Delta of a currency forward contract that price follows Ornstein–Uhlenbeck process

Question

Considering a currency forward contract that matures at time $T$, and its price $F_t$ follows the OU process such that \begin{equation} F_t = F_0 e^{-Kt} + a(1 - e^{-Kt}) + \sigma\int^t_0 e^{K(s-t)} dW_s \end{equation} where $W_t$ represents the Wiener process, and at the maturity the forward price will converge to the spot price, such that $F_T = S_T$. Rearrange it we have \begin{equation} F_t = F_0 e^{-Kt} + a(1 - e^{-Kt}) + \frac{\sigma}{\sqrt{2K}} W_{1-e^{-2Kt}} \end{equation} where $W_{1-e^{-2Kt}}\sim N(0, 1-e^{-2Kt})$ is the possible position of the Wiener process at $t = 1-e^{-2Kt}$. At any time $t$ before maturity, the value of the forward contract is $V_t = S_t - F_t$, I was wondering, what is the delta of this forward? \begin{equation} \Delta = \frac{d V_t}{ dF_t}? \end{equation}

Answer 1

Tradable assets cannot be mean-reverting otherwise there are arbitrage opportunities