Principles of Financial Engineering, 3rd Edition

(9.68)

But, this is equal to the payoff of a put with strike price $K{e}^{-r(T-T_0)}$ and exercise date T₀. Thus, the pricing formula for the chooser option is given by

$C^h(t)=[S_{t}N(d_1)–K{e}^{–r(T–t)}N(d_2)]+[–S_{t}N(–{\overline{d}}_1)+K{e}^{-r(T-T_0)}{e}^{-r(T_0-t)}N(-{\overline{d}}_2)]$ (9.69)

(9.69)

Simplifying:

$C^h(t)=[S_t(N(d_1)–N(–{\overline{d}}_1))]+K{e}^{-r(T-t)}(N(-{\overline{d}}_2)–N(d_2))$ (9.70)

(9.70)

with

$d_{1,2}=\frac{\ln (S_t}{}$