# Tagged Questions

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1answer
230 views

### How to handle coupon payments when pricing a bond with an embedded option?

I'm using a binomial tree to price a bond that has an embedded call or put option. On every node that has a coupon payment, do you include the coupon payment then max/min out the value, or do you max/...
1answer
440 views

### Fixed income modeling

I am currently working on my research paper and trying to explain a two-dimensional variable: volume and instrument of corporate debt financing. Independent variables that I believe must be included ...
2answers
598 views

### Demonstration of Ito's correction term/lemma in binomial tree

I am preparing an undergraduate QuantFinance lecture. I want to demonstrate the ideas of Ito's correction term and Ito's lemma in the most accessible manner. My idea is to take the "working horse" of ...
1answer
568 views

### How to use binomial tree for portfolio of equity products

How can I use a binomial tree to price a European option that's based on a portfolio of equity products? I have volatility and correlation matrix of all underlying products? Looking for a formula ...
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 ...
2answers
866 views

### Is the binomial model wrong?

In the standard MBA one-period binomial model, the value of an option is $v = \frac{1}{R}\bigl(\frac{u - R}{u - d}V(sd) + \frac{R - d}{u - d}V(su)\bigr)$ where $R$ is the realized return over the ...
2answers
710 views

### BDT model implementation

I am looking for a nice and readable description of how to implement BDT model: $d log(r(t)) = [\theta(t)-\frac{\sigma'(t)}{\sigma(t)}log(r(t))]dt + \sigma(t) dW$. I assume I already have steady-...
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 ...
1answer
73 views

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 $S_d=90$, ...
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 ...
1answer
681 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 ...
1answer
255 views

### Value of option-free instruments with a short-rate model vs the spot curve

You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly. Alternatively, apparently you can use a single-factor short rate model in a ...
1answer
75 views

1answer
611 views

### What is the difference between the methods (listed in content) in pricing convertible bond?

To price the convertible bond, one of the models is the bond plus equity option method. That is, the value of convertible bonds is evaluated by finding the value of the straight bond and the value of ...
1answer
587 views

### Risk neutral probability in binomial short rate model assumed to be 0.5?

This should be a basic question but I have not been able to find a satisfying explanation. In the simplest binomial model, the risk neutral probability is computed using the up/down magnitude and the ...
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 $0 < d < 1 + r < u$. ...
1answer
316 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 ...
0answers
138 views

### How to simulate a Geometric Binomial Process with state/tie dependent increments?

I want to simulate a geometric binomial process with state/time dependent increments. So the model is given by \begin{align}R_t=\frac{X_t}{X_{t-1}}\end{align} \begin{align}P(R_t=u)=p(X_{t-1},t) \...
2answers
472 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 ...
1answer
698 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 ...
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 ...
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 ...
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?
2answers
124 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 ...
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 ...
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 ...
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 ...
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 ...
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?
2answers
746 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 ...
3answers
547 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 ...
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 ...
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 ...
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 ...
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^{...
0answers
835 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 ...