Questions tagged [binomial-tree]
The binomial-tree tag has no usage guidance.
136
questions
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Failing to replicate Wilmott's results for binomial option pricing
I am working through Paul Wilmott introduces Quantitative Finance, 2nd ed. I am failing to reproduce one of his numerical examples and I would like to understand why.
I chapter 3, Wilmott introduces ...
1
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1answer
53 views
Black & Scholes formula derivation from a Binomial Tree - John C. Hull
I am reading "Option, Futures and other Derivatives" by John C. Hull, and on Appendix chapter 13, he derives BSM formula from a Binomial Tree.
When he builds U2, I just don't understood how to get ...
1
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1answer
65 views
Arbitrage strategy using binomial tree
Suppose that we have a one step binomial tree model for a company. Lets say that the time per step is T, and that price of the stock can go up to $p_1$ or go down to $p_2$. Suppose a T-month European ...
3
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1answer
65 views
Binomial tree with jumps
I am struggling with developing a binomial tree with jumps. although there are models such as CRR, could you suggest a book or have any idea to proceed?
Thanks,
Amir
0
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1answer
38 views
QuantLib convertible bond pricing generates strange delta
I am trying to generate equity delta for convertible bond using QuantLib(version 1.14) functions, but the deltas generated either using a repricing approach or by directly obtaining from the tree(code ...
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1answer
70 views
Reference of using $\mu = \frac{1}{T}(\log K - \log S_0)$ in binomial tree model
Notations: Given a binomial tree with $N$ periods and time to maturity $T,$ let $\Delta t = T / N.$
It is well-known that CRR uses the up and down multipliers as
$$u = e^{\sigma\sqrt{\Delta t}} \...
2
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0answers
26 views
Futures vs Forward pricing with different interest rates using binomial model
I'm given the aforementioned parameters for a two-step binomial model where the underlying pays no dividend, $S_0=50$ and $T=2$. With this information I was able to calculate the risk-neutral ...
3
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1answer
60 views
What are the relation between the risk neutral measures in binomial tree and in Black Scholes model?
I appreciate that both are the direct result of constricting a replicate portfolio using stock and bonds.
Are there deeper relationship between the two?
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0answers
39 views
Trinomial Trees for Hull-White model
I am studying trinomial trees and trying to implement them in Python to compare them to the monte carlo simulation. I searched 3-4 hours in the web; but can't find any implementation on binomial or ...
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0answers
27 views
Replication Portfolios and Binomial Option Pricing
To price a call/put option with two possible future states of the world, I understand we can price the option by essentially calculating the price of a replicating portfolio that gives the same ...
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0answers
54 views
Hedging a short position in the Lookback Option
SOLUTION
I got the correct answer using this formula
$X_2(HH)=(1+r)*[X_1(H)-\Delta_1(H)*S_1(H)]+\Delta_1(H)*S_2(HH)$
$(1+0.25)[2.24-(.06667*8)]+0.06667*16=3.20$
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1answer
59 views
How to get all the paths of a binomial tree
I'm trying to implement a pricing method for exotic options based on binomial tree's. The problem i'm having is that i'm not being able to generate all the paths of the tree. I have the following code ...
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0answers
35 views
Does the price of an American Put often exceed the Payoff?
According to shreve the value of a put is equivalent to or greater than the possible payoff, before a stopping time with the condition that its value equals the intrinsic value. First what does it ...
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0answers
27 views
swap discrete market model
Let be $M = (S_0,E,\Phi)$ a market where the risk-free rate is $r = 0$ and the Euribor $E$ evolves (annually) in discrete time following a three-period binomial model. Assume that $E_0 = 0.031$, the ...
1
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1answer
85 views
What is the probability of a lookback option ending in the money (CRR-model)
I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff $h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\} $ where $K$ ...
0
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1answer
63 views
Stock pricing using Binomial model
A stock is prices at $ \$100$ and follows a one-period binomial process with an up move that equals 1.05 and a down move that equals 0.97. If one million Bernoulli trials are performed and the average ...
0
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1answer
149 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 ...
1
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0answers
56 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
$$...
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0answers
41 views
Binomial Model - completeness in presence of arbitrage
Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is
$$ V_0 = B_0 + hS_0, $$
...
2
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1answer
50 views
Definition of interest rates in binomial tree model
I'm studying financial mathematics from Shreve's text. I have two problems.
1) "for a binomial tree with three steps, where $S_0=20$, $u=1.05$, $d=.95$ and continuously compounded risk-free interest ...
0
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1answer
93 views
Finding distinct possible values in binomial tree
I wonder how to solve this problem.
Lets say we have a binomial tree with the following parameters:
$u=1.25,\ d = 1/u,\ T=15$.
How many distinct possible values are there for $X_{7}$?
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49 views
Risk neutral measure in the binomial approximation of geometric Brownian motion
Suppose an asset is described by geometric Brownian motion with a drift, i.e.
$$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
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1answer
157 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
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3answers
138 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
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1answer
96 views
Binomial model in Björk's Arbitrage Theory in Continuous Time
I am having some trouble with variable $Z$ introduced in chapter $2$ in Bjƶrk's text. In the beginning, it is the random variable that attains $u$ resp. $d$ with probabilities $p_{1}$ and $p_{2}$, i.e....
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1answer
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 ...
2
votes
2answers
83 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
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1answer
75 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
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1answer
316 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
53 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
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2answers
166 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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0answers
51 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
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1answer
111 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
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1answer
55 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 $ššš(š_{š+1})=š_š^2š^2Īš”$ where $\Delta t = \frac{T}{...
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0answers
56 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
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1answer
124 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
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1answer
47 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
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1answer
142 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
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1answer
131 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
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2answers
206 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
229 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
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2answers
148 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
276 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
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0answers
198 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
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0answers
286 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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0answers
41 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
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1answer
841 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:
$$u = e^{\sigma\...
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1answer
193 views
How to calculate riskless profit out of call options?
I'm having trouble with working out a question that I can't currently ask my lecturer as they're away. Hoping for some help here with why the answer is (a).
A stock price is currently \$40. It is ...
2
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0answers
61 views
Interest model calibration and binomial trees
Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
2
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1answer
39 views
calibrating two (or X) equity diffusion trees
I have two equities S1 and S2.
Each one follows the following tree evolution :
$$S_1 \rightarrow \left \{
\begin{matrix} S_1 (1+u_1) & \text{with probability } p_1 \\
S_1 (1-d_1)...
