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Unformatted text preview: her (or not lower) for options with higher T. 2) This would not be true for European style options, since they can only be exercised at time T, and a more distant T does not confer an advantage. 3) As the expiration date nears, both time remaining and time value approach zero, which implies that option premiums approach their intrinsic (exercise) values at expiration: • Ct → max {ST – K, 0} as t → T • Pt → max {K – ST, 0} as t → T c) Volatility of stock price (σ). 1) A stockholder will gain if St rises, but lose if St falls. The more volatile the stock price (i.e., the greater standard deviation σ), the greater the possible gain and also the risk of loss. With diminishing MU and risk aversion, greater σ reduces the value of the stock to the investor, and reduces the price S0 he/she is willing to pay. 2) Option holders are different. They are protected against risk of large loss, since the most they can lose is the price of the option itself (P or C). • A call holder gets payoff ST – K or 0, and high σ makes high ST more likely • A put holder gets payoff K – ST or 0, and high σ makes low ST more likely 3) Therefore, both C and P (and c and p) should be higher for more volatile stocks. d) The risk free discount rate rf also affects option values, but changes in rf seldom occur ceteris paribus. e) Dividends. 1) Suppose you would pay $10 on Monday for a share that will pay dividend D = $2 on Tuesday, because you will get the $2. Would you still pay $10 on Wednesday? No, more like $8, since the previous stockholder got the $2. So anticipated dividends reduce stock prices on the ex dividend date (the day dividends are declared for distribution). Ec 174 OPTIONS II p. 3 of 18 2) Call holders get payoff St – K or 0, and dividends reduce St, so Ct should fall with an increase in D (true for both American and European style options). 3) Put holders get payoff K – St or 0, and dividends reduce St, so Pt should rise wi...
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 Winter '08
 Foster,C

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