chp9optionpricingwhenunderlyingstockreturnsar(編輯修改稿)
2025-02-27 20:32 本頁面
【文章內(nèi)容簡介】 rmation。 – Jump partimportant new information, usually firm (or even industry) specific such as discovery of an important new oil or the loss of a court suit, “nonsystematic” risk. ? 跳躍部分屬于非系統(tǒng)風(fēng)險(xiǎn)，不產(chǎn)生風(fēng)險(xiǎn)溢價(jià)，根據(jù) CAPM *p r? ?wwrr ?????? ?? ? ? ? ? ?? ?221 ,2 SS SS F r k SF F rF F SY F S?? ? ? ? ? ?? ? ? ? ? ?? Even though the jumps represent “pure” nonsystematic risk, the jump ponent does affect the equilibrium option price. That is, one cannot “act as if” the jump ponent was not there and pute the correct option price (nonsystematic risk has s none zero price?) ? Define W to be the BS option pricing formula for the nojump case. ? ? ? ? ? ? ? ?? ?? ?21221 / 2, 。 , , e xp1e xp22yW S E r S d E r dsy ds? ? ?? ??? ? ? ? ???? ? ??????? Define Xn the random variable to have the same distribution as the product of n . (identically distributed to Y) random variables ? ? ? ? ? ? ? ?? ?20e xp, e xp , 。 , ,!nnnnF S W SX k E rn? ? ? ?? ? ? ? ? ???? ???????? There is not a closedform solution, but it does admit to reasonable putational approximation ? There are two special cases where can be vastly simplified. ? Example 1: There is a positive probability of immediate ruin, . if the Poisson event occurs, then the stock price goes to 0. that is Y=0 with probability one. ? ? ? ? ? ?22, e xp e xp , 。 , , , 。 , ,F S W S E r W S E r? ? ? ? ? ? ? ? ? ?? ? ? ?? ? ? ?? ? ? ?? inedntical with the standard BS solution but with a larger “interest rate,”. As was shown in Merton (1973a, ), the option price is an increasing function of the interest rate, and therefore an option on a stock that has a positive probability of plete ruin is more valuable than an option on a stock that dose not. ? Example 2: Y has a lognormal distribution ? Define ? then ? ? ? ?2, , 。 , ,n n nf S W S E v r???? ? ? ? ? ?0e xp, ( , )!nnnF S f Sn? ? ? ??????? ?? Clearly, is the value of the optio
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