Paper 3, Section II, J
First, what is a Brownian motion?
(i) The price of an asset evolving in continuous time is represented as
where is a standard Brownian motion, and and are constants. If riskless investment in a bank account returns a continuously-compounded rate of interest , derive a formula for the time-0 price of a European call option on the asset with strike and expiry . You may use any general results, but should state them clearly.
(ii) In the same financial market, consider now a derivative which pays
at time . Find the time-0 price for this derivative. Show that it is less than the price of the European call option which you derived in (i).
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