# Tag Info

### What's the logic behind binomial model ups and downs?

one of the most fundamental results states that the binomial model converges towards the Black Scholes model if the step size $\Delta t$ converges to zero. The Black Scholes model is an option ...
• 1,456
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### Geometric Brownian Motion as the limit of a Binomial Tree?

We can show that the moments of the Binomial tree agree with the moments of the continuous model for the case where we pick symmetrical probability value $p=0.5$. I will change the notation slightly (...
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### Approximation of CRR as Black Scholes PDE

Assuming continuously compounded returns for a multi-period model with $N$ being the number of periods: \begin{cases} &\log u \quad \text{with probability q}\\ &\log d \quad \text{with ...
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### Binomial Option Pricing Model

Note that the tree is recombining. You have $u=1.2$ and $d=0.8$ with $ud=0.96$. Your tree for the asset price reads as At time zero: 100 At time one: 80 or 120 At time two: 64 or 96 or 144 The ...
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### What are the relation between the risk neutral measures in binomial tree and in Black Scholes model?

There is a deeper relationship between the two risk-neutral measures. Take any event in the binomial model with a finite number of steps and calculate the risk-neutral probability of it. Take the ...
• 126
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### Does CRR Model lose completeness if we add another instrument?

I answer from a general discrete time/discrete state model point of view. This includes the binomial tree model as a special case. In finite dimensions, you can interpret asset payoffs and returns as ...
• 16.1k
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### Difference in formulas for u & d in Binomial trees

there are many different trees. The first one, the CRR tree, used $$u = e^{\sigma\sqrt{h}}$$ and $d = 1/u.$ However, you can take any real-world drift and still get the same prices in the limit so ...
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### Why does changing the step size in my Binomial Tree changes the final stock prices so much?

You only got one minor bug, but let me explain why the range increases. Let us denote $n:=timesteps$, then You are looping one iteration too little when filling your $S$ matrix array, causing you to ...
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### What discount rate to use when valuing binomial option with real probabilities

The Pricing equations are derived from duplicating portfolios consisting of underlying and a risk free asset. This means that the price of your option is relative only to the price of the underlying. ...
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### Explanation on the application of CLT in bionomial tree model

Thanks to P.Windridge's comment, I can now answer my own question. Indeed the convergence to standard normal in question can follow from a triangular array version of CLT called the Lindeberg-Feller ...
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### Demonstration of Ito's correction term/lemma in binomial tree

Actually it is quite simple to demonstrate Ito's correction term in a binomial tree. Details can be found in my new paper (p. 8-10): von Jouanne-Diedrich, Holger: Ito, Stratonovich and Friends (April ...
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### Trinomial tree VBA code

Joe, I wrote this a while ago and it could be cleaned up a little. It is for European Calls and Puts. I have a couple of lines commented out. I was probably going to add American pricing in but ...
• 4,348
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### Is American option price lower than European option price?

You compare the result of an analytical solution (european call) with the numerical solution for the american option. It seems as if you use to few steps to calculate your American option price. Just ...
• 278
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### What happens in the binomial model if the real-world probability is $0$

If I understand your question correctly, another way to word it is: if an event that has probability 0 under the physical measure $\mathbb{P}$, how can it have a positive probability under the risk-...
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### Binomial model arbitrage

In theory, we do not suppose there are transaction costs (or costs for short selling or even buying a security). In practice, effectively, you will have to pay the people that lend you the security ...

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### Replication (binomial tree)

When the dividend is paid, the stock price on your tree should drop by the same amount. Ie if the dividend is 10 and the value of stock is 100 before the dividend at a node, you should change it to 90 ...
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Here's one algebraic way to derive it:  \frac{(1 - e^{-\sigma\sqrt{h}})(1 + e^{\sigma\sqrt{h}})}{(e^{\sigma\sqrt{h}} - e^{-\sigma\sqrt{h}})(1 + e^{\sigma\sqrt{h}})} = \frac{1 - e^{-\sigma\sqrt{h}} + ...