User WHYisTHAT - Quantitative Finance Stack Exchange most recent 30 from quant.stackexchange.com 2023-02-09T01:15:28Z https://quant.stackexchange.com/feeds/user/46897 https://creativecommons.org/licenses/by-sa/4.0/rdf https://quant.stackexchange.com/q/65911 0 how can properties of transition matrix be applied in the transcation cost of option WHYisTHAT https://quant.stackexchange.com/users/46897 2021-07-07T04:38:39Z 2021-07-07T04:38:39Z <p>I am currently reading the PP BOYLE's article ' Option Replication in Discrete Time with Transaction Costs' written in 1992. Here is one place i couldn't figure out:</p> <p><a href="https://i.stack.imgur.com/UslXB.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/UslXB.png" alt="enter image description here" /></a></p> <p><a href="https://i.stack.imgur.com/EBGxp.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EBGxp.png" alt="enter image description here" /></a></p> <p>Where does that <span class="math-container">$\widehat{p}$</span> come from? And the <span class="math-container">$\bar{P} = \begin{pmatrix} \bar{p_{u}} &amp; \bar{p_{d}}\\ 1-\bar{p_{u}} &amp; 1-\bar{p_{d}} \end{pmatrix}$</span></p> <p>What are <span class="math-container">$X_{i}$</span> and <span class="math-container">$\bar{P}^{i-1}$</span> ?</p> <p>Thank you, this is my first time reading academic paper, i tried to google the transition matrix and Markov chains with expectations but the result is not useful.</p> https://quant.stackexchange.com/questions/65911/how-can-properties-of-transition-matrix-be-applied-in-the-transcation-cost-of-op?cid=93409 Comment by WHYisTHAT on how can properties of transition matrix be applied in the transcation cost of option WHYisTHAT https://quant.stackexchange.com/users/46897 2021-07-07T08:31:48Z 2021-07-07T08:31:48Z Thank you. Do you know what does the $\bar{P}^{(i-1)}$ mean? Based on the author&#39;s definition of $\bar{P}$, can i say that the first column of $\bar{P}^{(i-1)}$ means the probability distribution of $X_{i}$ if $X_{i-1} = ln(u)$ and the second column means the probability distribution of $X_{i}$ if $X_{i-1} = ln(d)$