Questions tagged [binomial]

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57 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 ...
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1answer
98 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)...
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25 views

Binomial tree for elementary security

I'm coursing a financial engineering course and must build a binomial tree for a security that is valued 1 in state and time 0. I dont get the formula given by the instructors, and trying to apply the ...
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1answer
42 views

Option pricing models relation between theoretical and actual price

I have trying to figure out the relationship between theoretical option price and actual market price spotted from market which is determined by supply and demand. I yet cannot understand how to ...
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0answers
15 views

Binomial correlation measure in the trivariate case

I have a question about the binomial correlation measure at page 530 in Hull(2009), Options futures and other derivatives (7th Edition) which is defined for the bivariate case as: $\beta_{AB}(T)=\...
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3answers
943 views

The State-Price Deflator in a Binomial pricing model

This question comes from a Financial Economics exam and I'm very confused about a state-price deflator which doesn't seem to exist. I've included the whole question for completeness, but my actual ...
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2answers
534 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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1answer
145 views

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 ...
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1answer
172 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 ...
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0answers
182 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 ...
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0answers
17 views

Question about Paul Kupiec's “concentrated Bond loss rate distribution”

I wonder if anyone here has read the following paper by Paul Kupiec in which he approximates a loss rate distribution for a portfolio composed of (possibly) concentrated bond positions. https://www....
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1answer
257 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?
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1answer
257 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 ...
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2answers
362 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 ...
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2answers
3k views

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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1answer
524 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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3answers
236 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 ...
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1answer
83 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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4answers
553 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/...
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0answers
145 views

R/fOptions Binomial Options Pricing warning message

Trying to compute theoretical prices for a set of options using the R package fOptions: ...
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1answer
1k views

Calculating expected shortfall

I'm trying to calculate the expected shortfall for the below scenario. I don't understand why the 1.04% probability of 0 bonds defaulting is used as a weight when calculating ES, since the binomial ...
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2answers
714 views

Calculate volatility under the binomial model for option pricing

The original question is quoted below. The underlying stock price is now \$100, and tomorrow it will be either \$101 (with probability $p$) or \$99 (with probability $1-p$). A call option with ...
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1answer
588 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 ...
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1answer
2k 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 ...
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1answer
835 views

Delta of an option derived from the binomial model

I have the following function $V=V(S,t)$, $V^- = V(vS,t+\delta t)$, $V^+ = V(uS, t +\delta t)$. The book proceeds to explain that if we use Taylor series expansion on the above we will confirm that $\...
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0answers
231 views

Two-period binomial model for American option

Consider a two-period binomial model for a risk asset with each period equal to a year and take $S_0 = 1$, $u = 1.5$, and $l = 0.6$. The interest rate for both periods is $R = .1$. a.) Price an ...
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2answers
1k 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 ...
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0answers
59 views

Jabbour-Kramin-Young ABMC Binomial Parameterization

The JKY ABMC Model (taken from Jabbour, et al. 2001) parameterizes the binomial model (in a risk-neutral world) such that, $u = e^{r\Delta t} + e^{r\Delta t}\sqrt{e^{\sigma^2\Delta t} - 1}$ $d = e^{...
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1answer
45 views

binomial - parameters at which american option hits early exercise possibility

I am looking for a set of parameters (d,u,r,So,K, N=?) for pricing an american call using binomial where the call hits the early exercise possibility. Do you have any exemplary set?
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1answer
217 views

completeness of the binomial model - proof

I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...
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1answer
59 views

Complete Multiperiod Binomial model

I have the following deifnition of a Complete multiperiod binomial model: A multi period binomial model can be called complete if every derivative security can be replicated by trading in the ...
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1answer
173 views

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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1answer
249 views

binomial option pricing model - problem with risk-neutral probability

I have a little problem: in the binomial option pricing model, the price of a european derivative security $V_{n}$ satisfies: $V_{n}=[1/(1+r)]*[\tilde{p}*optionUp +\tilde{q}*optionDown]$ where: $\...
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1answer
118 views

Pricing of a call option in one period binomial model

You are given a $5\%$ call option worth $\$2.66$. The strike price $k$ is $\$41.00$. $S(0)=40$, $Sd=35$ (i.e the lower price of the stock at $t=1$) find $Su$ (i.e the high price of the stock at $t=1$)....
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1answer
134 views

Maximizing utility subject to a wealth constraint

Let $\tilde{E}$ be the risk neutral expectation, and $X_t$ the wealth that time t and $R$ the return of a risk-free investment. Consider maximizing the function $EU(X_N)$ subject to $\tilde{E}\frac{...
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1answer
290 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 ...
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2answers
250 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 ...
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3answers
1k views

Arbitrage free implies complete market?

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition It seems that to show that the model is complete, we must show that the claims are reachable. That is, we ...
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3answers
90 views

Interpretation of equation derived from the delta of a call European call option

I have started reading an introductory book called: A Course in Derivative Securities by Kerry Back. On page 12 they mention the following: The delta of the call option is $\delta = (C_{u} - C_{d}) / ...
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1answer
332 views

Prove that the binomial algorithm implies the arbitrage free price at t=0 of a T-claim

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ these propositions How does the first formula follow from from the algorithm? I get that $\Pi(0;X) = V_0(0)$, but I don't ...
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3answers
413 views

Divergence between binomial pricing and monte carlo simulation for vanilla european call?

I notice a divergence in my own code, but it's evident even in public code: http://www.thalesians.com/finance/index.php/Knowledge_Base/Finance/Option_Pricing_in_Python_and_Simple_English Pricing a ...
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0answers
211 views

How to price an option with a “step up” feature using binomial tree?

I have a call option with expiry in two years. In my case the option is bermudan style with first 9 months w/o ability to exercise (i.e. European) and after exercise at any time (i.e. American), but I ...
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1answer
438 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 ...