The trinomial tree is a lattice based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar.It can also be shown that the approach is equivalent to the explicit finite difference method for option pricing.
Formula and algorithm guide  
Under the trinomial method, the underlying stock price is modeled as a recombining tree, where, at each node the price has three possible paths: an up, down and stable or middle path.These values are found by multiplying the value at the current node by the appropriate factor u, d or m, where
$$ u = e^{\alpha \sqrt {2 \Delta t}} $$
$$ d = e^{ \alpha \sqrt {2 \Delta t}} = \frac 1u(the \space structure \space is \space recombining) $$
$$ m = 1 $$
and the corresponding probabilities are: $$P_u = \bigg ( \frac {e^ {(rq) \Delta t/2} e^{ \sigma \sqrt {\Delta t/2} } } {e^{\sigma \sqrt {\Delta t/2}} e^{ \sigma \sqrt {\Delta t/2} }} \bigg ) ^ 2 $$ $$P_d = \bigg ( \frac {e^ {\sigma \sqrt {\Delta t/2}} e^{{(rq) \Delta t/2} } } {e^{\sigma \sqrt {\Delta t/2}} e^{ \sigma \sqrt {\Delta t/2} }} \bigg ) ^ 2 $$ $$P_m = p{(P_u+P_d)} .$$In the above formulae: Δt is the length of time per step in the tree and is simply time to maturity divided by the number of time steps; r is the riskfree interest rate over this maturity; σ is the corresponding volatility of the underlying; q is its corresponding dividend yield. As with the binomial model, these factors and probabilities are specified so as to ensure that the price of the underlying evolves as a martingale, while the moments  considering node spacing and probabilities  are matched to those of the log normal distribution (and with increasing accuracy for smaller timesteps). Note that for Pu, Pd or Pm to be in the interval (0,1) the following condition on Δt has to be satisfied $$ \Delta t < 2 \frac {\sigma^2 }{(rq)^2} $$ Once the tree of prices has been calculated, the option price is found at each node largely as for the binomial model, by working backwards from the final nodes to today. The difference being that the option value at each nonfinal node is determined based on the three  as opposed to two  later nodes and their corresponding probabilities. The model is best understood visually 

For the Algorithm guide click here 
Variables 
K(29.00) = strike price 
S(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) = riskfree 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 exdividend: 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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