# Tagged Questions

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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### 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 ...
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### 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{...
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### 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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### 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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### 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 ...