# Questions tagged [binomial]

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### Black Scholes vs Binomial Model

I'm trying to confirm my understanding of the 2 models. It is my understanding that the black-scholes is a special case of a binomial model with infinite steps. Does this mean that if I were to start ...
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319 views

### Intuition behind American Option pricing

The price of an American option is given by $$V_n = \max\left(G_n,\frac{pV_{n +1}H^d + qV_{n + 1}H^u}{1 + r}\right)$$ where p, q are the risk neutral probabilities. I have two questions: How can ...
2answers
963 views

### Does the Binomial Pricing Model require a no-arbitrage assumption?

In a binomial option model, if we take the uptick as 6%, downtick as 5% (assume equally probable), and RFR of 6% (continuous compounding), then we have a violation of $0 < d < 1 + r < u$. ...
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118 views

### Looback Put Option - finding the number of paths that reach each level

In a 4 period binomial model, I have a lookback put option that pays $\left [M_{4}-4 \right ]^{+}$, where $M_{4}$ is the maximum price reached during the sequence of 4 trials. Lets say the starting ...
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### Error on Paul Wilmott Section 5.2?

I gave this a long and hard thought because Paul Wilmott is a respected quant and I don't want to criticize his book, but am I correct in concluding that this section contains lots of errors? These ...
1answer
368 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 ...
3answers
265 views

### Proof of optimal exercise time theorem for American derivative security in N-period binomial asset-pricing model

At least two textbooks (Shreve's Stochastic Calculus for Finance - I, theorem 4.4.5 or Campolieti & Makarov's Financial Mathematics, proposition 7.8) prove the optimal exercise theorem that says ...
1answer
3k views

### Pricing American Put Options via Binomial Tree in Matlab

I currently am completing a Computational Finance Assignment, and am trying to figure out how to alter this Matlab code which prices a European put or call option, in order to price an American Put ...
1answer
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### Call option pricing using CCR model - derivation problem

I'm viewing the following derivation of a Call Option price using the CRR model. There is one piece of the derivation which I cannot understand. \begin{align} C_0 &= e^{-rT} \sum_{i=0}^{N} (S_{0}\...
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549 views

### Will pricing a Bermudan option default to a value of a European option?

I have a call option with 2 expiry in two years. For the first 9 months I cannot excercise the option. After that the I can exercise at any time. I am pricing this option using a binomial tree using ...
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234 views

### American put option in binomial model - arbitrage opportunity?

I'm sorry this must be an elementary question. I spent a good deal of time searching through webs including this site for the problem but I got none. Here's the problem: Say we have a binomial tree ...
2answers
2k views

### Discrepancy between binomial model, Black-Scholes and Monte-Carlo Simulation

I try to use Monte-Carlo Simulation to price a 10-year call option. Based on below parameter, S = 1, X = 1, volatility = 80%, T = 10, risk-free rate = 0.22% The option value based on Monte-Carlo ...
2answers
101 views

### 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 ...
1answer
178 views

### Python Numpy FFT array size limit?

I am trying to find the price of an Option based on the fft technique within the binomial model and it works fine until N>40000 where I start getting negative values and weird convergene and I am not ...
1answer
398 views

### Replicating an option

When we replicate a portfolio of cash and stock for a call option, shouldn't the replicating portfolio's greeks be equal to options greeks? Is that true? If it is, how is it that a portfolio of cash ...
1answer
405 views

### Number of Time Steps in Binomial Option Pricing - Problem?

I am trying to price a digital option and the final price under different number of time steps are as follows: Is it possible to have a graph like this?
4answers
716 views

### Volatility smile risk (negative effect) on dynamically hedged portfolio?

About last week you can see MSFT call & put option appears to be resembling volatility smile. And then I open trade positions on a 4 MSFT long call option contract (all 4 contract with fixed/...
2answers
274 views

### Non-Negativity of up-factor and down-factor in Binomial No-Arbitrage Pricing Model

Consider a stock which is trading at $S_0$ at time $t=0$ and is expected to be trading at price $uS_0$ or $dS_0$ at time t=1 where $u$ and $d$ are up-factor and down-factor. The theory says that to ...
1answer
51 views

### call vs average of prices

Consider a two-period binomial model, with one risky asset. The are two types of options: call option with strike price $K$, i.e., the payoff is given by $g(S_T)=(S_T-K)^{+}$ option with payoff given ...
2answers
578 views

### Why risk neutral probabilities should be strictly greater than zero for no arbitrage condition?

I was recently told by a colleague that the risk neutral probabilities should ALWAYS be greater than zero to have a no arbitrage condition. Intuitively, we know probabilities cannot be < 0, but how ...
1answer
894 views

### Why does arbitrage free imply complete market?

Proposition 2.10 of Tomas Bjork's "Arbitrage Theory in Continuous Time" states that if the general binomial model is free of arbitrage then it is also complete i.e. every contingent claim has a ...
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### american option confusion

I've coded up a binomial tree version of the "Known Dollar Dividend" part of section 21.3 of Hull 10th Edition. I reproduce the answer in the book's example and also reproduce correctly a ...
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### Breakdown of Wilmott's Binomial Tree derivation of Black-Scholes equation

Hi guys, I tried to follow the chapter of PWIQF on binomial model and got stuck when it derived the Black-Scholes (please see image). I tried to backtrack the said equations but couldn't trace back ...
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### Find yield (bid and ask spread)

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.86, and an ask discount of 5.80. Calculate the best estimate of the risk-free rate to be used in valuing options with the Black ...
1answer
951 views

### Zero Coupon Bond Forward Price

I'm currently working on the Coursera Financial Engineering and Risk Management course. In one of the questions I was asked to build a binomial pricing model for fixed-income securities. Specifically ...