bv_cvxbook_extra_exercises

# Show that e x f is a convex function of x on x k x

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Unformatted text preview: or value that depends on S , the value of the underlying asset at the end of the investment period. We will assume that the underying asset can only take on m diﬀerent values, S (1) , . . . , S (m) . These correspond to the m possible scenarios or outcomes described in Example 5.10. A risk-free asset has value r > 1 in every scenario. A put option at strike price K gives the owner the right to sell one unit of the underlying stock at price K . At the end of the investment period, if the stock is trading at a price S , then the put option has payoﬀ (K − S )+ = max{0, K − S } (since the option is exercised only if K > S ). Similarly a call option at strike price K gives the buyer the right to buy a unit of stock at price K . A call option has payoﬀ (S − K )+ = max{0, S − K }. A collar is an option with payoﬀ C − S0 S>C S − S0 F ≤ S ≤ C F −S S <F 0 114 where F is the ﬂoor, C is the cap and S0 is the price of the underlying at the start of the investment period. This...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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