Questions tagged [binomial-tree]
The binomial-tree tag has no usage guidance.
167
questions
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1answer
64 views
Noob Question - Monte Carlo vs BAPM European Option Pricing Discrepancy
It's winter break (happy new year!), and I'm trying implement a few options pricing models (bapm, tapm, monte carlo, Fast Fourier etc.) for practice.
The issue: My BAPM CRR model converges to 8....
0
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1answer
102 views
Optimize call option purchase
If it is predicted that the price of a stock will increase from P1 to between P2 and P3 in time T (assume the distribution of the price will be evenly distributed between the range of [P2, P3] at time ...
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2answers
162 views
Find the value of put option using a two-period binomial model
I've been asked to find the price of a two-month European Put Option with strike price $£40$.
The price at $S_0=£30$, this can move up to $£40$ or down to $£25$ ($1/3$ chance to go up, $2/3$ chance to ...
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0answers
33 views
How to find probabilities of moves in a trinomial tree?
I'm given a non-dividend stock with price $p$ and volatility $v$ and given a European Call option corresponding to this stock.
I want to calculate the probabilities of the following moves:
$M_U = \...
3
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0answers
119 views
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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30 views
N-period state price deflators
Given that the non-dividend paying share is at $5. In each 6 future 6 month period its value can either rise by 25% or fall by 10%. The continuously compounded risk free rate is 5% p.a.
Consider a ...
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0answers
48 views
Option pricing when stock price follows binomial tree
Assume that the stock price is currently trading at $S_0$. It is known that the stock price follows a binomial tree, such that its price will be either $S_0e^{\theta_u}$ or $S_0e^{−\theta_d}$ over the ...
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28 views
What is the number of nodes, which have to evaluated, in a binomial tree for an option on dividend-paying stock?
In John Hull's book "Options, futures and other derivatives" 10th Edition, Chapter 21, there are two examples, on how binomial trees on dividend-yield stock option look like.
The first ...
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0answers
101 views
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 ...
0
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0answers
49 views
Risk-Neutral Probability in a Binomial Tree
This question is probably very simple and I'm just missing the easy solution but I'm a bit confused so I thought I might as well try ask here.
I've been given this question:
When I tried to calculate ...
0
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0answers
27 views
Initial value of an investment project in a binomial real option valuation model
How do you measure the initial value of a project in a binomial tree ROV? I'm not specifically working in the valuation scene, but sort of had an interest in how the models work logically. It's not ...
2
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0answers
37 views
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 ...
0
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2answers
87 views
Prove the Euro call option value has positive relationship with the risk-free rate under discrete time model (Binomial tree model)
Could anyone show me how to prove that the European call option value has a positive relationship with the risk-free rate in a two-step binomial model with strike price K and different risk neutral ...
3
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1answer
145 views
Does CRR Model lose completeness if we add another instrument?
Consider the multiperiod binomial/CRR model with one risky asset $S^{1}$ and a numeraire $S^{0}$. By seeing that the equivalent martingale measure is uniquely determined, we obtain that the market is ...
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1answer
126 views
What's the price of a lookback call option in the arbitrage-free CRR-model?
If we consider the CRR-model in two periods, i.e. T=2. Let $S^1$ be the risky asset with $S_0^1=100$ and $S^0$ the bond with $S_0^0=1$. Furthermore, we assume the model is arbitrage-free with $y_b=-0....
1
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1answer
75 views
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 ...
4
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1answer
122 views
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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0answers
124 views
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 ...
1
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1answer
477 views
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 ...
1
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2answers
200 views
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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0answers
95 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 ...
0
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1answer
62 views
Maximal increase payoff
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 $...
2
votes
1answer
173 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 ...
0
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1answer
235 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?...
0
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1answer
53 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 ...
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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 ...
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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_{...
0
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1answer
66 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 ...
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1answer
66 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 ...
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1answer
107 views
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104 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 ...
0
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1answer
105 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 ...
2
votes
1answer
173 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 ...
2
votes
1answer
108 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 ...
2
votes
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 ...
1
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2answers
131 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 ...
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1answer
120 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 ...
1
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1answer
100 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 ...
3
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1answer
106 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
0
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1answer
250 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 ...
0
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1answer
83 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}} \...
2
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0answers
92 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 ...
3
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1answer
91 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?
0
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1answer
783 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 ...
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0answers
101 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 ...
0
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1answer
559 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 ...
2
votes
1answer
203 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 $K$ ...
0
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1answer
540 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 ...
0
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1answer
589 views
Should U and D change with the number of steps in a Binomial Tree?
In everyone's binomial trees online I see constant U and D. Even when I read Option Volatility and Pricing by Natenburg, all his diagrams use a constant U and D (where U is the upwards magnitude from ...
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0answers
62 views
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
$$
S_t= 120 \, \text{with probability}\, 0.5
$$
$$
S_t= 60\, \text{with probability}\, 0.5
$$...
