The BaroneAdesi Whaley quadratic approximation is defined as follows: 
= Generalized Black Scholes call formula. = Generalized Black Scholes put formula.


c = call option value. p = put option value. S = spot price of the underlying asset. X = exercise price (strike). r = riskfree 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: This equation can be solved by using the NewtonRaphson Iteration Procedure. The slope of RHS* at S_{i} is: 

S** is the critical spot price for the put option that satisfies the following This equation can be solved by using the NewtonRaphson Iteration Procedure. The slope of RHS** at S_{j} is: 

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