Compute the arbitrage-free price [ Cleft(t, S_{t}ight)=mathrm{e}^{-(T-t) r} mathbb{E}_{alpha}left[left(S_{T}ight)^{2} mid mathcal{F}_{t}ight] ] at time (t in[0, T])
Question:
Compute the arbitrage-free price
\[
C\left(t, S_{t}ight)=\mathrm{e}^{-(T-t) r} \mathbb{E}_{\alpha}\left[\left(S_{T}ight)^{2} \mid \mathcal{F}_{t}ight]
\]
at time \(t \in[0, T]\) of the power option with payoff \(\left(S_{T}ight)^{2}\) in the framework of the Bachelier (1900) model of Exercise 7.16.
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Related Book For
Introduction To Stochastic Finance With Market Examples
ISBN: 9781032288277
2nd Edition
Authors: Nicolas Privault
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