# Questions tagged [binomial-tree]

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### Delta-hedge experiment of American Put option

I am trying to run a delta-hedge experiment for an American Put option but there's a (systematic) hedge error which I cannot seem to understand or fix. My implementation is found in the bottom of this ...
• 548
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### Why Vasicek model on a tree is a bad choice for pricing American option on credit prepayment?

I have an American option on a credit prepayment, i.e. the holder of the option can prepay the remaining credit if the interest rate falls below the initial strike. The pricing of this option was done ...
• 814
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### binomial trees and finite differences

I was reading Tavella Randall book and their explanation why binomial trees are a particular example of finite differences. I started having additional questions. So, they way they do that is saying ...
• 493
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### Cash less exercise and redemption feature in SPAC warrants

Public and private warrants of a SPAC post merger (Initial Business Combination or IBC) are often very similar. Notable differences are 1) cashless exercise of the private warrants and 2) redemption ...
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### Is there a more efficient data structure to implement binomial trees than 2d array?

I'm just curious what is the "industry standard" for implementing a binomial tree (if "standards" exist in this case). For simplicity, let's just talk about the simplest trees with recombining nodes. ...
• 903
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### Binomial Option Pricing Model gives increasingly higher value for out-of-the-money options

I was developing the binomial option pricing model via Python, according to the explanation given on Wikipedia. After computing the errors against the pricing of real options, I find an interesting ...
• 21
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### Futures vs Forward pricing with different interest rates using binomial model

I'm given the aforementioned parameters for a two-step binomial model where the underlying pays no dividend, $S_0=50$ and $T=2$. With this information I was able to calculate the risk-neutral ...
• 35
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### Binomial Model Implementation Trouble - American and European options come out equal

I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options ...
108 views

### Interest model calibration and binomial trees

Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
145 views

### Second order convergence for the Leisen-Reimer tree

I have a question about this paper "Achieving higher order convergence for the prices of European options in binomial trees" by Mark Joshi, (Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
155 views

### Efficient construction of binomial tree

The goal is to build a $n$ step binomial tree knowing the end nodal probabibilities $p_1, \dots, p_m$, which correspond to the time $T$ states $S_1, \dots, S_m$. We assume that all paths ending in the ...
• 624
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### How to simulate a Geometric Binomial Process with state/tie dependent increments?

I want to simulate a geometric binomial process with state/time dependent increments. So the model is given by \begin{align}R_t=\frac{X_t}{X_{t-1}}\end{align} \begin{align}P(R_t=u)=p(X_{t-1},t) \...
1 vote
73 views

### Optimal exercise time in Binomial model

Let (B, S) a multi period binomial model that is arbitrage free. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove ...
1 vote
78 views

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1 vote
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### Risk neutral probabilities in binomial option pricing with discrete dividends — whose argument is correct?

In trying to discover more about pricing American options with dividend payouts, I found the the post linked here. I notice two disagreeing answers when it comes to determining the replicating ...
• 609
1 vote
350 views

### Practical implementation of Vellekoop-Nieuwenhuis model/interpolation

Have read the 2006 VELLEKOOP-NIEUWENHUIS paper (Efficient Pricing of Derivatives on Assets with Discrete Dividends) (Download) many times re Discrete dividends on American Options, but remain baffled ...
• 11
1 vote
258 views

### Expected life (Fugit) of American Option

How can I use the binomial tree pricing method for American options to determine the expected time of exercise for the option (or "Fugit")? In particular, how would I modify the algirithm ...
1 vote
175 views

### Replication Portfolios and Binomial Option Pricing

To price a call/put option with two possible future states of the world, I understand we can price the option by essentially calculating the price of a replicating portfolio that gives the same ...
• 151
1 vote
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### One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$S_t= 120 \, \text{with probability}\, 0.5$$ $$S_t= 60\, \text{with probability}\, 0.5$$...
1 vote
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### Binomial Model - completeness in presence of arbitrage

Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is $$V_0 = B_0 + hS_0,$$ ...
• 111
1 vote
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### How does LR binomial Tree Model handle input values which would cause NA result?

I am using C++ to implement a LR binomial Tree algorithm to price American options, but I find it would constantly generate invalid output, which is "nan" value in C++, although the input value seems ...
1 vote
156 views

### Binomial Option Pricing - Hedging

I'm working on a project which is requiring me to test Binomial option pricing on real data. So far I have just been working with test data and my option pricing method works fine. The issue I'm ...
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1 vote
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### Building implied binomial tree with American input options

i want to build an implied volatility binomial tree with American input options, so the setup is the following: 1) We know the market Price P of the American Put $P_{am}(t_i,K)$, where $t_i$ is the ...
• 177
1 vote
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### Quantlib binomial tree

I was trying to price options with the extendedBinomialTree class of quantlib. I actually tried at some point to modify this class in order to optimize it. Normally the drift and diffusion of the ...
1 vote
256 views

### negative transition probability in trinomial trees

I was pricing a option with big dividend in the underlying. However, I got negative transition probability in a trinomial tree. Will it cause arbitrage? Does anyone have reference paper or book ...
1 vote
79 views