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Questions tagged [binomial-tree]

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How to check if arbitrage is possibile in a recombining Binomial tree

Consider the recombining Binomial tree below; knowing that: $S_0 = 100$ is the cost of an asset at $t=0$ (now), $∆t$ is the distance between two time points, e.g. $∆t = 0.5 =$ six months, $...
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0answers
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How does LR binomial Tree Model handle input values which would cause NA result?

I am using C++ to implement a LR binomial Tree algorithm to price American options, but I find it would constantly generate invalid output, which is "nan" value in C++, although the input value seems ...
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1answer
141 views

Why my implementation of CRR model does not converge?

Recall that CRR (Cox-Ross-Rubinstein) model for option pricing is the usual binomial tree model with $u$ (up-factor) and $p$ (one of the risk-neutral probabilities) defined as follows: $$u = e^{\sigma\...
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1answer
54 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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0answers
23 views

Pricing European Call on Coupon Bond in Lattice

What's the best approach to pricing a par call option on a coupon paying bond? Is it to discount the greater of the price and strike through the lattice? And for this, is the price used the dirty or ...
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0answers
35 views

Interest model calibration and binomial trees

Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
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1answer
30 views

calibrating two (or X) equity diffusion trees

I have two equities S1 and S2. Each one follows the following tree evolution : $$S_1 \rightarrow \left \{ \begin{matrix} S_1 (1+u_1) & \text{with probability } p_1 \\ S_1 (1-d_1)...
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0answers
51 views

OAS of a perpetual bond

How is the OAS (Option Adjusted Spread) of a perpetual bond with embedded option calculated? My specific point of doubt is the maturity that has to be used to construct the binomial tree for ...
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51 views

Binomial Representation Theorem proof, Baxter and Rennie

I am currently reading Financial Calculus of Baxter and Rennie and have one question regarding proof of Binomial Representation Theorem. In the text, we assume that increments of $N$ martingale are $$\...
2
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1answer
54 views

Optimal number of nodes for binomial lattice?

Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
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1answer
105 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
52 views

Is this the correct shape of Cox-Ross-Rubinstein's recombining binomial tree?

Most texts display the binomial tree like this: However when I run my calculation the tree in reality looks like this: Does this look correct to you? I am using these standard formulas: $$u=e^{\...
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0answers
138 views

Difference between binomial and CRR model

What is the difference between a binomial and CRR model. I know what a binomial model is, but in CRR also there are subintervals where prices change like a one period binomial. I think I haven't ...
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1answer
128 views

Convertible Bond in Foreign Currency - Quanto Adjustment

I need to value the following convertible bond: The bond notional and interest is denoted in USD, but is convertible into Euro denominated equity. Normally, I would value such a bond with a ...
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0answers
86 views

FX rates and Binomial Model

I was confused when doing my homework assignment in FE class. "Consider a one-period binomial model for a foreign exchange rate. At time 0, the exchange rate is S0. At time T, the exchange rate is ...
0
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1answer
101 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
203 views

Arbitrage strategies in Rubinstein's binomial tree one-step

Suppose that the current stock price is $S_0=20$ and the call option price with no arbitrage is $c=0.633$. Knowing that the expiry stock price can be $S_T=22$ with call option price $1$ or $S_T=18$ ...
2
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1answer
304 views

What discount rate to use when valuing binomial option with real probabilities

We all know that we can use the argument of risk-neutrality and the law of one price, to get the option value without the real world probability. However, suppose if we use the real world probability ...
2
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0answers
82 views

Second order convergence for the Leisen-Reimer tree

I have a question about this paper "Achieving higher order convergence for the prices of European options in binomial trees" by Mark Joshi, (Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
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1answer
365 views

Black Derman Toy model: from tree to differential equation

The Black Derman Toy model of interest rates is usually introduced as the model governed by the stochastic differential equation: $$d \ln r = \left[\theta(t) + \cfrac{\sigma'(t)}{\sigma(t)}\ln r \...
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0answers
116 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 ...
0
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1answer
162 views

Put-Call Parity on Currency and Binomial Trees

I tried solving the below problem without knowing the shortcut of thinking about this in terms of a put versus a call. I can't seem to arrive at the correct answer using my method and I'm wondering ...
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2answers
298 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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1answer
188 views

Previsibility in Binomial Representation Theorem

I'm working through Baxter and Rennie's "Financial Calculus: An Introduction to Derivative Pricing". It was going very well and I've actually found it an easy read up until the point where they ...
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1answer
172 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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0answers
81 views

Binomial Option Pricing - Hedging

I'm working on a project which is requiring me to test Binomial option pricing on real data. So far I have just been working with test data and my option pricing method works fine. The issue I'm ...
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1answer
177 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 ...
3
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1answer
207 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 ...
3
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1answer
163 views

How to price the American style Asian option with recent N day average

How to price the American style Asian option with recent N day average, for example, we exercise at t day, then the payment is $$...
2
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2answers
323 views

Risk neutral probabilities for foreign currency exchange rate

Suppose that there are two currencies INR(domestic) and USD(foreign). Let the for exchange rate be S_inr. Using historical data, one can find out the volatility. For example, assume that, S_inr=60,σ=0....
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2answers
1k views

Trinomial tree VBA code [closed]

I am studying binomial trees and I'm implementing them in VBA to see their convergence to the BS model. I searched 3-4 hours in the web; the only good site I know is Volopta. Very simply question by ...
2
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0answers
197 views

Building implied binomial tree with American input options

i want to build an implied volatility binomial tree with American input options, so the setup is the following: 1) We know the market Price P of the American Put $P_{am}(t_i,K)$, where $t_i$ is the ...
2
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1answer
95 views

Explanation on the application of CLT in bionomial tree model

We have a stock price binomial tree model of $n$ steps, with step length $\Delta t=T/n$, stock price volatility $\sigma$ s.t. $u_n=e^{\sigma\Delta t}$ and $d_n=1/u_n$, and the risk neutral probability ...
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1answer
277 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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1answer
151 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
141 views

Clarification on the Black-Derman-Toy model regarding measuring time and notation

I'm self-studying BDT and I'm having some difficulty with what is meant by the "short-rate volatility parameter for the first year" and "the short-rate volatility parameter for the second year," as in ...
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1answer
304 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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0answers
281 views

binomial trees and finite differences

I was reading Tavella Randall book and their explanation why binomial trees are a particular example of finite differences. I started having additional questions. So, they way they do that is saying ...
2
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1answer
161 views

Calculating the annual return on an option using a replicating porfolio

I am self-studying and encountered the following problem: My idea was to calculate the price of the put using a replicating portfolio, then use the formula: $$Pe^{\gamma h} = S\Delta e^{\alpha h} + \...
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3answers
543 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 ...
1
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1answer
262 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
83 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 ...
3
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1answer
267 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
105 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
2k 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
184 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
272 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
4k 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 ...
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2answers
355 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
508 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 ...