# Questions tagged [binomial-tree]

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52 views

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

In everyone's binomial trees online I see constant U and D. Even when I read Option Volatility and Pricing by Natenburg, all his diagrams use a constant U and D (where U is the upwards magnitude from ...
54 views

### One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$S_t= 120 \, \text{with probability}\, 0.5$$ $$S_t= 60\, \text{with probability}\, 0.5$$...
38 views

### Binomial Model - completeness in presence of arbitrage

Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is $$V_0 = B_0 + hS_0,$$ ...
37 views

### Definition of interest rates in binomial tree model

I'm studying financial mathematics from Shreve's text. I have two problems. 1) "for a binomial tree with three steps, where $S_0=20$, $u=1.05$, $d=.95$ and continuously compounded risk-free interest ...
66 views

### Finding distinct possible values in binomial tree

I wonder how to solve this problem. Lets say we have a binomial tree with the following parameters: $u=1.25,\ d = 1/u,\ T=15$. How many distinct possible values are there for $X_{7}$?
40 views

### Risk neutral measure in the binomial approximation of geometric Brownian motion

Suppose an asset is described by geometric Brownian motion with a drift, i.e. $$dS_t = S_t\mu dt + S_t \sigma dW_t$$ for a Wiener process $W_t$ and $S_0=1$. By some consequence of Girsanov's theorem (...
94 views

### On pricing american put options

How come we pick the highest between the discounted weighted average (with risk neutral probabilities) and the early exercise value at each node of the binomial tree? I dont understand why, I can ...
96 views

### Binomial model arbitrage

I've recently started studying math finance from Shreve's Stochastic calculus text. In the binomial model, there is no arbitrage $\iff d<1+r<u$. To show that no arbitrage implies $1+r<u$, ...
91 views

### Binomial model in Björk's Arbitrage Theory in Continuous Time

I am having some trouble with variable $Z$ introduced in chapter $2$ in Björk's text. In the beginning, it is the random variable that attains $u$ resp. $d$ with probabilities $p_{1}$ and $p_{2}$, i.e....
52 views

### A question on the binomial model

I dont understand the introduction and/or idea of the variable $X$ on page $80$ in the following handout. http://www.maths.lth.se/matstat/kurser/fmsn25masm24/ht17/Ch3.pdf Does someone know whats the ...
69 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 ...
70 views

### stochastic interest rate in binomial pricing model and in continuous models

Is the interest rate allowed to be truly stochastic in the binomial pricing model and in continuous models so that we are still able to switch to the risk-neutral measure? Shreve mentions multiple ...
208 views

### Binomial Option Pricing Model

This isn't homework. I'm going through sample questions for an exam. They include the answer, but no explanation. I've studied this model, but I don't know how to setup this tree to get any of the ...
51 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%...
152 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 ...
46 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 ...
88 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:...
51 views

57 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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### 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 ...
246 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 ...
428 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 $S_T=18$ ...
787 views

### 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 ...
114 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=...
523 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 \...
200 views

### 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 ...
256 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 ...
455 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 ...
311 views

### 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 ...
305 views

### 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 = ...