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(a)Suppose that it is now ???? = 0 and ???? > 0 is some later time. Carefully show that the probability in a risk-neutral world satisfies the equation, ????(???????? > ????) = ????(????2). Here, ?????
(a)Suppose that it is now ???? = 0 and ???? > 0 is some later time. Carefully show that the
probability in a risk-neutral world satisfies the equation, ????(???????? > ????) = ????(????2). Here, ???????? is a
stock’s price at time ????, ????(????) is the cumulative distribution of a standard normal random
variable, and ????2 = (ln(s0/k ) (????− ????^2/2 )???? )/ (????√???? )
(b) Consider a European call with expiration date ????, underlying stock price ????(????), volatility ????, risk-free rate ????, and strike price ????. If ????(????0, 0) is its price at time ???? = 0, then compute
lim????(????0,0). σ→0
