Expanding Forward Starting Options

24 Pages Posted: 28 May 2008

See all articles by Daniel Alexandre Bloch

Daniel Alexandre Bloch

Université Paris VI Pierre et Marie Curie

Date Written: May 19, 2008

Abstract

Using the properties of the Affine and Quadratic models, we derive the price of a forward starting call option in a jump-diffusion model. Conditioning that price at the determination time of the strike we use a general pricing approximation technique for call options in a jump-diffusion model to calculate the price at that time. We then show that the resulting price no longer depends on the stock price but only depends on the instantaneous variance process and the time to maturity. Using this property, we apply Ito's lemma to each of the expanded terms of the call price and compute their expected value.

Keywords: Jump-Diffusion, Forward Start Option, Price Expansion, Malliavin Calculus

Suggested Citation

Bloch, Daniel Alexandre, Expanding Forward Starting Options (May 19, 2008). Available at SSRN: https://ssrn.com/abstract=1138162 or http://dx.doi.org/10.2139/ssrn.1138162

Daniel Alexandre Bloch (Contact Author)

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

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