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21 views

Does the solution to this problem on floorlets have an error?

I'm self-studying and encountered the below problem and solution. I believe the payoff of the put at node $dd$ would be $(1.044)^{-1}\max(0.05 - 0.02, 0) = 0.019157088,$ and similarly the payoff at ...
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1answer
47 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
11 views

Zero coupon prices in 2-period binomial tree?

If I have a two-period binomial tree with given short rate process (i.e, rate on the bank account) and the equivalent martingale measure $Q$, what are the zero coupon prices at time t = 0? The reason ...
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1answer
24 views

Is Asian option in binomial asset pricing model a martingale?

Since it does not have a closed form solution for the price, it's unlikely to be a martingale. However, on the other hand, if we represent the price as a function of the current stock price and the ...
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1answer
21 views

Reference for option pricing, binomial multi-period model using martingales and conditional expectations

The title basically says it all. I am looking for a reference text on the pricing of options in a binomial multi-period model. It should be mathemathically rigorous using martingales and conditional ...
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0answers
52 views

Hull white tree and the pricing of an interest rate swap

Currently, I have been able to set up the hull white tree. To price the swap, and we use the formula from Wilmott "Introduces Quantitative Finance", where we use the discount factors for all ...
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0answers
55 views

Replicating American call option

Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$,$u = 1.2$, and $l=0.8$. The interest rate for both periods is $R = .05$ a.) If the asset ...
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1answer
75 views

Deriving $u$ and $d$ coefficients using binomial tree approach

From Hull's book when deriving coefficients of up and down movements, $u$ and $d$, of a stock price using binomial tree approach, at some point we get the following equation: $$e^{\mu\Delta t}(u+d) - ...
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2answers
80 views

Counting random paths

Assume the path of a certain stock can be modeled using a binomial tree. The initial price of the stock at time $t=0$ is 1024. The upstage factor of the stock price is $x=1.25$ and downstage factor of ...
2
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1answer
57 views

Option pricing: Risk neutral probability calculation

Let $u=1.3$ $d=0.9$ $r=.05$ $S(0)=50, X = \text{strike} = 60$. Assume binomial model Why isn't the risk neutral probability found by solving the following for $p$: $$E[S(T)]=p65+(1-p)45=S(0)(1+r)^T=...
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3answers
140 views

What does a negative stock amount mean in a single-period, binomial market model?

Consider a single-period, binomial market model with a $r > 0$ interest rate (in USD per period) and a portfolio $(x, y)$ consisting of two assets: a savings/lendings account and a stock, both ...
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1answer
58 views

Put-on-call option confusion

So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = 􀀀20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a ...
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1answer
83 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 ...
0
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2answers
66 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 ...
4
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1answer
104 views

How to price and find a replicating portfolio for a call spreads using a two-period binomial model?

Consider a two-period binomial model for a risky asset with each period equal to a year and take $S_0 = 1$, $u = 1.03$ and $l = 0.98$. a.) If the interest rate for both periods is $R = .01$, find the ...
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0answers
42 views

Quantlib binomial tree

I was trying to price options with the extendedBinomialTree class of quantlib. I actually tried at some point to modify this class in order to optimize it. Normally the drift and diffusion of the ...
4
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1answer
73 views

Is there an error in this problem on pricing an asset using the true probability of an up move?

I'm self-studying for an actuarial exam and I encountered the following problem: The true probability of an up move, $p$, must satisfy: $$p = \frac{e^{{(\alpha - \delta})h} - d}{u - d},$$ where $\...
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1answer
22 views

Calculating the price of a call and put using multinomial trees and risk-neutral probabilities

I am self-studying for an actuarial exam and I encountered this example. The books shows one method of solving using a replicating portfolio, and then shows this solution involving risk-neutral ...
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1answer
27 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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5answers
167 views

Why don't real-world probabilities affect the price of a call in a 1-step binomial model?

I was a bit hesitant to post this question because it seems so basic...but I wasn't able to figure it out on my own. Say we setup a one-step binomial tree with $S_0=100$, $S_u=110$ and $S_d=90$, ...
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3answers
72 views

How would I exploit arbitrage if risk-neutral pricing doesn't hold? (Option Pricing)

We are just learning about binomial option pricing, and how the up-factor and the down-factor must match the risk-neutral price. p * u + (1 - p) * d = continuous risk free rate compounded CRR ...
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0answers
39 views

Efficient construction of binomial tree

The goal is to build a $n$ step binomial tree knowing the end nodal probabibilities $p_1, \dots, p_m$, which correspond to the time $T$ states $S_1, \dots, S_m$. We assume that all paths ending in the ...
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1answer
65 views

Binomial tree notation

Can someone clarify for me the notation of the nodes in a binomial tree with more than 1 step? Is this notation correct?
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0answers
29 views

