk premium for holding volatile assets, which means the expected return on any asset must equal the risk-free rate. My attempt For FX, the solution with $\mathbb{Q}$ is governed by Garman-Kohlhagen framework (the FX extension of Black-Scholes). $dX_t = (r_d - r_f) X_t dt + \sigma X_t dW_t^{\mathbb{Q}}$ where: $X_t$ is the exchange rate (how many USD per 1 EUR). $r_d$ is the domestic interest rate (USD rate, since USD is the pricing currency). $r_f$ is the foreign interest rate (EUR rate, acting exactly like a continuous dividend yield $q$ in the classic Black-Scholes formula. Applying Itô's Lemma under the $\mathbb{Q}$ measure gives the exact solution for the exchange rate at time $T$ : $X_T = X_0 \exp\left( \left((r_d - r_f) - \frac{1}{2}\sigma^2\right)T + \sigma W_T^{\mathbb{Q}} \right)$ To see how this differs from the real-world calculation, let's look at the risk-neutral expected value, which is used directly to calculate forward rates and price options: $E^{\mathbb{Q}}[X_T] = X_0 e^{(r_d - r_f)T}$ Current Rate ( $X_0$ ): $1.14376$ . US Interest Rate ( $r_d$ ): let's assume a standard risk-free rate of $4.5\%$ ( $0.045$ ). Eurozone Interest Rate ( $r_f$ ): let's assume the European Central Bank rate is at $3.25\%$ ( $0.0325$ ). Time ( $T$ ): $1$ year. \begin{align*} E^{\mathbb{Q}}[X_T] &= 1.14376 \cdot e^{(0.045 - 0.0325) \cdot 1}\ &= 1.14376 \cdot e^{0.0125}\ &= 1.14376 \cdot 1.01258\ &= \boxed{1.1581} \end{align*} My questions Would this be correct? Also, do quants/analysts typically separate the entire financial universe into two distinct domains: the $\mathbb{Q}$ -World (Risk-Neutral)? and, the $\mathbb{P}$ -World (Physical/Real-World)? So, if we are market-making options traders or a derivatives pricing quants, we'd work exclusively with $\mathbb{Q}$ (Risk-Neutral Measure)? If we are risk managers or a directional algorithmic traders, we would use without $\mathbb{Q}$ ( $\mathbb{P}$ -Measure)? Also, to find the explicit solution to this SDE without using $\mathbb{Q}$ , we apply Itô's Lemma directly to the real-world process. The exact solution for the exchange rate at a future time $T$ is: $X_T = X_0 \exp\left( \left(\mu - \frac{1}{2}\sigma^2\right)T + \sigma W_T^{\mathbb{P}} \right)$ Current Rate ( $X_0$ ): $1.14376$ Real-World Annual Drift ( $\mu$ ): $-0.0288$ (from the $-2.88\%$ 1-year return on the screen) Annual FX Volatility ( $\sigma$ ): let's assume a standard $\approx 7\%$ ( $0.07$ ) for G10 currencies. Time ( $T$ ): $1$ year If we want to find the expected mathematical baseline for the exchange rate next year without pricing options, we take the expected value \begin{align*} E^{\mathbb{P}}[X_T] &= X_0 e^{\mu T}\ &= 1.14376 \cdot e^{-0.0288 \cdot 1}\ &= 1.14376 \cdot 0.9716\ & = \boxed{1.1113} \end{align*} As such?