Questions tagged [binomial-tree]
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Is this the correct shape of Cox-Ross-Rubinstein's recombining binomial tree?
Most texts display the binomial tree like this:
However when I run my calculation the tree in reality looks like this:
Does this look correct to you? I am using these standard formulas:
$$u=e^{\...
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Convertible Bond in Foreign Currency - Quanto Adjustment
I need to value the following convertible bond:
The bond notional and interest is denoted in USD, but is convertible into Euro denominated equity.
Normally, I would value such a bond with a ...
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Confusion in forward contract pricing on a stock using the binomial model
In the financial engineering course I am taking we are studying how to use the binomial model to price derivatives, one of which is the forward. For this question it is related to a forward contract ...
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Arbitrage strategies in Rubinstein's binomial tree one-step
Suppose that the current stock price is $S_0=20$ and the call option price with no arbitrage is $c=0.633$. Knowing that the expiry stock price can be $S_T=22$ with call option price $1$ or $S_T=18$ ...
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What discount rate to use when valuing binomial option with real probabilities
We all know that we can use the argument of risk-neutrality and the law of one price, to get the option value without the real world probability.
However, suppose if we use the real world probability ...
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Second order convergence for the Leisen-Reimer tree
I have a question about this paper "Achieving higher order convergence for the prices of European options in binomial trees" by Mark Joshi, (Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
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Black Derman Toy model: from tree to differential equation
The Black Derman Toy model of interest rates is usually introduced as the model governed by the stochastic differential equation:
$$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
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How to estimate $\sigma$ and $r$ in binomial pricing model?
I am writing a program to price American put options with binomial pricing model and to compare it with the market price.
When I used made-up numbers for $\sigma$ and $r$, the price by binomial ...
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Put-Call Parity on Currency and Binomial Trees
I tried solving the below problem without knowing the shortcut of thinking about this in terms of a put versus a call. I can't seem to arrive at the correct answer using my method and I'm wondering ...
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Basic binomial option pricing example
A security is currently trading at 100, and with 99% probability it will be at 110 tomorrow, and with 1% probability at 90. What is the value of an ATM call option today expiring tomorrow? Assume nil ...
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Previsibility in Binomial Representation Theorem
I'm working through Baxter and Rennie's "Financial Calculus: An Introduction to Derivative Pricing". It was going very well and I've actually found it an easy read up until the point where they ...
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Why does option pricing not depend on probabilities in a binomial tree style valuation
I am new into learning option pricing and read that option pricing using binomial valuation does not depend on probabilities (real or risk neutral).
Example:
A 1 period binomial tree with $u = 1/d = ...
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Binomial Option Pricing - Hedging
I'm working on a project which is requiring me to test Binomial option pricing on real data.
So far I have just been working with test data and my option pricing method works fine.
The issue I'm ...
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Option price in a neutral risk world is the same as in the real world. I can not understand! [closed]
Good evening. I know there are several posts on the subject but unfortunately I can not fully understand this concept and I hope you can help me.
To price the option the fundamental assumption ...
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Real Options: Calculating the "option to switch use" using binomial lattices
I'm currently looking into calculating the "option to switch use" to determine the benefit of the ability to switch between two technologies at any point in time (american option). This is also called ...
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How to price the American style Asian option with recent N day average
How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is
$$...
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Risk neutral probabilities for foreign currency exchange rate
Suppose that there are two currencies INR(domestic) and USD(foreign). Let the for exchange rate be S_inr. Using historical data, one can find out the volatility. For example, assume that, S_inr=60,σ=0....
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Trinomial tree VBA code [closed]
I am studying binomial trees and I'm implementing them in VBA to see their convergence to the BS model.
I searched 3-4 hours in the web; the only good site I know is Volopta.
Very simply question by ...
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Building implied binomial tree with American input options
i want to build an implied volatility binomial tree with American input options, so the setup is the following:
1) We know the market Price P of the American Put $P_{am}(t_i,K)$, where $t_i$ is the ...
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Explanation on the application of CLT in bionomial tree model
We have a stock price binomial tree model of $n$ steps, with step length $\Delta t=T/n$, stock price volatility $\sigma$ s.t. $u_n=e^{\sigma\Delta t}$ and $d_n=1/u_n$, and the risk neutral probability ...
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Binomial Model for options pricing with continuous compounding
I'm reading about Binomial Model on "Arbitrage Theory in Continuous Time" by Tomas Bjork. I found an important result which allow us to state that in a one period model $q_u$ and $q_d$ are actually ...
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Difference in formulas for u & d in Binomial trees
For a binomial tree, everywhere in Hull and other literature, we have found the formulas for
$$u = \exp(\sigma \sqrt{h})$$
but for binomial trees based on forward prices, we get a different formula
...
