(9.68)

But, this is equal to the payoff of a put with strike price $K{e}^{-r(T-{T}_{0})}$ and exercise date *T*_{0}. Thus, the pricing formula for the chooser option is given by

${C}^{h}(t)=[{S}_{t}N({d}_{1})\u2013K{e}^{\u2013r(T\u2013t)}N({d}_{2})]+[\u2013{S}_{t}N(\u2013{\overline{d}}_{1})+K{e}^{-r(T-{T}_{0})}{e}^{-r({T}_{0}-t)}N(-{\overline{d}}_{2})]$ (9.69)

(9.69)

Simplifying:

${C}^{h}(t)=[{S}_{t}(N({d}_{1})\u2013N(\u2013{\overline{d}}_{1}))]+K{e}^{-r(T-t)}(N(-{\overline{d}}_{2})\u2013N({d}_{2}))$ (9.70)

(9.70)

with

${d}_{1,2}=\frac{\mathrm{ln}({S}_{t}}{}$

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