Questions tagged [market-model]

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Generate payoff matrix of multiple BSM assets

I have some troubles generating a random one-step BSM market model that is arbitrage-free. Concretely, the BSM market model in one time step is just a payoff matrix of $N$ assets and $K$ events, so ...
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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{...
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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 ...
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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 (...
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2 votes
2 answers
640 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 ...
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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^...
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2 votes
1 answer
81 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)}\...
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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 ...
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213 views

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-\...
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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 ...
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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 ...
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-2 votes
1 answer
86 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 ...
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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)...
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1 answer
227 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 ...
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67 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 ...
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3 votes
1 answer
96 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 ...
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1 answer
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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 ...
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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-...
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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 ...
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2 votes
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269 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 ...
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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/...
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1 vote
1 answer
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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 ...
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2 votes
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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 ...
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3 votes
1 answer
662 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 ...
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228 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 ...
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2 votes
1 answer
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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 ...
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3 votes
0 answers
84 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 ...
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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 ...
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4 votes
1 answer
263 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^*)-\...
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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 ...
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4 votes
2 answers
129 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 ...
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7 votes
3 answers
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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 ...
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2 votes
1 answer
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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 ...
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1 vote
4 answers
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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 ...
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0 votes
1 answer
185 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-...
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1 vote
0 answers
85 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 ...
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4 votes
1 answer
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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'...
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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 ...
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0 votes
1 answer
352 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 ...
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1 vote
1 answer
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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 ...
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0 votes
1 answer
119 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 ...
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4 votes
0 answers
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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 ...
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3 votes
1 answer
302 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 ...
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1 answer
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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 ...
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8 votes
1 answer
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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 ...
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3 votes
2 answers
874 views

Why Markov Functional Models (Hunt 2000) are not yet so popular?

I refer to MFM introduced by Hunt [2000]. These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-...
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5 votes
2 answers
1k views

Libor Market Model: numeraire change

I am currently studying the Libor forward market model, and although I get the mechanics behind the main arguments, I still do not have an intuitive idea of what's exactly the objective behind ...
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2 votes
2 answers
154 views

Art market specificities

I am looking for some reference on the art market in light of quantitative finance. I am interested in some things: The market in general, how is it compared to financial market ? What about common ...
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4 votes
2 answers
501 views

question on Leif Andersen's "Interest Rate Modeling, vol 2 Term Structure Models"

I'm reading Leif Andersen's "Interest Rate Modeling, vol 2 Term Structure Models" and met a problem on Chapter 14 LM Dynamics and Measures, $\S$ 14.2.5 Stochastic Volatility, Lemma 14.2.6, on page 602....
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3 votes
1 answer
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What's the underlying idea of definition of constrained market in Skiadas' Asset Pricing Theory?

I'm self-studying Skiadas' Asset Pricing Theory, and find the definition of constrained market on page 21 confusing(you can find it here in the sample chapter). Definition 1.26. A constrained market ...
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