New answers tagged binomial-tree
1
It does not need to be so always. You can always relax that assumption and come with the pricing by using the fundamental principles. As @Kermittfrog and @Dimitri Vulis commented it is just a matter of convenience for calculations and is called the recombining property.
You can find an example in this link here which does not use this assumption to price the ...
0
I can't believe how long it took me, but I finally found (almost) all the answers and I found my mistake.
This paper: Derivation of the Up and Down Parameters of the Binomial Option Pricing Model by R. Stafford Johnson and James E. Pawlukiewicz (1998) https://www.jstor.org/stable/41917712 does what I tried to do and from there I realized that setting $u*d=1$...
1
Earlier in the chapter, Wilmott derives the equation
$$V = \frac{V^+ - V^-}{u-v} + \frac{uV^- - vV^+}{\left(1 + r\delta t\right)\left(u - v\right)}$$
from the non-arbitrage argument $\delta\Pi = r\Pi\delta t$, where $\Pi = V - \Delta S$.
If you then use the expansions for $u$ and $v$,
$$u \approx 1 + \sigma\sqrt{\delta t} + \frac{1}{2}\sigma^2\delta t \\
v \...
2
Since dividends and interest rates mature annually and the time of expiry is two years, we can model the option as a two-step binomial tree, structured as the one in figure:
Data from OP question:
$S_0 = 45$ current price of the underlying $S$; $\hspace{2.5cm}$ $\sigma = 0.2\;\text{per annum}$ volatility of $S$;
$r = 0.02\;\text{per annum}$ interest rate; ...
1
Our company chose to use FDM for calculating American Options. According to colleagues I talked with, binomial trees are efficient and accurate When there are a small number of option values. But it has a couple of weaknesses:
(1) Binomial tree models are generally inefficient when cash dividends should be taken into consideration;
(2) Compared with FDM, ...
0
If I may draw your attention the answer I gave on this post here: "risk neutral probability for stock with continuous dividend" There I explain how the binomial tree is set up originally, and there you can see why you simply work with $U=e^{\sqrt{\Delta t}\sigma}$ and $D=U^{-1}$ as a modeller's choice. The influences from the dividend yield (...
-3
The dividend yield is already included when computing $S_u$ and $S_d$. Please check the formula (10.9) in the link below that gives u and d using risk free rate, dividend yield and volatiltiy:
http://www.princeton.edu/~markus/teaching/Eco467/yyy
In case you want to test your delta computation, you can use this website that includes binomial tree for american ...
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