ACT370H1 Lecture Notes - Complete Market, Partial Differential Equation, Log-Normal Distribution
Document Summary
The binomial distribution tends to a normal distribution as n-> . Because for large n, p(k|n) = (nck) pk qn-k is hard to compute. For binomial payoff = 1, 0 failure, 1 success n = number of trials p = prob of success q = prob of failure mean = np variance = npq. Suppose i have some returns r ~ n( , 2) Then er has a lognormal distribution er > 0 not symmetrical (even if r is) r ~ n( , 2) er ~ lognormal(exp[ + 2/2], exp[( 2/2-1)exp(2 + 2)]) Black-scholes partial differential equation model for option pricing ln( s. = dividend rate r = risk-free rate. N(d) = standard normal cdf at point d (area under the curve before d) European options return on s ~ n -> er ~ lognormal constant volatility over the period of interest future dividends known constant risk-free rate over period of interest no taxes or transaction costs complete market.
