# Questions tagged [binomial-tree]

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### Calculate the size of the up move from volatility for Binomial model [closed]

I'm given a European Put option, current and exercise prices, $p$ and $P$ and stock volatility $q$. What is the way of finding the size of the up move from the problem?
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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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### Binomial Pricing Model d and u

In the binomial pricing model, why do the magnitude of the up factor $(u)$ and down factor $(d)$ have to be multiplicative inverses? I have read from multiple sources that the reason for this is that ...
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### Binomial Option pricing, paper by John C. Cox, I don't understand the calculation / choice of u.d.q

[EDIT] Question is answered, just cleaned up some clerical errors in the formulas. [EDIT] Based on the comment I got, let me clarify, I am not stuck on the relationship between the binomial model vs ...
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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 ...
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### How to price an European put option using binomial model with dividend yield?

The initial stock price (S0) is 45, the stock volatility is 0.20 (20% per annum), and the risk-free rate is 0.02 (2% per annum). Consider a European put option whose strike price is equal to 30, with ...
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### Delta hedging for an American call option on a stock with a continuous dividend yield

Let the dividend yield be $\delta$ and $C_u, C_d$ and $S_u, S_d$ be the up and down values for the stock and the call respectively over the period $\Delta t$. In Hull and all other resources I've ...
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### 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 ...
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I am interested in the following problem. We have a Multi-Step Binomial Model with discrete time $T=1,\dots,n$. We also assume that the stock $S_t$ is a martingale and there is a risk-free bond with $... 1answer 128 views ### Risk neutral probability for stock with continuous dividend Setting: binomial tree with one step over time$\Delta t$. I'm trying to derive the risk neutral probability for a stock which pays a continuous dividend, say$\delta$. i.e. probability$p$such that ... 1answer 200 views ### How to price barrier options (binomial tree) What is the easiest way to price single barrier options using binomial tree? I found This method. Is this method good or maybe should I use another one? Does this price converge to price from BS model?... 1answer 49 views ### Replication (binomial tree) Hey what is the replication strategy on the binomial tree when I have for example 10 step model and dividend is paid at step 3? I have a well-written price tree but I do not know what the replication ... 0answers 26 views ### Reproducing a short put position using known binomial option tree Suppose a put option follows prices according the the binomial tree I've made and posted below and consider writing a put ($S$is the stock value,$P$is the put value, obviously). I want to find the ... 0answers 25 views ### Backward differential equation with binomial tree I'm trying to understand/solve the following question but I honestly don't know what it's even asking about. I've included my attempt following the picture of the question. I would approximate the ... 0answers 34 views ### Binomial Model Strike Price Assumption Let us have the standard single-period binomial pricing model, and denote the up and down states of the underlying by$S_u$,$S_d$respectively. Let us say we have a call option on the underlying with ... 0answers 76 views ### How to prove that a series of random variables$Z_j = 1$or$-1$occurring at risk-neutral probability, converges to normal, using the CLT? Context When pricing options with trees, it is convenient to prove that the asset value at expiry$S_t$be of log-normal distribution: $$\log{S_t} = \log{S_0} + \mu T + \sigma \sqrt{\frac{T}{n}} \sum_{... 1answer 55 views ### Log-normal risk-neutral price derivation from binomial trees, not clear about step in derivation process At page 64 of the book Concepts and practice of mathematical finance, 2nd edition by M. Joshi, paragraph 3.7.2 (Trees and option pricing - A log-normal model - The risk-neutral world behaviour) a ... 