Questions tagged [binomial-tree]

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145 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
818 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
9k views

Replication strategy of European call option

So the question asks: L et $S(0) = 120$ dollars, $u = 0.2$, $d = βˆ’0.1$ 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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1answer
138 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 ...
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1answer
82 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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1answer
294 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
561 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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1answer
59 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 ...
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1answer
149 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 ...
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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 ...
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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 $π‘‰π‘Žπ‘Ÿ(𝑆_{π‘š+1})=𝑆_π‘š^2𝜎^2Δ𝑑$ where $\Delta t = \frac{T}{...
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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 ...
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2answers
466 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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3answers
717 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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0answers
23 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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47 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
51 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
33 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 ...
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0answers
40 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 $$ V_0 = B_0 + hS_0, $$ ...
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0answers
47 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 (...
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0answers
50 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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0answers
241 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 ...
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1answer
491 views

Binomial Model for options pricing with continuous compounding

I'm reading about Binomial Model on "Arbitrage Theory in Continuous Time" by Tomas Bjork. I found an important result which allow us to state that in a one period model $q_u$ and $q_d$ are actually ...
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2answers
833 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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1answer
355 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 = ...
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1answer
185 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 ...
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1answer
179 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
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1answer
282 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 ...

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