# Questions tagged [binomial-tree]

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### Geometric Brownian Motion as the limit of a Binomial Tree?

Consider the price of a stock whose drift and volatility parameters are $\mu, \sigma$ respectively, over the time interval $[0, t]$. Suppose we use an $n$-stage binomial tree to model the price ...
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### Up and Down Multiplicative Factors of the Binomial Option Pricing Model

When computing these factors, according to some sources, $u=e^{r\Delta t+\sigma \sqrt{\Delta t}}$, where $r$ is the risk-free interest rate, $T$ is the time for maturity, and $\sigma$ is the ...
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### Obtain B-S-M from a binomial tree as n goes to infinty using Lebesgue integral

My question is simple, consider a European call with payoff max(S_T-K, 0), Let's suppose that the underlying stock follows a binomial tree with up and down factors I know as we take n goes to infinity ...
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### Mark Joshi, The concepts and practice of mathematical finance exercise 3.6

This is an exercise from Mark Joshi's book (exercise 3.6): "A stock is worth 100. Each month its value increases or decreases by precisely 10. The riskless bond is worth $e^{r t}$ at time $t$ ...
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### Two-period binomial model probability question

I have started to work with given two period binomial model S(0)=100 u=1.25 d=0.8 r=0.05 and the market probability of stock going up each period is p=0.55. I am trying to calculate two probabilities; ...
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### Convergence in the CRR model

Under certain conditions, the option price of the CRR (Cox-Ross-Rubinstein) Binomial model converges to the Black-Scholes price as the maximal step size of the partition converges to zero (i.e. a ...
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### Why do we simply assume the risk neutral probabilities to be "0.5"?

I am aware that there was a question similar to this but my question is a little different. Firstly, in context of binomial short rate, why do we simply assume the risk neutral probabilities p=1-p=0.5?...
366 views

### 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 ...
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### How to fit (find $u$) in the binomial options pricing model?

In the binomial tree options pricing literature, I see frequent reference to the definition that $$u = e^{\sigma \sqrt{n/t}}$$ I think I understand the model, but how do we derive this, i.e. how do ...
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### Binomial tree convergence tree towards BS equation - Struggle with a limit

I am trying to prove that the Binomial tree pricing method converges towards the Black and Scholes model, but I am struggling on a specific step. I don't understand how the limit of p*(1-p) is ...
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### One Period Risk Neutral Probability for Caplet

I am studying some financial modeling put together by the Society of Actuaries in the USA. In it, the following practice problem was given: Find the Risk Neutral price of an at-the-money interest ...
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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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1 vote
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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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### Calculating European call option, the Bjork way

We have a 3 period binomial tree with values: ...
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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### 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 ...
419 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 ...
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