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May 10th, 2022, 3:25 am
Forum: Technical Forum
Topic: How to estimate this stochastic model?
Replies: 7
Views: 1277

### Re: How to estimate this stochastic model?

Thank you so much for your suggestions. Actually this model appears frequently in Prof. Alvaro Cartea’s high frequency trading paper. I need to figure out a way to calculate $\alpha_t$ and estimate parameters in real trading efficiently. Maybe I can some approximations of this model by following t...
May 9th, 2022, 11:04 am
Forum: Technical Forum
Topic: How to estimate this stochastic model?
Replies: 7
Views: 1277

### Re: How to estimate this stochastic model?

Is the left hand of your second equation correct? Did you mean to include dt in it?
sorry, that's a typo. You are right. How can I edit the equation after submission?
May 9th, 2022, 9:53 am
Forum: Technical Forum
Topic: How to estimate this stochastic model?
Replies: 7
Views: 1277

### How to estimate this stochastic model?

$$dS_t=\alpha_tdt+\sigma_1dW^1_t$$ $$d\alpha_tdt=-\xi\alpha_tdt+\sigma_2dW^2_t$$ where $S_t$ is the observable price; $\alpha_t$ is the unobservable trend; $dW^1_t$ and $dW^2_t$ are two Brownian motions. I think $S_t$ can be sampled with regular discrete time, so that this model can be fo...
February 14th, 2022, 6:45 am
Forum: Technical Forum
Topic: How to get this limit order fill probability?
Replies: 0
Views: 1905

### How to get this limit order fill probability?

I find this power class limit order fill probability $$h(\delta)=\frac{1}{1+(\kappa\delta)^{\gamma}}$$  where $\delta$ is the distance to mid price;$\kappa$ and $\gamma$ need to be calibrated from data   . in https://tspace.library.utoronto.ca/bitstream/1807/68262/1/Ricci_Jason_201411_PhD_thes...
August 11th, 2021, 4:51 am
Forum: Numerical Methods Forum
Topic: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?
Replies: 6
Views: 2655

### Re: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?

I can think of one more problem. Ornstein-Uhlenbeck process has been used to study interday mean-reversion. Usually daily data is used to estimate model parameters. But can we use millisecond level or minute level data to study interday mean-reversion? If not, it seems that, for practical financial ...
August 10th, 2021, 2:58 am
Forum: Numerical Methods Forum
Topic: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?
Replies: 6
Views: 2655

### Re: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?

$\alpha_t$ still tends to be infinity even in the case of volume weighted mid-market price.
August 9th, 2021, 6:53 am
Forum: Numerical Methods Forum
Topic: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?
Replies: 6
Views: 2655

### Re: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?

Thank you all for your suggestions. I can calibrate the model to get close parameters with simulated data sampled at difference frequencies. So I think the parameter estimation should be correct. A weighted mid-market prices based on available volumes on best bid and ask seem improve the result slig...
August 5th, 2021, 11:20 am
Forum: Numerical Methods Forum
Topic: Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?
Replies: 6
Views: 2655

### Is it necessaet to resample data before Maximum likelihood estimation of mean reverting processes?

I am working on high frequency data and try to implement an Ornstein-Uhlenbeck mean reverting process to model short-term momentum $\alpha$.  $${d\alpha_t=\eta(\theta-\alpha_t)dt+\sigma dB_t}$$ The timestamp interval between each best bid-ask sample is 0 - 30 milliseconds, irregularly.  I am con...
June 29th, 2021, 3:21 am
Forum: Numerical Methods Forum
Topic: How to calibrate this stochastic model?
Replies: 4
Views: 2455

### Re: How to calibrate this stochastic model?

Thank you so much. I find the problem. Eq (4.5)  in your reference is clear.
June 28th, 2021, 12:23 pm
Forum: Numerical Methods Forum
Topic: How to calibrate this stochastic model?
Replies: 4
Views: 2455

### How to calibrate this stochastic model?

I meet some problems when calibrating the stochastic model, given in Eq(3.2) and appendix (E.2) of thesis: https://tspace.library.utoronto.ca/bitstream/1807/68262/1/Ricci_Jason_201411_PhD_thesis.pdf I give a simplified version here. $$d\lambda_t=\beta(\theta-\lambda)dt+\eta dM$$ where M is a poisson...
June 28th, 2021, 11:32 am
Forum: Numerical Methods Forum
Topic: Is it necessary to piecewisely fit power-law distribution in empirical data?
Replies: 2
Views: 2395

### Re: Is it necessary to piecewisely fit power-law distribution in empirical data?

I see. Thank  you so much.
June 23rd, 2021, 2:35 pm
Forum: Numerical Methods Forum
Topic: Is it necessary to piecewisely fit power-law distribution in empirical data?
Replies: 2
Views: 2395

### Is it necessary to piecewisely fit power-law distribution in empirical data?

In AARON CLAUSET’s paper power-law distributions in empirical data: ‘’In practice, few empirical phenomena obey power laws for all values of x. More often the power law applies only for values greater than some minimum x_min. In such cases we say that the tail of the distribution follows a power law...
December 10th, 2020, 2:44 pm
Forum: Technical Forum
Topic: Is there any mathematical tool to solve this HJB-like problem?
Replies: 0
Views: 2839

### Is there any mathematical tool to solve this HJB-like problem?

In typical stochastic control problems, the control variables in HJB equation are usually continuous or discrete values in action space. However, what if the action space is constructed by unknown continuous functions? For example, in market making problem, the Avellaneda-Stoikov model calculates th...
June 15th, 2020, 7:37 am
Topic: How to interpret the switching between price and time priority of the limit order?
Replies: 5
Views: 5740

### Re: How to interpret the switching between price and time priority of the limit order?

I have no good way to handle the wide spread and manipulation issues now. Maybe those are real challenges and I have to expect a long process of trial and error.
June 12th, 2020, 2:17 pm
Topic: How to interpret the switching between price and time priority of the limit order?
Replies: 5
Views: 5740

### Re: How to interpret the switching between price and time priority of the limit order?

I find the queues are frequently long enough. A market making strategy for large tick asset may be suitable.
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