Chapter Proposal submission form
1. Provisional title of the proposed manuscript:
2. Author details
Scientific Title: Doctor in Business Management
Full Name: Pedro Henrique Melo Albuquerque
Affiliation: University of Brasilia
Position: Adjunct Professor
3. Co-authors (include all your co-authors if possible at this stage)
3.1.
Scientific Title: Master’s in Business Management
Full Name: Leonardo Melo Bosque
Affiliation: University of Brasilia
Position: Research Assistant
3.2.
Scientific Title: Master’s in Business Management
Full Name: Pedro Alexandre Moura Barros Henrique
Affiliation: University of Brasilia
Position: Research Assistant
4. Keywords (enter min.5):
PIN, Probability of Informed Trading, Asymmetry of Information, Private Information,
Market Microstructure Model.
5. Define your subject area:
Quantitative Finance.
6. Write a short description of the chapter, clearly explaining the aims topics research methods
and key results of the chapter.
Introduction (max 150 words) :
One of the main methodologies that provides a mathematical formulation for the
occurrence of informed trading in a competitive financial market is the PIN model. During the
late 1980s and over the 1990s, a series of papers were published by Easley et al (1987, 1996,
1997(a), 1997(b), 2002) showing the theoretical demonstrations of a market microstructure
model capable of giving evidence about the existence of informed trading on the US stock
market.
Because of its solid theoretical foundation, the PIN model has been well received by
academic researches and has been used in many academic papers. According to Nyholm (2002)
the PIN model has been adopted in many financial areas such as the division of shares (Easley,
O’hara and Saar, 2001), the relation between information and expected stock’s returns (Easley,
Hvidkjaer and O’hara, 2002), the role of anonymity in the trading process (Gramming, Shcierek
and Theissen, 2001) and so forth.
Body - research methods (max 150 words):
Consider that in the beginning of a trading day an offered asset could be under the
influence of a relevant informational event that is capable of modifying its market value. A
graphical example of this process is given by the tree diagram below:
Figure 1: Tree diagram of the trading process
Suppose that information events are independently distributed and occur with
probability 𝛼. Those events could be good news events (that could increase the value of the
asset) with probability 1 − 𝛿 or bad news with probability 𝛿. Consider that uninformed buyers
and uninformed sellers arrive in the market according to independent Poisson process with an
arrival rate of 𝜀𝑏 and 𝜀𝑠 , respectively, and informed traders arrive in the market under an arrival
rate of 𝜇.
A proxy to identify that a trade is information-based, is given by:
𝑃𝐼𝑁 =
𝛼𝜇
𝛼𝜇 + 𝜀𝑏 + 𝜀𝑠
The equation above indicates the fraction of the arrival rate of information-based orders
with the arrival rate of all orders. Its parameters can be estimated by the optimization of the
likelihood function below:
𝑒 −𝜀𝑏 𝜀𝑏 𝐵 𝑒 −𝜀𝑠 𝜀𝑠 𝑆
𝑒 −𝜀𝑏 𝜀𝑏 𝐵 𝑒 −(𝜀𝑠+𝜇) (𝜀𝑠 + 𝜇) 𝑆
+ 𝛼𝛿
𝐵! 𝑆!
𝐵! 𝑆!
𝑒 −(𝜀𝑏+𝜇) (𝜀𝑏 + 𝜇)𝐵 𝑒 −𝜀𝑠 𝜀𝑠 𝑆
+ 𝛼(1 − 𝛿)
𝐵! 𝑆!
𝐿(𝐵, 𝑆|𝜃) = (1 − 𝛼)
Conclusion- key results (max 150 words):
In order to exemplify how the PIN model works in a real situation, we verified the price
series of SPY, the S&P 500 exchange trade fund (ETF) between 02/02/2016 to 05/03/2016. We
analyzed SPY’s data of buys and sells orders according to the PIN model.
The optimization of the PIN likelihood function resulted on these estimates for the
vector θ = (α, δ, εb , εs , μ) = (0,68; 0,37; 244,54; 253,73; 93,98).
According to parameter α, the probability of occurring an information event with SPY’s
data is 0,68. So, according to the previous estimated parameters it is possible to calculate the
PIN:
PIN ≅ 0,1146
Therefore, the probability of observing informed trades with S&P 500 exchange trade
fund on the analysed period was 0,1146. This number has been also interpreted as a proportion:
the value of PIN indicates that 11,48% of the analysed orders were made by informed traders.
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