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oRGW( ) Model Definition

The Roll (1977), Geske (1979) & Whaley (1981) option pricing model is defined as follows:

Equation Template

 

Equation Template

Equation Template

 

C = call option value.

S = spot price of the underlying asset.

X = exercise price (strike).

D = single discrete dividend.

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

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

t = time to dividend payment measured in years (actual/365 basis).

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

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

Equation Template = cumulative bivariate normal distribution function with upper integral limits a and b, and correlation coefficient Equation Template.

I = critical ex-dividend stock price that equates the following: Equation Template

c(.) = value of European call with stock price I and time to maturity T.

 

Note that if Equation Template or Equation Template, it will not be optimal to exercise the option before maturity hence the price of the American call can be found by using the oBSdd( ) function.

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