Questions tagged [binomial-tree]

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942 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 ...
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0answers
105 views

Binomial Model Implementation Trouble - American and European options come out equal

I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options ...
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50 views

Interest model calibration and binomial trees

Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
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0answers
100 views

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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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 ...
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147 views

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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2answers
3k 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 ...
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2answers
114 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 ...
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2answers
106 views

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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1answer
363 views

Binomial pricing model: When the Cox-Ross-Rubinstein assumption is not arbitrage-free

I understand that in an arbitrage-free Binomial model, we assume that $S_{t+1} = S_t \cdot u$ in the event of an up-jump and $S_{t+1} = S_t \cdot d$ in the event of a down-jump. We call $u$ and $d$ ...
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1answer
304 views

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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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 ...
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1answer
174 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?
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1answer
77 views

Replication of the portfolio in single step binomial model

I would be grateful if anyone would comment how to construct this: Assume $S_{i}^k$ is a stock price at time level $i$ and at price level $k$. Assume option is written on $S$ with a a payoff $f_{T}^{...
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2answers
168 views

Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example

I am reading Rebonato's Volatility and Correlation (2nd Edition) and I think it's a great book. I'm having difficulty trying to derive a formula he used that he described as the expression for ...
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1answer
40 views

Domestic and foreign interest rate; dividends?

The spot price AUD/USD is 0.6868, strike price is 0.6915,the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% and the 6 month AUD deposit rate is 1.45%...
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1answer
68 views

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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2answers
410 views

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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1answer
179 views

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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1answer
319 views

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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1answer
85 views

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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3answers
186 views

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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1answer
321 views

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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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?
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2answers
6k views

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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3answers
1k views

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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1answer
377 views

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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0answers
46 views

One Period Binomial Option Valuation Model [closed]

My question here is how is the probability of an up move calculated by $(1+Rf-D)\over(U-D)$ derived where Rf is the risk free rate, D is the down move factor and U represents the up move factor. ...
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32 views

How does LR binomial Tree Model handle input values which would cause NA result?

I am using C++ to implement a LR binomial Tree algorithm to price American options, but I find it would constantly generate invalid output, which is "nan" value in C++, although the input value seems ...
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1answer
196 views

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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0answers
104 views

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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0answers
241 views

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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0answers
98 views

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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0answers
131 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 ...
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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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0answers
3k views

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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2answers
180 views

Is stock price priced in the uncertainty?

Consider a one step binomial tree model for stock price. The classical setup is as below: At time $t=0$, the stock price is $S_0$. At time $t=1$, the stock has probability $p$ to jump up to price $...
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1answer
61 views

American Put Option Pricing

I am trying to solve a question of American Put Option pricing as below. Build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with:...
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1answer
213 views

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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2answers
108 views

Is American option price lower than European option price?

I used to think under the same condition, the American option is always more expensive than the European option, because American option can be exercised at any time (has more rights than European ...
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1answer
296 views

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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1answer
166 views

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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1answer
47 views

How underlying asset price variance is connected with time

I'm dealing with option pricing models and there is a statement that says the variance of underlying asset price is propotional with time $𝑉𝑎𝑟(𝑆_{𝑚+1})=𝑆_𝑚^2𝜎^2Δ𝑡$ where $\Delta t = \frac{T}{...
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1answer
38 views

Infinite Binomial Pricing no arbitrage

How to price a contract that pays only 1 at the first stock price drop? The stock follows an infinite binomial with no arbitrage $d<R<u$ condition. So the probability of the price going down is ...
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2answers
363 views

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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1answer
406 views

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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3answers
637 views

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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1answer
6k views

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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0answers
39 views

Value of portfolio with fixed discrete dividends

I know that this is a very simple question, but i want to make sure to grasp the concept of ex dividend and value of portfolio. Suppose that we have a two period binomial tree of a stock with initial ...
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35 views

Pricing European Call on Coupon Bond in Lattice

What's the best approach to pricing a par call option on a coupon paying bond? Is it to discount the greater of the price and strike through the lattice? And for this, is the price used the dirty or ...