3.0.Background - Options
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Define Call & Put Option
Call option
: gives the option buyer the right to
buy
an asset for a given price at some date.
Put option
: gives the option buyer the right to
sell
an asset for a fiven price at some date.
American vs European option
American
option can be exercised any time, while
european
can only be exercised on the expiration date.
Factors that affect the price of an option
Current stock price
Exercise price or strike price
Time to expiration
Volatility
Risk-free rate
Dividends
Put-Call parity
C + Ke
^{-rT}
= P + S
Black-Scholes formula
C = N(d
_{1}
) - N(d
_{2}
)Ke
^{-rT}
d
_{1}
= [ln(S/K) + (r + ½σ²)T] / σ√T
d
_{2}
= [ln(S/K) + (r - ½σ²)T] / σ√T
d
_{2}
= d
_{1}
- σ√T
Special case when
K = Se
^{-rT}
, C ≈ 0.4S σ√T
Ito's Lemma
Geometric Brownian Motion
:
dS = μSdt + σSdz
dG = [(δG/δS)μS + (δG/δt)μS + ½(δ
^{²}
G/δS²)σ²S²]dt + (δG/δS)σSdz
Card Set Information
Author:
Exam9
ID:
64851
Filename:
3.0.Background - Options
Updated:
2011-02-09 01:38:50
Tags:
Goldfarb
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