Two-period pricing of a European put via riskless portfolio

The current price of a stock is $40. It is known that it either increases or decreases by 12.5% every 3-months over the next 6-month period. The risk-free rate of interest is 8% per annum (continuous ...
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0answers
51 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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4answers
114 views

pricing american calls on non dividend paying stocks

It is never optimal to exercise an american call option early if it is written on a stock that doesn't pay dividends, yet when pricing such an option, using a binomial model, we check whether or not ...
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0answers
41 views

negative transition probability in trinomial trees

I was pricing a option with big dividend in the underlying. However, I got negative transition probability in a trinomial tree. Will it cause arbitrage? Does anyone have reference paper or book ...
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0answers
50 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^{...
3
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1answer
675 views

Ho-Lee Model; Please explain

I'm having trouble with the Ho-Lee model for short rates and differentiating between how to find the values for the free parameter λ versus using the model to predict future rates. The Ho-Lee model ...
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0answers
833 views

Calculating Greeks using BinomialTree in Matlab [closed]

section 1. Calculating sensitivity of the price of derivatives American or European option using binomial tree model section 2. Calculating first order greeks the code compiles till this point ...
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2answers
75 views

Binomial representation of stochastic processes

It is common knowledge that a random walk can be represented in the form of a binomial process. Is it possible to represent any generic stochastic process (including non-linear) of the form $dX=adt+...
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1answer
93 views

Binomial pricing model: When the Cox-Ross-Rubinstein assumption is not arbitrage-free

I understand that in an arbitrage-free Binomial model, we assume that $S_{t+1} = S_t \cdot u$ in the event of an up-jump and $S_{t+1} = S_t \cdot d$ in the event of a down-jump. We call $u$ and $d$ ...
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2answers
467 views

Estimate simple option price without a calculator

I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it. If you have an European ...
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1answer
824 views

Binomial tree vs trinomial tree in pricing options

Very new to pricing models. Is there a general guideline when to use binomial tree and when trinomial tree is preferred? As far as I know, unlike binomial tree, trinomial tree only gives a range ...
0
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1answer
41 views

Replication of the portfolio in single step binomial model

I would be grateful if anyone would comment how to construct this: Assume $S_{i}^k$ is a stock price at time level $i$ and at price level $k$. Assume option is written on $S$ with a a payoff $f_{T}^{...
3
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2answers
99 views

Time 0 value of an American Put in Cox-Ross-Rubinstein model

This is a question from a problem sheet which I have handed in and have solutions for. The only examples of this in class I have seen are examples where the interest rate is 0. "Consider a Cox-Ross-...
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2answers
742 views

How to price an option on a dividend-paying stock using the binomial model?

This is actually an exercise from a course. But I don't completely understand the wording of the question. A stock is now trading at 100 dollars. Its price over the next 6 months evolves as a two ...
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2answers
245 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
2
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1answer
1k views

How to draw a binomial option tree graph?

I am writing a paper and need to create a png or jpeg file for binomial option price tree. In the past I would have used the tikZ package in LaTeX, but that won't work in this case. So I want a ...
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1answer
164 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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3answers
545 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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2answers
165 views

Is stock price priced in the uncertainty?

Consider a one step binomial tree model for stock price. The classical setup is as below: At time $t=0$, the stock price is $S_0$. At time $t=1$, the stock has probability $p$ to jump up to price $...
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2answers
123 views

Standard Deviation as listed in Rebonato's Volatility and Correlation: Binomial Replication 2.3.4 Worked-Out Example

I am reading Rebonato's Volatility and Correlation (2nd Edition) and I think it's a great book. I'm having difficulty trying to derive a formula he used that he described as the expression for ...
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1answer
315 views

A question about pricing convertible bond with two different underlying assets

I have a question regarding the pricing of convertible bond. If I value the convertible bond with two different underlying assets, how can I incorporate two volatility and the correlation in the ...
3
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2answers
385 views

How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model

Given that $e^{r\Delta t}(u+d)-ud-e^{2r\Delta t} = \sigma^2\Delta t$ I would like to show that $u=e^{\sigma\sqrt{\Delta t}}$ I know I must somehow use Taylor's approximation $e^x = 1 + x + \frac{...
3
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1answer
195 views

Minimum Variance Hedge Ratio in Binomial Framework

In order to find the minimum variance hedge ratio when holding a portfolio of vanilla call options and hedging with stock, you can do an OLS regression. In a binomial model framework, given ...
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0answers
89 views

Approximating the PDE price of an option with a binomial model

I'm trying to replicate, with a binomial model, the price of an option obtained with a PDE. It doesn't really work, so I was wondering, if there are some caveats when doing that. The PDE model use a ...
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1answer
697 views

How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model. Originally I thought the path dependency exists because in binomial tree model, we will ...
0
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1answer
242 views

How to construct the binomial model for European option?

The annual interest rate is 5.3% and the annualized volatility of a non-dividend paying stock over the next six months will be 12.5% (annualized). i) Construct binomial trees of 5, 10 and 30 periods ...
3
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1answer
145 views

Binomial lattice convergence

How do I measure how quickly a binomial lattice converges to an option value as the number of steps is increased? I'm charting option value versus number of steps for various binomial lattice models ...