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But, this is equal to the payoff of a put with strike price $K{e}^{-r\left(T-{T}_{0}\right)}$ and exercise date T0. Thus, the pricing formula for the chooser option is given by

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

Simplifying:

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

with

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

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