## Trinomial Barrier Option calculator

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.

Algorithms and guide.

### Abstract

A trinomial Markov tree model is studied for pricing options in which the dynamics of the stock price are modeled by the first-order Markov process. Firstly, we construct a trinomial Markov tree with recombining nodes. Secondly, we give an algorithm for estimating the risk-neutral probability and provide the condition for the existence of a validation risk-neutral probability. Thirdly, we propose a method for estimating the volatilities.

Lastly, we analyze the convergence and sensitivity of the pricing method implementing trinomial Markov tree. The result shows that, compared to binomial Markov tree, the proposed model is a natural combining tree and, while changing the probability of the node, it is still combining, so the computation is very fast and very easy to be implemented.

### Trinomial Barrier Option guide

 Variables X(29.00) = strike price S(30.00) = spot price H(120) = Barrier R(0.00 ) = Rebate 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 Barrier Type = up & out ,down & out , up & in ,down & in

 Strike price ($): Underlying asset price ($): Barrier ($): Days to expiration (In Day): Dividend (%): Enter an amount ($.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 Knockout rebate No. Tree Steps (1- 150): (max. 15 displayed) Barrier Type: Up&Out Down&Out Up&In Down&In Option type : Call Put Exercise style: American European

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