Risk Neutral Pricing and Financial Mathematics: A Primer

$p_{0,\mathrm{call}}=X_2{\mathrm{e}}^{-r{T}_2}M\left(-d_2,y_2;-\sqrt{\frac{T_1}{T_2}}\right)-S_{0}M\left(-d_1,y_1;-\sqrt{\frac{T_1}{T_2}}\right)+X_1{\mathrm{e}}^{-r{T}_1}N(-d_2)$

$c_{0,\mathrm{put}}=X_2{\mathrm{e}}^{-r{T}_2}M\left(-d_2-y_2;\sqrt{\frac{T_1}{T_2}}\right)-S_{0}M\left(-d_2-y_2;\sqrt{\frac{T_1}{T_2}}\right)-X_1{\mathrm{e}}^{-r{T}_1}N(-d_2)$

$p_{0,\mathrm{put}}=S_{0}M\left(d_1-y_1;-\sqrt{\frac{T_1}{T_2}}\right)-X_2{\mathrm{e}}^{-r{T}_2}M\left(d_2-y_2;-\sqrt{\frac{T_1}{T_2}}\right)+X_1{\mathrm{e}}^{-r{T}_1}N(d_2)$

Let c_t,call, p_t,call, c_t,put, and p_t,put denote the values of a call on a call, a put on a call, a call on a put, and a put on a put at time t, respectively. To obtain the ...