Consider two assets whose prices \(S_{t}^{(1)}, S_{t}^{(2)}\) at time \(t \in[0, T]\) follow the geometric Brownian dynamics

\[
d S_{t}^{(1)}=r S_{t}^{(1)} d t+\sigma_{1} S_{t}^{(1)} d W_{t}^{(1)} \quad d S_{t}^{(2)}=r S_{t}^{(2)} d t+\sigma_{2} S_{t}^{(2)} d W_{t}^{(2)} \quad t \in[0, T]
\]

where \(\left(W_{t}^{(1)}ight)_{t \in[0, T]},\left(W_{t}^{(2)}ight)_{t \in[0, T]}\) are two standard Brownian motions with correlation \(ho \in[-1,1]\) under a risk-neutral probability measure \(\mathbb{P}^{*}\), with \(d W_{t}^{(1)} \cdot d W_{t}^{(2)}=ho d t\).

Estimate the price \(\mathrm{e}^{-r T} \mathbb{E}^{*}\left[\left(S_{T}-Kight)^{+}ight]\)of the spread option on \(S_{T}:=S_{T}^{(2)}-S_{T}^{(1)}\) with maturity \(T>0\) and strike price \(K>0\) by matching the first two moments of \(S_{T}\) to those of a Gaussian random variable.