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6 votes

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 ...
Cettt's user avatar
  • 1,456
6 votes
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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 (...
Jan Stuller's user avatar
  • 6,213
5 votes

Black Derman Toy model: from tree to differential equation

From the gentleman and scholar Emanuel Derman. Emanuel states "the last two pages answer the question asked". https://www.dropbox.com/s/cg299qsbquuqdru/TwitterNotesOnBDT.2017.pdf?dl=0&m= Please ...
Paul Portesi's user avatar
5 votes
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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 ...
FunnyBuzer's user avatar
  • 1,012
5 votes

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 ...
Kevin's user avatar
  • 16.1k
5 votes

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 ...
Peter Carr's user avatar
5 votes
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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 ...
Kevin's user avatar
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4 votes
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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 ...
Mark Joshi's user avatar
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4 votes
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Put-Call Parity on Currency and Binomial Trees

You have forgotten the combinatorial factors for binomial probabilities on your terms. You need $$ {n\choose k} p^n(1-p)^{n-k},$$ not just $$ p^n(1-p)^{n-k}.$$ The second term should have a factor of $...
spaceisdarkgreen's user avatar
4 votes
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Why my implementation of CRR model does not converge?

from the look of it your discounting is incorrect because as you increase M you should discount with 1/(1+r0*t) (assuming r0=0.0214 is the annual interest rate where as you seem to discount by 1/(1+r0*...
Ezy's user avatar
  • 2,187
4 votes

Binomial Trees vs FDM

Actually recombining binomial trees are only a particular case of an explicit FDM scheme. But they have obvious limitations, the foremost being that they cannot accomodate local volatilities. Also 1/2 ...
Antoine Conze's user avatar
4 votes

Risk-neutral pricing and statistical arbitrages

What you say is perfectly true and there is no contradiction. Arbitrage means risk free profit , so your ‘statistical arbitrage’ is not arbitrage at all. It just says that if you take risk, your ...
dm63's user avatar
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4 votes
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Reference of using $\mu = \frac{1}{T}(\log K - \log S_0)$ in binomial tree model

It appears that the motivation for $\mu = (\log K - \log S_0)/T$ may be that K is in the middle of the tree at $T$. I could see how this may improve accuracy since K is where the ‘action’ is. @...
dm63's user avatar
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4 votes
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How to price barrier options (binomial tree)

This may not be answering your question - but it is worth noting that valuing barrier options on a binomial / trinomial tree is at best problematic. It is difficult to enforce the boundary conditions ...
Marco's user avatar
  • 139
4 votes

Optimize call option purchase

Assuming the options available to you are priced using the Black-Scholes model and because your predicted prices of the stock at time $T$ are evenly distributed between $P_2$ and $P_3$ where $P_3 \ge ...
Alper's user avatar
  • 1,046
4 votes
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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 ...
Pontus Hultkrantz's user avatar
3 votes

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. ...
Lennart_R's user avatar
  • 181
3 votes
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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 ...
Vim's user avatar
  • 903
3 votes
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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 ...
vonjd's user avatar
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3 votes
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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 ...
amdopt's user avatar
  • 4,348
3 votes
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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 ...
JohnDoe's user avatar
  • 278
3 votes
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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-...
AdB's user avatar
  • 714
3 votes
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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 ...
JeanGuillaume's user avatar
3 votes

Should U and D change with the number of steps in a Binomial Tree?

You can choose $U=e^{(r-\sigma^2/2)\delta t + \sigma \sqrt{\delta t}}$ and $D=e^{(r-\sigma^2/2)\delta t - \sigma \sqrt{\delta t}}$ to have the binomial model converge to the BS model when $\delta t=T/...
Antoine Conze's user avatar
3 votes
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QuantLib convertible bond pricing generates strange delta

You have a conversion ratio of $100/12.1 \approx 8.26$, so the convertibility is an option on about 8 underlying stocks and the delta scales accordingly. I'm not familiar about the way it's quoted, ...
Luigi Ballabio's user avatar
3 votes
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Binomial tree with jumps

Try this paper (although it's advanced): https://www.sciencedirect.com/science/article/pii/S0377042702009032 The topic you picked is not necessarily an easy one :)
Jan Stuller's user avatar
  • 6,213
3 votes
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Black & Scholes formula derivation from a Binomial Tree - John C. Hull

In the Black Scholes formula the $N(\alpha)$ gives you cumulative probability, i.e, the probability of a randomly selected occurence being below $\alpha$. To transform the distribution of your ...
David Duarte's user avatar
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3 votes
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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?

The equality $1 + R = q_u · u + q_d · d $ is not particularly significant or difficult to prove. In fact, any number $b$ can be written as a linear combination of 2 other distinct arbitrary numbers $a,...
nbbo2's user avatar
  • 11.5k
3 votes
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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 ...
piterbarg's user avatar
  • 940
2 votes
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How to derive the formula for risk-neutral probability for a Standard Binomial Tree (Forward Tree)

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}} + ...
KarolisR's user avatar
  • 693

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