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oGBS( ) Net Cost of Carry Definitions

The generalized Black Scholes option pricing model can be validly applied to options on stocks, futures, currencies, and commodities. The appropriate adjustment for options written on each of the underlying assets is incorporated via the net cost of carry parameter. Note that particular values for the net cost of carry parameter result in the generalized model reducing to other well known pricing models. The appropriate settings for each of the underlying assets are listed below:

 

Underlying Asset

Net Cost of Carry

Equivalent Model

.

Stock - no dividend

b = r

Black Scholes (1973)

Stock - continuous dividend yield

b = r - q

Merton (1973)

Futures

b = 0

Black (1976)

Currencies

b = r - rf

Garman Kohlhagen (1983)

Commodities

b = r - c

 

 

 

 

Where,

b = net cost of carry.

 

r = riskless interest rate.

 

rf = foreign riskless interest rate.

 

q = continuous dividend yield.

 

c = continuous net convenience yield (convenience yield less storage costs) of the underlying asset

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