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Summary of Derivations and Applications of Greek Letters
What are “Greek Letters”?
Greek letters are a set of risk measurement that indicates how exposed an option is
to time-value decay(Theta), implied volatility(Vega) and changes in underlying
price of the commodity (delta and gamma), well Greek letters help us in
understanding the factors driving the price. Financial institutions manage their risk
by Greek letter analysis when selling shares to client.
Greek Letters can be Simplified as:
1) Delta: Direction (impact of change in price of underlying)
2) Gamma: Acceleration (rate of Change in delta)
3) Theta: Time (Impact of change in time remaining)
4) Vega: Volatility (Impact of change in volatility)
5) Rho: Interest Rate (impact of change in interest rates)
Delta: is the rate of change in an option’s price,
, resulting on the basis of
changing in underlying price asset (stock, indes, currency or commodity)
Formula:
S
=
,
where
is the option price and S is underlying asset price.
For European call option on a Non- dividend Stock can be shown as
1
N(d )=
or simply the value of D1 from the formula we saw in the Black Scholes
option pricing model.
For European call option on a Non- dividend Stock can be shown as
1
N(d ) 1 = −
For European call option where dividend is paid on underlying asset:
St = Current stock Price
X = Exercise Price
R = risk free rate
Q = dividend yield rate
Ϭ = Volatility
T = time.
Where,
2
ts
1
s
S
ln r q
X2
d
+ − +
=
2
