# Questions tagged [binomial-tree]

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### Convergence in the CRR model

Under certain conditions, the option price of the CRR (Cox-Ross-Rubinstein) Binomial model converges to the Black-Scholes price as the maximal step size of the partition converges to zero (i.e. a ...
132 views

### Why do we simply assume the risk neutral probabilities to be "0.5"?

I am aware that there was a question similar to this but my question is a little different. Firstly, in context of binomial short rate, why do we simply assume the risk neutral probabilities p=1-p=0.5?...
299 views

### Delta-hedge experiment of American Put option

I am trying to run a delta-hedge experiment for an American Put option but there's a (systematic) hedge error which I cannot seem to understand or fix. My implementation is found in the bottom of this ...
46 views

### How to fit (find $u$) in the binomial options pricing model?

In the binomial tree options pricing literature, I see frequent reference to the definition that $$u = e^{\sigma \sqrt{n/t}}$$ I think I understand the model, but how do we derive this, i.e. how do ...
1 vote
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### Optimal exercise time in Binomial model

Let (B, S) a multi period binomial model that is arbitrage free. I would like to prove that the unique optimal exercise time for an American call option is the maturity time T. My idea is to prove ... 29 views

### Risk Neutral Pricing - Why the Risk Free rate for Risky security (Intuition) [duplicate]

I am struggling with this concept of risk neutral probabilities. My understanding of how a risk neutral pricing framework works is as follows: (discrete, binomial lattice for simplicity) I do not know ...
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### Binomial Option Pricing [duplicate]

We are currently working on the "standard" binomial option pricing. If the market agrees that a specific stock will raise by, let's say, 90% next period. At first glance, this seems to have ...
134 views

### Binomial tree convergence tree towards BS equation - Struggle with a limit

I am trying to prove that the Binomial tree pricing method converges towards the Black and Scholes model, but I am struggling on a specific step. I don't understand how the limit of p*(1-p) is ...
30 views

### Binomial model returning linear IV smile when estimating for IV

So I've been attempting to align the Binomial model with the American put option price so that I can calculate accurate Greeks taking into account the optimal exercise boundary of these options. The ...
31 views

### How to price an american put option on a dividend-paying stock? [duplicate]

There is no Black Scholes formula for the value of an American put option on dividend paying stock eithe has been produced ? Should I use the binomial model ?
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### One Period Risk Neutral Probability for Caplet

I am studying some financial modeling put together by the Society of Actuaries in the USA. In it, the following practice problem was given: Find the Risk Neutral price of an at-the-money interest ...
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### Time steps in CRR Binomial Option Pricing for American Options

how do you determine the time steps required as inputs to the Cox Rubinstein Binomial Option Pricing model when trying to determine the fair price of an American option? Most textbooks and literature ...
1 vote
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1 vote
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### Binomial Pricing Model d and u

In the binomial pricing model, why do the magnitude of the up factor $(u)$ and down factor $(d)$ have to be multiplicative inverses? I have read from multiple sources that the reason for this is that ...
208 views

### Binomial Option pricing, paper by John C. Cox, I don't understand the calculation / choice of u.d.q

[EDIT] Question is answered, just cleaned up some clerical errors in the formulas. [EDIT] Based on the comment I got, let me clarify, I am not stuck on the relationship between the binomial model vs ...
1 vote
201 views

### Risk neutral probabilities in binomial option pricing with discrete dividends — whose argument is correct?

In trying to discover more about pricing American options with dividend payouts, I found the the post linked here. I notice two disagreeing answers when it comes to determining the replicating ...
1 vote
2k views

### How to price an European put option using binomial model with dividend yield?

The initial stock price (S0) is 45, the stock volatility is 0.20 (20% per annum), and the risk-free rate is 0.02 (2% per annum). Consider a European put option whose strike price is equal to 30, with ...
1 vote
406 views

### Delta hedging for an American call option on a stock with a continuous dividend yield

Let the dividend yield be $\delta$ and $C_u, C_d$ and $S_u, S_d$ be the up and down values for the stock and the call respectively over the period $\Delta t$. In Hull and all other resources I've ...
1 vote
288 views

### Practical implementation of Vellekoop-Nieuwenhuis model/interpolation

Have read the 2006 VELLEKOOP-NIEUWENHUIS paper (Efficient Pricing of Derivatives on Assets with Discrete Dividends) (Download) many times re Discrete dividends on American Options, but remain baffled ...
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1 vote
132 views

### Calculating European call option, the Bjork way

We have a 3 period binomial tree with values: ...
1 vote
216 views

### Expected life (Fugit) of American Option

How can I use the binomial tree pricing method for American options to determine the expected time of exercise for the option (or "Fugit")? In particular, how would I modify the algirithm ...
3 step binomial tree process with $S_0=4,u=2,d=0.5,r=0.25.$ Determine the probability p and q such that the stock price process is a martingale (i.e. $E[S3]=S_0)$ I know P = 1/3 and Q = 2/3 but having ...