# Questions tagged [binomial-tree]

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### 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 ...
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 ...
9k 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 ...
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 ...
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 $X_{7}$?
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 ...
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 ...
59 views

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 ...
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 ...
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 ...
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 ...
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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### 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 ...
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 ...
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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### 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 $$V_0 = B_0 + hS_0,$$ ...
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 (...
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 ...
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 ...
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 ...
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 ...
355 views