Questions tagged [binomial-tree]
The binomial-tree tag has no usage guidance.
2
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2answers
100 views
Approximation of CRR as Black Scholes PDE
I have a formula for intermediate european option price calculated at, say, m-th possible tree value.
$S_n^{(m)}$ is a price at node after going up $n$ times and down $n - m$ times
$V(S_n^{(m)}, t + ...
3
votes
1answer
89 views
Binomial Trees vs FDM
Binomial trees as the number of time steps is increased (or equivalently as the time step tends to 0), converge to the exact value for an option.
So why do people use FDM for pricing options (for ...
0
votes
2answers
87 views
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 ...
2
votes
1answer
88 views
Binomial Tree Option Pricing Model. Lets talk dividends and futures
I am writing an option pricing model for production use. Its not for arb or anything so it doesn't need to be 100% as accurate as possible. Just good enough for "what happens to my book if we jump 10 ...
3
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0answers
62 views
Is there a more efficient data structure to implement binomial trees than 2d array?
I'm just curious what is the "industry standard" for implementing a binomial tree (if "standards" exist in this case). For simplicity, let's just talk about the simplest trees with recombining nodes.
...
1
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0answers
45 views
Binomial Model Implementation Trouble - American and European options come out equal
I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options ...
1
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0answers
29 views
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 ...
3
votes
1answer
259 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:
$$u = e^{\sigma\...
-2
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1answer
69 views
How to calculate riskless profit out of call options?
I'm having trouble with working out a question that I can't currently ask my lecturer as they're away. Hoping for some help here with why the answer is (a).
A stock price is currently \$40. It is ...
0
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0answers
27 views
Pricing European Call on Coupon Bond in Lattice
What's the best approach to pricing a par call option on a coupon paying bond? Is it to discount the greater of the price and strike through the lattice? And for this, is the price used the dirty or ...
2
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0answers
44 views
Interest model calibration and binomial trees
Are there any good books for beginners on calibrating interest rate models and creating binomial trees based on these interest rate models and using them in pricing
1
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1answer
32 views
calibrating two (or X) equity diffusion trees
I have two equities S1 and S2.
Each one follows the following tree evolution :
$$S_1 \rightarrow \left \{
\begin{matrix} S_1 (1+u_1) & \text{with probability } p_1 \\
S_1 (1-d_1)...
0
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0answers
58 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 ...
0
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0answers
61 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 $$\...
2
votes
1answer
60 views
Optimal number of nodes for binomial lattice?
Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
-4
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1answer
124 views
What is martingle measure with risk free asset in numeraire or stock price in numeraire [closed]
What is martingle measure with risk free asset in numeraire or stock price in numeraire
1
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1answer
55 views
Is this the correct shape of Cox-Ross-Rubinstein's recombining binomial tree?
Most texts display the binomial tree like this:
However when I run my calculation the tree in reality looks like this:
Does this look correct to you? I am using these standard formulas:
$$u=e^{\...
1
vote
1answer
155 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 ...
0
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1answer
124 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 ...
1
vote
1answer
257 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
votes
1answer
412 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
88 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=...
6
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1answer
399 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 \...
0
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0answers
129 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
votes
1answer
175 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 ...
0
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2answers
315 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 ...
1
vote
1answer
206 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 ...
-1
votes
1answer
197 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 = ...
1
vote
0answers
90 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 ...
-4
votes
1answer
204 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
votes
1answer
230 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
votes
1answer
181 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
351 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....
-1
votes
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
votes
0answers
219 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
votes
1answer
99 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 ...
0
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1answer
307 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 ...
0
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1answer
174 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
...
1
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1answer
153 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 ...
0
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1answer
346 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 ...
4
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0answers
313 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
votes
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:
$$Pe^{\gamma h} = S\Delta e^{\alpha h} + \...
0
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3answers
576 views
Pricing of convertible bonds
I'm trying to evaluate a convertible bond using the structural approach : the price of convertible bond is an option (call) on the firm value. We suppose that the firm value is equal to the sum of the ...
1
vote
1answer
275 views
Is Asian option in binomial asset pricing model a martingale?
Since it does not have a closed form solution for the price, it's unlikely to be a martingale. However, on the other hand, if we represent the price as a function of the current stock price and the ...
1
vote
1answer
84 views
Reference for option pricing, binomial multi-period model using martingales and conditional expectations
The title basically says it all. I am looking for a reference text on the pricing of options in a binomial multi-period model. It should be mathemathically rigorous using martingales and conditional ...
3
votes
1answer
318 views
Deriving $u$ and $d$ coefficients using binomial tree approach
From Hull's book when deriving coefficients of up and down movements, $u$ and $d$, of a stock price using binomial tree approach, at some point we get the following equation:
$$e^{\mu\Delta t}(u+d) - ...
1
vote
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
votes
1answer
3k 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=...
1
vote
3answers
186 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 ...
1
vote
1answer
294 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 ...
