Questions tagged [binomial-tree]

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Fixed income modeling

I am currently working on my research paper and trying to explain a two-dimensional variable: volume and instrument of corporate debt financing. Independent variables that I believe must be included ...
FES's user avatar
  • 121
11 votes
1 answer
345 views

How to handle coupon payments when pricing a bond with an embedded option?

I'm using a binomial tree to price a bond that has an embedded call or put option. On every node that has a coupon payment, do you include the coupon payment then max/min out the value, or do you max/...
user1443's user avatar
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9 votes
3 answers
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Demonstration of Ito's correction term/lemma in binomial tree

I am preparing an undergraduate QuantFinance lecture. I want to demonstrate the ideas of Ito's correction term and Ito's lemma in the most accessible manner. My idea is to take the "working horse" of ...
vonjd's user avatar
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9 votes
1 answer
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How to use binomial tree for portfolio of equity products

How can I use a binomial tree to price a European option that's based on a portfolio of equity products? I have volatility and correlation matrix of all underlying products? Looking for a formula ...
Ryan's user avatar
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7 votes
1 answer
946 views

Black Derman Toy model: from tree to differential equation

The Black Derman Toy model of interest rates is usually introduced as the model governed by the stochastic differential equation: $$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
pinaki's user avatar
  • 121
6 votes
1 answer
410 views

Intuition behind American Option pricing

The price of an American option is given by $$V_n = \max\left(G_n,\frac{pV_{n +1}H^d + qV_{n + 1}H^u}{1 + r}\right)$$ where p, q are the risk neutral probabilities. I have two questions: How can ...
user7348's user avatar
  • 298
6 votes
0 answers
323 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 ...
Landscape's user avatar
  • 548
5 votes
7 answers
3k views

Why don't real-world probabilities affect the price of a call in a 1-step binomial model?

I was a bit hesitant to post this question because it seems so basic...but I wasn't able to figure it out on my own. Say we setup a one-step binomial tree with $S_0=100$, $S_u=110$ and $S_d=90$, ...
Karim L's user avatar
  • 118
5 votes
1 answer
6k views

Ho-Lee Model; Please explain

I'm having trouble with the Ho-Lee model for short rates and differentiating between how to find the values for the free parameter λ versus using the model to predict future rates. The Ho-Lee model ...
AfterWorkGuinness's user avatar
5 votes
1 answer
4k views

Binomial tree vs trinomial tree in pricing options

Very new to pricing models. Is there a general guideline when to use binomial tree and when trinomial tree is preferred? As far as I know, unlike binomial tree, trinomial tree only gives a range ...
user6396's user avatar
  • 203
5 votes
2 answers
547 views

Time 0 value of an American Put in Cox-Ross-Rubinstein model

This is a question from a problem sheet which I have handed in and have solutions for. The only examples of this in class I have seen are examples where the interest rate is 0. "Consider a Cox-Ross-...
Ross's user avatar
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2 answers
2k views

Risk neutral probability in binomial lattice option coming greater than 1...what's wrong?

I am substituting reasonable values in the below fomula (like r=0.12, T=20, nColumn=16, sigma=0.004)...why is probability coming out to be greater than 1? Any help? Thanks! ...
user avatar
5 votes
2 answers
2k views

Does the Binomial Pricing Model require a no-arbitrage assumption?

In a binomial option model, if we take the uptick as 6%, downtick as 5% (assume equally probable), and RFR of 6% (continuous compounding), then we have a violation of $0 < d < 1 + r < u$. ...
P. Cha's user avatar
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5 votes
1 answer
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Rubinsteins Implied Binomial Tree - how to calculate the cumulative returns

I am working on Rubinsteins IBT and use the following paper to implement this into excel: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=541744 the original paper can be found here: http://www....
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5 votes
2 answers
1k views

Is the binomial model wrong?

In the standard MBA one-period binomial model, the value of an option is $v = \frac{1}{R}\bigl(\frac{u - R}{u - d}V(sd) + \frac{R - d}{u - d}V(su)\bigr)$ where $R$ is the realized return over the ...
Keith A. Lewis's user avatar
5 votes
0 answers
199 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 ...
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0 answers
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binomial trees and finite differences

I was reading Tavella Randall book and their explanation why binomial trees are a particular example of finite differences. I started having additional questions. So, they way they do that is saying ...
Medan's user avatar
  • 493
4 votes
2 answers
2k views

BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have steady-...
Rustam's user avatar
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3 answers
267 views

How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing)

We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ...
user18466's user avatar
4 votes
2 answers
216 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 ...
et_85's user avatar
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4 votes
1 answer
2k views

How to price and find a replicating portfolio for a call spreads using a two-period binomial model?

Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$, $u = 1.03$ and $l = 0.98$. a.) If the interest rate for both periods is $R = .01$, find the ...
Wolfy's user avatar
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4 votes
1 answer
5k views

How to draw a binomial option tree graph?

