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oBAW( ) Model Definition

The Barone-Adesi Whaley quadratic approximation is defined as follows:

Equation Template

 

Equation Template = Generalized Black Scholes call formula.

Equation Template = Generalized Black Scholes put formula.

 

Equation Template

 

c = call option value.

p = put option value.

S = spot price of the underlying asset.

X = exercise price (strike).

r = risk-free interest rate, expressed with continuous compounding.

b = cost of carry for the underlying asset, expressed with continuous compounding.

vol = volatility of the relative price change of the underlying asset.

T = time to maturity measured in years (actual/365 basis).

N(.) = cumulative normal distribution of (.).

 

S* is the critical spot price for the call option that satisfies the following:

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This equation can be solved by using the Newton-Raphson Iteration Procedure. The slope of RHS* at Si is:

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S** is the critical spot price for the put option that satisfies the following

Equation Template

This equation can be solved by using the Newton-Raphson Iteration Procedure. The slope of RHS** at Sj is:

Equation Template

 

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