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black-scholes-merton model

continuous time model where the passage of time occurs continuously

dynamic hedging

the process of adjusting hedge ratios to maintain a riskless portfolio

option is european

assumptions of BSM model (8)

log return

continuously compounded return

Stock

Capital raised by a corporation through the issue of shares entitling holders to an ownership interest (equity).

the absence of profitable arbitrage

the relationship between the call price and the stock price develops an option theory derived from

hedge ratio (one to two)

call price raises one dollar when the stock price raises two dollars

risk free portfolio

risk free because backed by the government

risk free

to rule out opportunity for profitable arbitrage means the rate of return on the portfolio must be

black scholes model

formula for the call price, assume stock price follows a random walk with a constant mean and variance of the rate of return

variables that affect the call price

stock price, time to expiration, striking price, variance of the rate of return, mean rate of return, risk free rate of return

what must satisfy it?

the partial derivative equation

how to solve the black scholes formula

work backwards from expiration to determine call price at earlier times

rises, increases, falls

from the no-arbitrage argument the call price _______ as the time to expiration _______ or as the striking price _______

call price rises

as the stock prices the _______ price _______

what option is this?

raises the call price, higher

in the money option and variance?

higher variance increases chance of big decline in stock price, the probability that the option won't be exercised increases

increases, high

higer variance _______ potential for _______ profit

higher, rises

higher mean gives a _______ chance of profitable arbitrage, so arbitrage _______

discounted at a higher rate

what does this effect do to profit

lowers

increase in the risk free return _______ the call price