Questions tagged [binomial-tree]

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Difference between closed form binomial option value and monte carlo simulation

I am trying to calculate the price of a European call option using both the the closed form expression and a monte carlo simulation. But the value's I get from both these methods are not the same: ...
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Interest Rate Volatility for Binomial Trees

Does anybody know where I can get the data or calculate interest rate volatility for modelling callable and putable bonds in binomial trees. I have swap curves data. Does any sources like Bloomberg ...
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2 votes
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Why does changing the step size in my Binomial Tree changes the final stock prices so much?

I am trying to price a convertible bond by using a binomial tree. For this, I wrote a binomial tree for the stock price. I noticed that changing the step size (timesteps), changes the final value of ...
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Pricing any Payoff structure using Binomial Tree(Pricing DDTPS)

I just wanted to confirm if its theoretically possible to value any derivative with a payoff that can be replicated by a portfolio of options,underlying and bonds. I wanted to value DDTPS which is a ...
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Equivalent martingale measure and derivative pricing [duplicate]

So I just recently saw in class that to price a derivative you use what is called an equivalent martingale measure which allows you to compute the price of the contract which then will be the expected ...
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Are risk neutral probabilities (for the arbitrage theorem) the same no matter what betting strategy is chosen?

I am learning the basics of risk neutral probability and arbitrage theorem. The arbitrage thm states that given a series of bets $r_{1}, ..., r_{n}$ either there is arbitrage, or there exists a ...
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Asset pricing using a two period binomial tree

Recall that in the binomial model the risk-neutral probability for the price going up is given by p = 1+r−d / u−d where u > 1 and d < 1 specify the possible price jumps in the risky asset and r ...
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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....
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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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2 answers
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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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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 = \...
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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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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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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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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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....
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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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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 $...
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2 votes
1 answer
305 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 ...
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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?...
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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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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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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_{...
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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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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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Calculating European call option, the Bjork way

We have a 3 period binomial tree with values: ...
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1 vote
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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 ...
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1 answer
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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 ...
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2 votes
1 answer
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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 ...
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2 votes
1 answer
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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 ...
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2 votes
1 answer
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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 ...
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2 answers
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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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2 votes
1 answer
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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 ...
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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 ...
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3 votes
1 answer
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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
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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 ...
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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}} \...
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2 votes
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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 ...
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3 votes
1 answer
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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?
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