Questions tagged [binomial-tree]
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119
questions
1
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0answers
50 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
$$
S_t= 120 \, \text{with probability}\, 0.5
$$
$$
S_t= 60\, \text{with probability}\, 0.5
$$...
0
votes
0answers
36 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
$$ V_0 = B_0 + hS_0, $$
...
2
votes
1answer
32 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 ...
0
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1answer
46 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 $X_{7}$?
0
votes
0answers
33 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 (...
0
votes
1answer
66 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 ...
0
votes
3answers
80 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 $1+r<u$, ...
1
vote
1answer
84 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....
0
votes
1answer
51 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 ...
2
votes
2answers
64 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 ...
1
vote
1answer
68 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 ...
0
votes
1answer
113 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 ...
2
votes
1answer
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%...
1
vote
2answers
145 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 ...
0
votes
0answers
45 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 ...
1
vote
1answer
81 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:...
0
votes
1answer
50 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}{...
1
vote
0answers
50 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.
...
2
votes
1answer
106 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)...
0
votes
1answer
43 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 ...
3
votes
1answer
101 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 ...
3
votes
1answer
94 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.
2
votes
2answers
156 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 + ...
3
votes
1answer
169 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 ...
0
votes
2answers
120 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 ...
2
votes
1answer
183 views
Binomial Tree Option Pricing Model. Lets talk dividends and futures
I am writing an option pricing model for production use. Its not for arb or anything so it doesn't need to be 100% as accurate as possible. Just good enough for "what happens to my book if we jump 10 ...
3
votes
0answers
133 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.
...
2
votes
0answers
205 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 ...
1
vote
0answers
39 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 ...
3
votes
1answer
540 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\...
-2
votes
1answer
141 views
How to calculate riskless profit out of call options?
I'm having trouble with working out a question that I can't currently ask my lecturer as they're away. Hoping for some help here with why the answer is (a).
A stock price is currently \$40. It is ...
2
votes
0answers
56 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
2
votes
1answer
38 views
calibrating two (or X) equity diffusion trees
I have two equities S1 and S2.
Each one follows the following tree evolution :
$$S_1 \rightarrow \left \{
\begin{matrix} S_1 (1+u_1) & \text{with probability } p_1 \\
S_1 (1-d_1)...
2
votes
1answer
92 views
Optimal number of nodes for binomial lattice?
Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
-3
votes
1answer
158 views
What is martingle measure with risk free asset in numeraire or stock price in numeraire [closed]
What is martingle measure with risk free asset in numeraire or stock price in numeraire
1
vote
1answer
74 views
Is this the correct shape of Cox-Ross-Rubinstein's recombining binomial tree?
Most texts display the binomial tree like this:
However when I run my calculation the tree in reality looks like this:
Does this look correct to you? I am using these standard formulas:
$$u=e^{\...
1
vote
1answer
244 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 ...
0
votes
1answer
212 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 ...
1
vote
1answer
388 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 $S_T=18$ ...
2
votes
1answer
711 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 ...
2
votes
0answers
107 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=...
7
votes
1answer
495 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 \...
0
votes
0answers
186 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 ...
0
votes
1answer
242 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 ...
0
votes
2answers
437 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 ...
2
votes
1answer
271 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 ...
-1
votes
1answer
287 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 = ...
1
vote
0answers
115 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 ...
-3
votes
1answer
266 views
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 ...
2
votes
1answer
287 views
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 ...
