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bsgreeks

Compute the Greeks for both a call and a put option in a Black and Scholes model. "Delta" is the derivative of the option price with respect to the price of the underlying asset. "Gamma" is the second derivative of the option price with respect to the price of the underlying asset. "Theta" is the derivative of the option price with respect to the time to maturity. "Rho" is the derivative of the option price with respect to the riskless interest rate. "Vega" is the derivative of the option price with respect to the volatility of the underlying (log-) return.

SYNOPSIS

[delta,gamma,theta,rho,vega]=bsgreeks(S,K,r,T,sigma);

Description

Function which computes the Greeks of both call and put option in a Black and Scholes framework

Parameters

S

current price of the underlying asset

K

strike price of the option

r
riskless interest rate (assumed to be constant until the maturity)
T
time to maturity; it must be in the same time unit of measure as the riskless interest rate (if the riskless interest rate is annual, then an option with maturity of 3 months must have T=3/12)
sigma
volatility of the underlying (log-) returns; it must be in the same time unit of measure as the riskless interest rate

Output

Delta

vector containing the first derivative of the call (first term) and put (second term) option prices with respect to the underlying asset price

Gamma
second derivative of the call (or put) option price with respect to the underlying asset price
Theta
vector containing the first derivative of the call (first term) and put (second term) option prices with respect to the time to maturity
Rho
vector containing the first derivative of the call (first term) and put (second term) option prices with respect to the riskless interest rate
Vega
first derivative of the call (or put) option price with respect to the standard deviation of the underlying (log-) returns

Example

We compute the Greeks on both a call and put option with: underlying price 25 euros, strike price 25 euros, 0.001 (annual) riskless interest rate, 3 month time to maturity (i.e. T=3/12), and 0.2 (annual) volatility.

-->[D,G,Th,R,V]=bsgreeks(25,25,0.01,3/12,0.2)

V = 4.9727729

R = 3.0550246

- 3.1793699

Th = 2.1113101

1.8619344

G = 4.9727729

D = 0.5298926

- 0.4701074

Authors

Francesco Menoncin - Brescia University - 2010

See Also


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