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.^{[1]} For fixed income and interest rate derivatives see Lattice model (finance) #Interest rate derivatives.
YouTube Encyclopedic

1/5Views:21 42037 9914196 0601 798

✪ BINARY OPTIONS SIGNALS: BINARY OPTIONS STRATEGY  BINARY OPTIONS TUTORIAL (TRADING BINARY OPTIONS)

✪ 21. Stochastic Differential Equations

✪ The Trinomial Distribution

✪ American Put (Three) 3 Step  Binomial Method  European Price  EXAMPLE

✪ Pricing American PUT (CRR,JRRN,TIAN) in C#  XLW  Debug Excel
Transcription
Contents
Formula
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.^{[2]} These values are found by multiplying the value at the current node by the appropriate factor , or where
 (the structure is recombining)
and the corresponding probabilities are:
 .
In the above formulae: is the length of time per step in the tree and is simply time to maturity divided by the number of time steps; is the riskfree interest rate over this maturity; is the corresponding volatility of the underlying; is its corresponding dividend yield.^{[3]}
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^{[4]} (and with increasing accuracy for smaller timesteps). Note that for , , and to be in the interval the following condition on has to be satisfied .
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  see, for example Trinomial Tree Option Calculator (Peter Hoadley).
If the length of timesteps is taken as an exponentially distributed random variable and interpreted as the waiting time between two movements of the stock price then the resulting stochastic process is a birthdeath process. The resulting model is soluble and there exist analytic pricing and hedging formulae for various options.
Application
The trinomial model is considered^{[5]} to produce more accurate results than the binomial model when fewer time steps are modelled, and is therefore used when computational speed or resources may be an issue. For vanilla options, as the number of steps increases, the results rapidly converge, and the binomial model is then preferred due to its simpler implementation. For exotic options the trinomial model (or adaptations) is sometimes more stable and accurate, regardless of stepsize.
See also
 Binomial options pricing model
 Valuation of options
 Option: Model implementation
 KornKreerLenssen Model
 Implied trinomial tree
References
 ^ Mark Rubinstein
 ^ Trinomial Tree, geometric Brownian motion Archived 20110721 at the Wayback Machine
 ^ John Hull presents alternative formulae; see: Hull, John C. (2002). Options, Futures and Other Derivatives (5th ed.). Prentice Hall. ISBN 9780130090560..
 ^ Pricing Options Using Trinomial Trees
 ^ OnLine Options Pricing & Probability Calculators
External links
 Phelim Boyle, 1986. "Option Valuation Using a ThreeJump Process", International Options Journal 3, 712.
 Rubinstein, M. (2000). "On the Relation Between Binomial and Trinomial Option Pricing Models". Journal of Derivatives. 8 (2): 47–50. CiteSeerX 10.1.1.43.5394. doi:10.3905/jod.2000.319149. Archived from the original on June 22, 2007.
 Paul Clifford et. al 2010. Pricing Options Using Trinomial Trees, University of Warwick
 Tero Haahtela, 2010. "Recombining Trinomial Tree for Real Option Valuation with Changing Volatility", Aalto University, Working Paper Series.
 Ralf Korn, Markus Kreer and Mark Lenssen, 1998. "Pricing of european options when the underlying stock price follows a linear birthdeath process", Stochastic Models Vol. 14(3), pp 647 – 662
 Tariq Scherer, 2010. "Create Trinomial Option Pricing Trees Using Excel Applescripts"