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How to formalize and validate models of fundamental factors involved price changes?

Suppose you have some stock X, and its price can be considered a time series. You believe that real-world number Y, like industry or government statistics, which is also time series, influences stock ...
uhbif19's user avatar
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1 answer
99 views

Incomplete market

How to prove that market with one risky asset $S_t$ and interest rate $r = 0$ is incomplete: $$dS_t = S_t (\mu dt + \sigma_t dW_t^{1}), \quad S_0 = 1,$$ $$\sigma_t = 1 + |W_t^{2}|,$$ $W_t^{1}$ and $...
Strike's user avatar
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1 answer
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Is stochastic control with the HJB equation used in market making/algo trading at institutions?

In chapter 5 of https://www.maths.ed.ac.uk/~dsiska/LecNotesSCDAA.pdf, they use stochastic control and the Hamiltonian Jacobi Bellman (HJB) equation in attempt to measure bid-ask spreads and optimal ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
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1 answer
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Assuming perfect liquidity

I encountered this phrase in the textbook by Hans Schumacher For the purposes of this textbook, a mathematical model for a financial market consists of a specification of the joint evolution of ...
Bio's user avatar
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1 answer
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Is beta stable over time for individual securities?

I'm reflecting on whether historically estimated $\beta$ is a "good" estimator of future $\beta$. Consider the problem as follows: Let $r_1$, $r_2$, ...., $r_{36}$ be the last 36 months of ...
MYK's user avatar
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2 votes
1 answer
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What are the parameters’ units in the Avellaneda and Stoikov model?

I'm studying a draft of the paper “Dealing with the Inventory Risk: A solution to the market making problem” by Guéant et al from July 2012. According to the paper, the closed form solution to the ...
JMNQC's user avatar
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Estimating market price of interest rate risk under CIR model

My goal is to find the market price of risk associated with the interest rate under the CIR model whose stochastic differential equation under the physical measure is given: \begin{eqnarray}\label{...
user53249's user avatar
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1 answer
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Calibration and pricing with the Stochastic Local Volatility model

I'm reading the stochastic local volatility model literature, e.g., the Heston Stochastic Local Volatility model (https://ir.cwi.nl/pub/22747/22747D.pdf); but I'm a bit unsure about its calibration ...
Michael's user avatar
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9 votes
3 answers
1k views

A question about the Grossman-Miller Market Making Model

I don't have any solid background in finance, but I have a strong mathematics and physics background. I am reading Algorithmic and high-frequency trading from A.Cartea, S.Jaimungal and J.Penalva, CUP (...
apt45's user avatar
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2 answers
971 views

Correlation and implied volatility

Say I want to write call options on a stock, with no options written already on it. I know some asset which is highly correlated to it. How can I proceed to make use of the correlation between this ...
Kupoc's user avatar
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standard/brownian market with different brownian motion

Consider for simplicity the following brownian market: $$dS^0_t= r S^0_tdt$$ $$dS^1_t= S^1_t(r dt + dW^1_t + dW^2_t) $$ where the filtration is generated by $W^1,W^2$ Consider now $W_t:= \frac{1}{2}(W^...
Steven Hunt's user avatar
2 votes
1 answer
125 views

Why does the LMM in Hull seem so different from the LMM in Brigo and Mercurio?

When I look at Hull's "Options Futures and Other Derivatives" the process for $F_k(t)$ in the rolling forward risk neutral world is specified as $\frac{dF_k(t)}{F_k(t)} = \sum^k_{i=m(t)}\...
JoeBass's user avatar
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1 answer
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Why does the definition of the riskless asset vary in discrete vs continuous time?

In a multi-period market model, let's say we have $d+1$ assets $(S^0,S)=(S^0,S^1,\dots,S^d) $, where $S^0$ is the riskless asset, invested in a money market account. In continuous-time finance I ...
phhhlpfk's user avatar
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Initial forward variance curve $\xi_0(t)$ in the Rough Bergomi model

The rough Bergomi model is defined as \begin{cases} \frac{dS_t}{S_t} = \sqrt{v_t}dW_t^1 \\ v_t=\xi_0(t)\exp(\eta \tilde{W}_t^H-\frac{1}{2}\eta^2t^{2H}) \\ \tilde{W}_t^H = \int_0^t \sqrt{2H}(t-s)^{H-\...
NN2's user avatar
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Can you calibrate the Heston model using stock price trajectories?