I am writing a paper and need to create a png or jpeg file for binomial option price tree. In the past I would have used the tikZ package in LaTeX, but that won't work in this case. So I want a ...
TJB's user avatar
  • 41
4 votes
1 answer
313 views

Value of option-free instruments with a short-rate model vs the spot curve

You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly. Alternatively, apparently you can use a single-factor short rate model in a ...
user1443's user avatar
  • 569
4 votes
1 answer
167 views

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 ...
cp123456's user avatar
  • 109
4 votes
1 answer
707 views

A question about pricing convertible bond with two different underlying assets

I have a question regarding the pricing of convertible bond. If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the ...
Dennis's user avatar
  • 501
4 votes
1 answer
869 views

Few questions on Binomial-Lattice Option Valuation

I have just started applying Binomial-Lattice, however I am yet to fully understand few things. My questions are: What is the concept of working backward (left side) from the values in terminal (...
user avatar
3 votes
2 answers
5k views

Estimate simple option price without a calculator

I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it. If you have an European ...
Sithered's user avatar
  • 808
3 votes
2 answers
2k views

How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model

Given that $e^{r\Delta t}(u+d)-ud-e^{2r\Delta t} = \sigma^2\Delta t$ I would like to show that $u=e^{\sigma\sqrt{\Delta t}}$ I know I must somehow use Taylor's approximation $e^x = 1 + x + \frac{...
mathjacks's user avatar
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3 votes
1 answer
179 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 ...
MinaThuma's user avatar
  • 459
3 votes
1 answer
200 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?
Preston Lui's user avatar
3 votes
2 answers
841 views

Binomial Trees vs FDM

Binomial trees as the number of time steps is increased (or equivalently as the time step tends to 0), converge to the exact value for an option. So why do people use FDM for pricing options (for ...
Victor's user avatar
  • 519
3 votes
1 answer
319 views

Binomial lattice convergence

How do I measure how quickly a binomial lattice converges to an option value as the number of steps is increased? I'm charting option value versus number of steps for various binomial lattice models ...
Joshua's user avatar
  • 183
3 votes
1 answer
2k views

Why my implementation of CRR model does not converge?

Recall that CRR (Cox-Ross-Rubinstein) model for option pricing is the usual binomial tree model with $u$ (up-factor) and $p$ (one of the risk-neutral probabilities) defined as follows: $$u = e^{\sigma\...
Hasek's user avatar
  • 814
3 votes
1 answer
200 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
Amir's user avatar
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3 votes
1 answer
367 views

What happens in the binomial model if the real-world probability is $0$

Consider a binomial model. Suppose we know that the price of a stock will become a certain value at the next timestep. That is, one of the two outcomes has $0$ real-world probability. Then it should ...
RandomStudent's user avatar
3 votes
1 answer
147 views

Is there an error in this problem on pricing an asset using the true probability of an up move?

I'm self-studying for an actuarial exam and I encountered the following problem: The true probability of an up move, $p$, must satisfy: $$p = \frac{e^{{(\alpha - \delta})h} - d}{u - d},$$ where $\...
user2521987's user avatar
3 votes
1 answer
9k views

Option pricing: Risk neutral probability calculation

Let $u=1.3$ $d=0.9$ $r=.05$ $S(0)=50, X = \text{strike} = 60$. Assume binomial model Why isn't the risk neutral probability found by solving the following for $p$: $$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=...
foshizzle's user avatar
  • 432
3 votes
1 answer
1k views

Risk neutral probability in binomial short rate model assumed to be 0.5?

This should be a basic question but I have not been able to find a satisfying explanation. In the simplest binomial model, the risk neutral probability is computed using the up/down magnitude and the ...
user avatar
3 votes
2 answers
391 views

Pricing of European put option with binomial model

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 $e^{rt}$ at time t years with ...
user11823918's user avatar
3 votes
1 answer
487 views

Difference between tree and lattice approach

Is there any difference between the tree and lattice approach for valuing derivatives? I was under the impression that both are the same.
paapi_91's user avatar
3 votes
1 answer
325 views

Minimum Variance Hedge Ratio in Binomial Framework

In order to find the minimum variance hedge ratio when holding a portfolio of vanilla call options and hedging with stock, you can do an OLS regression. In a binomial model framework, given ...
quantguy's user avatar
3 votes
0 answers
309 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 ...
PBD10017's user avatar
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3 votes
0 answers
622 views

Is there a more efficient data structure to implement binomial trees than 2d array?

I'm just curious what is the "industry standard" for implementing a binomial tree (if "standards" exist in this case). For simplicity, let's just talk about the simplest trees with recombining nodes. ...
Vim's user avatar
  • 903
2 votes
2 answers
1k views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
Summer_More_More_Tea's user avatar
2 votes
2 answers
714 views

Approximation of CRR as Black Scholes PDE

I have a formula for intermediate european option price calculated at, say, m-th possible tree value. $S_n^{(m)}$ is a price at node after going up $n$ times and down $n - m$ times $V(S_n^{(m)}, t + ...
Makina's user avatar
  • 273
2 votes
1 answer
254 views

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

I want to understand what is the underlying logic in the calculation of u and d in a binomial model. $$ u = \exp\Bigl(\sigma \sqrt{\Delta t} \Bigr), \quad d = \exp\Bigl(-\sigma \sqrt{\Delta t} \Bigr)...
user35032's user avatar
2 votes
2 answers
337 views

Binomial representation of stochastic processes

It is common knowledge that a random walk can be represented in the form of a binomial process. Is it possible to represent any generic stochastic process (including non-linear) of the form $dX=adt+...
user3294195's user avatar
2 votes
1 answer
3k views

How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model. Originally I thought the path dependency exists because in binomial tree model, we will ...
Summer_More_More_Tea's user avatar
2 votes
1 answer
234 views

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 ...
Daan Commandeur's user avatar
2 votes
3 answers
359 views

Risk-neutral pricing and statistical arbitrages

I'm studying the martingale approach to asset pricing. Dealing with the concept of risk-neutral probability, I came up with a question about the possibility of "arbitrages in expectation". I'll be ...
Kinderone's user avatar