## Cox-Ross-Rubinstein Method

The Cox-Ross-Rubinstein binomial option pricing model (CRR model) is a variation of the original Black-Scholes option pricing model. It was first proposed in 1979 by financial economists/engineers John Carrington Cox, Stephen Ross and Mark Edward Rubinstein. The model is popular because it considers the underlying instrument over a period of time, instead of just at one point in time. It does this by using a lattice-based model, which takes into account expected changes in various parameters over an option's life, thereby producing a more accurate estimate of option prices than created by models that consider only one point in time. Because of this, the CRR model is especially useful for analyzing American style options, which can be exercised at any time up to expiration (European style options can only be exercised upon expiration). And, unlike the original Black-Scholes option pricing model, the CRR model has the ability to take into account the effect of dividends paid out by a stock during the life of an option.

Click the below url to check the algorithms.

### Note: Calculate cox without dividend.

If dividend per share value = 0.0 then apply the following changes in equation

Example:

Values = matrix(0,0)

1) Dd = (D*exp(-rf*td)) #discounted dividend from Ex date assume Ex and pay date is same#
where D = 0.0

2) Sd = (S-Dd) #Stock adjusted for present value of dividends#
where Dd = 0.0 and calculate Sd = (S-Dd) = S

3) Xd1 = (X-D) #Strike adjusted after dividend paid#
where on D = 0.0 and Xd1 = (X-D0) = X

### For algorithms guide click the below links

COX WITH DIVIDEND ALGORITHM GUIDE
COX WITHOUT DIVIDEND ALGORITHM GUIDE
 Variables K(29.00) = strike price Spot(30.00) = spot price T(40) = Time in year (days/365) D(2.50) = Dividend per share v(30.0) = volatility in % r(5.00) = risk-free interest rate in % td(25) = Time to Dividend Payment n(6) = steps PutCall(P) = P for put and C for call OpStyle(E) = E for European option and A American option

 Strike price ($): Underlying asset price ($): Days to expiration (In Day): Dividend (%): Enter an amount (\$.cc) for discrete dividend, or an annual yield (eg 3.5 = 3.5% pa) Volatility (%): Interest rate (%): Days to ex-dividend: Enter days for discrete dividend; leave blank or zero for yield No. Tree Steps (1- 150): (max. 15 displayed) Option type : Call Put Exercise style: American European

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