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Clarification on the Black-Derman-Toy model regarding measuring time and notation
I'm self-studying BDT and I'm having some difficulty with what is meant by the "short-rate volatility parameter for the first year" and "the short-rate volatility parameter for the second year," as in ...
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How to derive the formula for risk-neutral probability for a Standard Binomial Tree (Forward Tree)
Consider a standard binomial tree. Let $u = e^{(r - \delta)h + \sigma\sqrt{h}}$ and $d = e^{(r - \delta)h - \sigma\sqrt{h}},$ where $\delta$ is the continuously compounded dividend yield, $h$ is the ...
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binomial trees and finite differences
I was reading Tavella Randall book and their explanation why binomial trees are a particular example of finite differences. I started having additional questions. So, they way they do that is saying ...
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Calculating the annual return on an option using a replicating porfolio
I am self-studying and encountered the following problem:
My idea was to calculate the price of the put using a replicating portfolio, then use the formula:
$$Pe^{\gamma h} = S\Delta e^{\alpha h} + \...
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Pricing of convertible bonds
I'm trying to evaluate a convertible bond using the structural approach : the price of convertible bond is an option (call) on the firm value. We suppose that the firm value is equal to the sum of the ...
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Is Asian option in binomial asset pricing model a martingale?
Since it does not have a closed form solution for the price, it's unlikely to be a martingale. However, on the other hand, if we represent the price as a function of the current stock price and the ...
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Reference for option pricing, binomial multi-period model using martingales and conditional expectations
The title basically says it all. I am looking for a reference text on the pricing of options in a binomial multi-period model. It should be mathemathically rigorous using martingales and conditional ...
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Deriving $u$ and $d$ coefficients using binomial tree approach
From Hull's book when deriving coefficients of up and down movements, $u$ and $d$, of a stock price using binomial tree approach, at some point we get the following equation:
$$e^{\mu\Delta t}(u+d) - ...
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Counting random paths
Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time $t=0$ is 1024. The upstage factor of the stock price is $x=1.25$ and downstage factor of ...
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Option pricing: Risk neutral probability calculation
Let $u=1.3$ $d=0.9$ $r=.05$ $S(0)=50, X = \text{strike} = 60$. Assume binomial model
Why isn't the risk neutral probability found by solving the following for $p$: $$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=...
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What does a negative stock amount mean in a single-period, binomial market model?
Consider a single-period, binomial market model with a $r > 0$ interest rate (in USD per period) and a portfolio $(x, y)$ consisting of two assets: a savings/lendings account and a stock, both ...
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Put-on-call option confusion
So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = 20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a ...
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Replication strategy of European call option
So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = −0.1$ and $r = 0.1$. Consider a call option with strike price $X = 120$ dollars and exercise time $T = 2$. Find the option price and ...
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Two-period binomial model with dividends
Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$, $u = 1.15$ and $l = 0.95$. The interest rate is $R = .05$.
a.) If the asset pays 10% of its ...
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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 ...
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Quantlib binomial tree
I was trying to price options with the extendedBinomialTree class of quantlib. I actually tried at some point to modify this class in order to optimize it. Normally the drift and diffusion of the ...
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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 $\...
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Calculating the price of a call and put using multinomial trees and risk-neutral probabilities
I am self-studying for an actuarial exam and I encountered this example. The books shows one method of solving using a replicating portfolio, and then shows this solution involving risk-neutral ...
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binomial - parameters at which american option hits early exercise possibility
I am looking for a set of parameters (d,u,r,So,K, N=?) for pricing an american call using binomial where the call hits the early exercise possibility.
Do you have any exemplary set?
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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 $S_d=90$, ...
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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 ...
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Efficient construction of binomial tree
The goal is to build a $n$ step binomial tree knowing the end nodal probabibilities $p_1, \dots, p_m$, which correspond to the time $T$ states $S_1, \dots, S_m$. We assume that all paths ending in the ...
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Binomial tree notation
Can someone clarify for me the notation of the nodes in a binomial tree with more than 1 step? Is this notation correct?
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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 $0 < d < 1 + r < u$. ...
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pricing american calls on non dividend paying stocks
It is never optimal to exercise an american call option early if it is written on a stock that doesn't pay dividends, yet when pricing such an option, using a binomial model, we check whether or not ...
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negative transition probability in trinomial trees
I was pricing a option with big dividend in the underlying. However, I got negative transition probability in a trinomial tree.
Will it cause arbitrage? Does anyone have reference paper or book ...
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Jabbour-Kramin-Young ABMC Binomial Parameterization
The JKY ABMC Model (taken from Jabbour, et al. 2001) parameterizes the binomial model (in a risk-neutral world) such that,
$u = e^{r\Delta t} + e^{r\Delta t}\sqrt{e^{\sigma^2\Delta t} - 1}$
$d = e^{...
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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 ...
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