1answer 60 views ### How does 1 + R = q_u · u + q_d · d follow from d ≤ (1 + R) ≤u in the Binomial Pricing Model? I've been reading Tomas Bjork's 'Arbitrage theory' and it says: To say that d ≤ (1 + R) ≤u holds is equivalent to saying that 1 + R is a convex combination of u and d, i.e. 1 + R = q_u · u + q_d ... 1answer 103 views ### Calculating European call option, the Bjork way We have a 3 period binomial tree with values: ... 0answers 91 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 ... 1answer 93 views ### Volatility input for American options I have to price an american option on a daily basis and I have some questions regarding the CRR binomial tree model: Is it correct to use implied volatility as an input? Or is it better to use ... 1answer 151 views ### Martingale Binomial Tree Process 3 step binomial tree process with S_0=4,u=2,d=0.5,r=0.25. Determine the probability p and q such that the stock price process is a martingale (i.e. E[S3]=S_0) I know P = 1/3 and Q = 2/3 but having ... 1answer 99 views ### Breakdown of Wilmott's Binomial Tree derivation of Black-Scholes equation Hi guys, I tried to follow the chapter of PWIQF on binomial model and got stuck when it derived the Black-Scholes (please see image). I tried to backtrack the said equations but couldn't trace back ... 1answer 106 views ### help with derivation of equation 8 in Derman and Kani's binomial tree for local vol in this paper "The Volatility Smile and Its Implied Tree" - Derman and Kani 1994 i understand the derivation of all equations up to 7. But eq 8 i cannot figure out how to derive! i have ... 2answers 122 views ### Failing to replicate Wilmott's results for binomial option pricing I am working through Paul Wilmott introduces Quantitative Finance, 2nd ed. I am failing to reproduce one of his numerical examples and I would like to understand why. I chapter 3, Wilmott introduces ... 1answer 104 views ### Black & Scholes formula derivation from a Binomial Tree - John C. Hull I am reading "Option, Futures and other Derivatives" by John C. Hull, and on Appendix chapter 13, he derives BSM formula from a Binomial Tree. When he builds U2, I just don't understood how to get ... 1answer 98 views ### Arbitrage strategy using binomial tree Suppose that we have a one step binomial tree model for a company. Lets say that the time per step is T, and that price of the stock can go up to p_1 or go down to p_2. Suppose a T-month European ... 1answer 97 views ### Binomial tree with jumps I am struggling with developing a binomial tree with jumps. although there are models such as CRR, could you suggest a book or have any idea to proceed? Thanks, Amir 1answer 216 views ### QuantLib convertible bond pricing generates strange delta I am trying to generate equity delta for convertible bond using QuantLib(version 1.14) functions, but the deltas generated either using a repricing approach or by directly obtaining from the tree(code ... 1answer 80 views ### Reference of using \mu = \frac{1}{T}(\log K - \log S_0) in binomial tree model Notations: Given a binomial tree with N periods and time to maturity T, let \Delta t = T / N. It is well-known that CRR uses the up and down multipliers as$$u = e^{\sigma\sqrt{\Delta t}} \... 0answers 84 views ### 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 ... 1answer 84 views ### What are the relation between the risk neutral measures in binomial tree and in Black Scholes model? I appreciate that both are the direct result of constricting a replicate portfolio using stock and bonds. Are there deeper relationship between the two? 1answer 655 views ### Trinomial Trees for Hull-White model I am studying trinomial trees and trying to implement them in Python to compare them to the monte carlo simulation. I searched 3-4 hours in the web; but can't find any implementation on binomial or ... 0answers 93 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 ... 1answer 443 views ### How to get all the paths of a binomial tree I'm trying to implement a pricing method for exotic options based on binomial tree's. The problem i'm having is that i'm not being able to generate all the paths of the tree. I have the following code ... 1answer 180 views ### What is the probability of a lookback option ending in the money (CRR-model) I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff$h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\} $where$K$... 1answer 469 views ### Stock pricing using Binomial model A stock is prices at$ \$100$ and follows a one-period binomial process with an up move that equals 1.05 and a down move that equals 0.97. If one million Bernoulli trials are performed and the average ...
I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$S_t= 120 \, \text{with probability}\, 0.5$$ $$S_t= 60\, \text{with probability}\, 0.5$$...