Questions tagged [binomial-tree]

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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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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 ...
559 views

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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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 $\... 1answer 90 views Calculating the price of a call and put using multinomial trees and risk-neutral probabilities I am self-studying for an actuarial exam and I encountered this example. The books shows one method of solving using a replicating portfolio, and then shows this solution involving risk-neutral ... 1answer 45 views binomial - parameters at which american option hits early exercise possibility I am looking for a set of parameters (d,u,r,So,K, N=?) for pricing an american call using binomial where the call hits the early exercise possibility. Do you have any exemplary set? 6answers 2k views Why don't real-world probabilities affect the price of a call in a 1-step binomial model? I was a bit hesitant to post this question because it seems so basic...but I wasn't able to figure it out on my own. Say we setup a one-step binomial tree with$S_0=100$,$S_u=110$and$S_d=90$, ... 3answers 167 views How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing) We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ... 0answers 120 views Efficient construction of binomial tree The goal is to build a$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 ... 1answer 175 views 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? 2answers 541 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$0 < d < 1 + r < u$. ... 4answers 565 views 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 ... 0answers 132 views 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 ... 0answers 59 views 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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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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Calculating Greeks using BinomialTree in Matlab [closed]

section 1. Calculating sensitivity of the price of derivatives American or European option using binomial tree model section 2. Calculating first order greeks the code compiles till this point ...
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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-...
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How to price an option on a dividend-paying stock using the binomial model?

This is actually an exercise from a course. But I don't completely understand the wording of the question. A stock is now trading at 100 dollars. Its price over the next 6 months evolves as a two ...
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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 ...
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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 ...
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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 ...
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Arbitrage free implies complete market?

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition It seems that to show that the model is complete, we must show that the claims are reachable. That is, we ...
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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 ...
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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 ...
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How to construct the binomial model for European option?

The annual interest rate is 5.3% and the annualized volatility of a non-dividend paying stock over the next six months will be 12.5% (annualized). i) Construct binomial trees of 5, 10 and 30 periods ...
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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 ...
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What is the difference between the methods (listed in content) in pricing convertible bond?

To price the convertible bond, one of the models is the bond plus equity option method. That is, the value of convertible bonds is evaluated by finding the value of the straight bond and the value of ...
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How to simulate a Geometric Binomial Process with state/tie dependent increments?

I want to simulate a geometric binomial process with state/time dependent increments. So the model is given by \begin{align}R_t=\frac{X_t}{X_{t-1}}\end{align} \begin{align}P(R_t=u)=p(X_{t-1},t) \...
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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-...
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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....
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 ...