Barone-Adesi and Whaley Model

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Definition: Barone-Adesi and Whaley Model

Also known as the quadratic approximation model, it is the American Version of Black- Scholes- Merton Model. The Black- Scholes model gives an estimation of European options. It is mainly utilized by the people who engage in options- trading. This model was first issued as the ‘Efficient Analytic Approximation of American Option Values’ by Giovanni Barone- Adesi and Robert E. Whaley. This model gives a simple approximation for price- exchanged American call and put options applied on commodities and futures based on commodities.


The assumptions of this model are as follows:

1. Short- term interest rate, r, and cost of carrying the commodity, b, are assumed constant and proportional rates

2. For non- dividend stock, cost of carrying equal to riskless rate i.e. b=r. According to Merton’s model, b<r for dividend- yield options


As b is assumed constant, the relation between futures and commodity prices is,

F= SebT


Where F, S= Current Futures and Spot prices respectively

T= Time of expiry of futures contract


According to Merton’s Model, the partial differential equation which explains the commodity option pricing discussion is

 

Where V determines the price of contingent claim.


To obtain the solution of this equation, the Barone Adesi and Whaley (BAW) Model divides the American price into two parts: The European Price and the early exercise premium (feature present only in an American option)


Where Ɛc is the early exercise premium

C(S, T) = American Commodity option value and

C(S, T)= European Commodity option value

This equation will have to satisfy the partial differential equation


Here, C(S, T) is given by:

 

The critical value of S* is obtained by solving the Newton’s algorithm of finding the root

By finding the value of C(S, T) and c(S, T), the partial differential equation can be solved and the American option- price can be determined


Advantages of this model:

1. Accurate

2. Computationally efficient

3. Less Expensive than binomial or compound option pricing models

 

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