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Level 124

Black Scholes Pricing Model

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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
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
increase in the risk free return _______ the call price