I'm interested in calibrating the Heston model so I was reading about it online. All procedures I could find was using market prices for European call options and using the (semi-)closed-form ...
Brickcity's user avatar
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how can we calculate options profit and loss using volatility and implied volatility in a span margin calculation

complete the table below, mainly we have to use black-scholes model for implied volatility calculations which I am getting as 43 % but now how to make a gain and loss table using this implied ...
Harsh Mathur's user avatar
-2 votes
1 answer
98 views

How Are Option Model Assumptions Justified In Practice

I am reading this article, and I am wondering how comments like there may be a 50/50 chance that the underlying asset price can increase or decrease by 30 percent in one period. are reconciled with ...
Joe Shmo's user avatar
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2 answers
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Why is diversifiable risk unrewarded?

I am currently looking through some actuarial study materials (CM2, formerly CT8) in which models of asset returns are being discussed. One such model is the market model (A.K.A The single-index model)...
John Smith's user avatar
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1 answer
255 views

Modelling limitations and understanding of long term goverment bonds

Been trying to understand the yield curve for a while now. This is what I collected so far, There is a relation between short rates and long rates that goes via the forward rate, and so by the ...
user123124's user avatar
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0 answers
83 views

Interpretation of SML (Security Market Line) parameters

I estimated a SML in terms of excess returns and I get the following parameters: $\gamma_0=0.0286$ $\gamma_1=0.0263$ How can i give an economic interpretation of these two values? How they shape ...
Roberto Rosina's user avatar
3 votes
1 answer
131 views

Economic interpretation of Time-varying beta (systematic risk) in portfolio analysis

What is the economic interpretation of Time-varying beta (systematic risk) in portfolio analysis and the main economic difference with costant beta. I'm not interested in how to estimate it but just ...
Roberto Rosina's user avatar
0 votes
1 answer
57 views

Currency-denomination for the index in an event study

Suppose I want to perform an event study on corporate CDS spreads using the market model. All my CDS are US dollar-denominated, whereas the market index is euro-denominated. Is this strategy ...
Niqx's user avatar
  • 21
1 vote
1 answer
64 views

Which models have non-smooth densities?

By smooth, I mean a density $f$ that lies in the space $C^\infty$, infinitely differentiable. Are there, in the literature, some known models where the underlying density of the state process is non-...
DomReyes's user avatar
0 votes
0 answers
68 views

Market model for european/american options on underlying paying discrete cash (and maybe proportional) dividends

Black Scholes is the market model for european and american options on an underlying paying no dividends. What is the standard market model for european or american options of underlyings paying ...
Olórin's user avatar
  • 1,223
2 votes
1 answer
335 views

Gibbons, Ross, Shanken Test derivation by MLE

I Am trying to derive the expression for the GRS test of the CAPM. I am following the book: The Econometrics Of Financial Markets by Campbell, Lo, McKinley (1997). Define $Z_t$ as an $N×1$ vector of ...
Alchemy's user avatar
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1 vote
1 answer
406 views

How to simulate market data and test strategies?

I am trying to implement my own exchange with simulated data and test some strategies on such data. What would be the best way to go about modelling the data that supports live interaction ( limit/...
Paul's user avatar
  • 71
1 vote
1 answer
767 views

LIBOR Market Model implementation in R

Does anyone know an available LIBOR market model implementation in R? It should not be too sophisticated, as this is a smaller task of a larger work. I am rather thinking about a similar ...
lrdbs's user avatar
  • 33
2 votes
0 answers
245 views

Modelling Order Flow

I am trying to model the number of order that come at a distance d from the top of the book on either side, both bid and ask. I was wondering what is a good way to model orders which improve the ...
nimbus3000's user avatar
3 votes
1 answer
1k views

High Frequency Trading in LoB - Sasha Stoikov and Marco Avellaneda

I am reading the paper High Frequecy Trading in a Limit Order Book by Sasha Stoikov and Marco Avellaneda. There is a point that I am having trouble understanding. The authors give a definition of ...
nimbus3000's user avatar
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0 answers
277 views

Deriving Single Index Model (Market Model)

$R_{it}=\alpha_i+\beta_i\cdot R_{mkt}+\epsilon_{it}$ $R_{it}$ is the return of the stock of observation $R_{mkt}$ is the return of the reference market $\beta_i$ is the regression coefficient between ...
Nipper's user avatar
  • 359
2 votes
1 answer
346 views

Extract market features to decide when to deploy or stop strategies

I have been live trading using algorithmic strategies for a year. I have good periods, lasting about two months, followed but bad periods of few weeks. I did the necessary statistical tests to ensure ...
David's user avatar
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3 votes
0 answers
106 views

Interpretation of Market Price of Volatility Risk

In option pricing with market model equipped with stochastic volatility, there are numerous times mentioning "market price of volatility risk" without even define or give any explanation regarding the ...
Ben's user avatar
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11 votes
1 answer
1k views

Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...
WolfgangP's user avatar
  • 285
4 votes
1 answer
323 views

Ho & Lee yield curve fitting with zero coupon bond market prices

The Ho & Lee model for interest rates is given by the SDE: $$ \mathrm d r = \eta(t) \mathrm d t + c\,\mathrm d X $$ The calibration function for $\eta(t)$ is given by $$ \eta^*(t)=c^2(t-t^*)-\...
WolfgangP's user avatar
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1 answer
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Is there a proxy for S&P 500 market/pricing inefficiency? [closed]

I need a variable or tool which can proxy for S&P 500's inefficiency (whether pricing efficiency or market inefficiency). Initially, I intended to use CAPM and consider the difference in ex-post ...
riskfree's user avatar
4 votes
2 answers
153 views

"Standard" Model for Effective Fed Funds Rate

Is there a "standard" model used to model the Effective Fed Funds Rate? I know that BGM is often used for LIBOR but haven't found a similar application to the Effective Fed Funds Rate. Do ...
MikeRand's user avatar
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7 votes
3 answers
3k views

Valuation of open FX-Forward

So called closed FX-Forwards are well known forward contracts where some amount of foreign currency is bought at a specified date in the future for a price fixed "today". Such contracts can be ...
Richi Wa's user avatar
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2 votes
1 answer
595 views

Normal Libor Market Model

Is anybody using normal Libor Market Model (LMM) (as opposed to shifted lognormal LMM)? It could be one of the approaches to dealing with negative rates. If you do, have you encountered any ...
ir7's user avatar
  • 5,043
1 vote
4 answers
1k views

Market making with resting orders?

I'm still confused on how to provide liquidity on the forex market using passive or resting orders and get the spread from that (selling at ask and buying from bid) And what's the dynamics on the LOB ...
Ariel Silahian's user avatar
0 votes
1 answer
251 views

Extending an incomplete market to generate a complete one

I am asking a question related to some comments and answers I have seen in the site while investigating characteristics of incomplete markets $-$ see for example @AFK 's answer in How to choose a risk-...
Daneel Olivaw's user avatar
1 vote
0 answers
90 views

What is the intuition to believe that a properly designed option can be dynamically hedged (just for the 1 stock case)?

I would always presume that the portfolio consists of 1 stock and 1 risk-free asset. And that the $r, \alpha,\sigma$ are all non-zero, but might be time-dependent. When I say "any" option, I am ...
Ethan's user avatar
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4 votes
1 answer
1k views

Model reference price of Limit order book

first of all, the description of this Stackexchange forum says its for professionals or academics. I'm doing a lot of self studying and with that I was able to understand some white papers but still I'...
flxh's user avatar
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2 votes
2 answers
1k views

What is Toxic FX Flow debate?

So, basically I want to debate and find out the real reason behind being flag by ECNs and venues as "toxic". How to avoid being flagged? What kind of strategies are toxic and why? Below is an article ...
Ariel Silahian's user avatar
0 votes
1 answer
444 views

completeness of the binomial model - proof

I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...
Michal's user avatar
  • 711
1 vote
1 answer
451 views

Fx Firm market making

I've been doing market making on forex using the last look feature so far. Now we are moving to do on firm making, but I'm kind of lost. To do firm making we need to post resting orders (currenex ...
Ariel Silahian's user avatar
0 votes
1 answer
139 views

Does presence of arbitrage necessarily make all derivatives have zero value?

Spin-off from: Pricing when arbitrage is possible through Negative Probabilities or something else I mean in a theoretical sense: If we have a particular market model with some fancy assumptions such ...
BCLC's user avatar
  • 921
4 votes
0 answers
488 views

Modeling market sentiment and pricing options by volume, open interest

Are there any empirically-proven methods/formulas for weighting IV surfaces, pricing a discount/premium in an option, and/or adjusting any of the 1st- or 2nd-order Greeks for the magnitude (volume or ...
CB001's user avatar
  • 61
3 votes
1 answer
313 views

Limits on Short selling

When back testing an algorithm that relies upon short selling certain stocks, how to limit the short selling so that the back-test results still remain reliable? What kind of controls are generally ...
user43115's user avatar
  • 149
1 vote
1 answer
81 views

Is it possible that some types of financial systems can resonate?

Financial systems can certainly be modeled using the same tools physicists use to model dynamic physical systems. The validity of such is evidenced by models such as that developed by Black and ...
docscience's user avatar
8 votes
1 answer
799 views

Do you have a validation set for Libor Market Model implementation?

I'm trying to calibrate a Libor Market Model (LMM) in Matlab with my user-defined function, not their package. I already fitted the market volatilities using SABR but failed to simulate the ...
Tulio Carnelossi's user avatar