6

Mispricing can only be measured relative to some asset pricing model Fama (1970) famously defined an efficient market as, "a market in which prices always 'fully reflect' all available information." A perhaps less widely understood point of Fama is that any test of market efficiency is a joint test of: (1) market efficiency and (2) an asset pricing model! ...


6

This is a problem commonly faced by investment banks and buy-side firms (such as hedge funds) that deal in lots of derivatives. There isn't much more one can do than employ a few rules of thumb, and those rules have not changed much over the decades. In this case, those tricks look something like the following: First, let's assume you have your stock $S$ ...


5

The primary way ECNs determine if a liquidity taker's flow is 'toxic' or not is by looking at aftermath charts. The aftermath chart shows the average mark-to-market profit of trades done by the liquidity taker as a function of either time or number of top-of-book updates (optionally broken down by currency pair). The trade profit is usually viewed from the ...


5

EDIT: I changed the answer to have it more on topic. Summary It boils down to Mark Joshi's answer. I wanted to add something more. Answer A probability measure $Q1$ and a numeraire $N1(t)$ are associated if all prices expressed relative to $N1$ are martingales under $Q1$: $$\frac{price(t)}{N1(t)} = \mathbb{E}^{Q1} \left[ \left. \frac{price(T)}{N1(T)} \, ...


4

Art markets typically have huge transaction costs of the order of 10%, caused by buyers premium and auction fees. Therefore long holding periods are unavoidable, with long-term returns somewhere between those of bonds and equities. By its very nature, art is not easily replicated so arbitrage or derivatives are out. The rationality of agents (aka collectors) ...


4

This reference price is also sometimes called intrinsic price. One of the simplest ways to improve it in regards to the mid-price (assuming you have the depth data) is the following: define a parameter: the size of a hypothetical market order. Let's say it's about the typical sum of first 3-10 order book levels of the instrument; execute a Buy order with ...


4

Let us say we have a yearly interest rate of $r$ that compounds over $n$ periods. With annual compounding that means $n=1$, with semi-annual compounding that means $n=2$ and with daily compounding that means $n=365$. We can calculate the value of putting \$1 into the bank account at time zero and withdrawing it after $n$ periods at time $t$ as $$ \left(1+\...


4

EDIT: Apologies, one more edit, but an important one: Note, as kindly pointed out to me by an interested reader a short time ago: there is a potential issue with the simple model I proposed. Namely, as it stands the model implies that the illiquid asset$Y_t$ is not a martingale. But all is not lost; the model could potentially still be used if the illiquid ...


3

This paper Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency (by L and Mounjid) is probably exactly what you expect. It is explained how (given a model of orderbook dynamics close to the Queue reactive model) to decide to cancel or not a limit order with respect of the state of the bid and ask queue sizes and your position ...


3

Different measures have different properties. Using a particular measure may make it easy to derive an analytic formula since a rate is driftless. When performing Monte Carlo, the sign of the drifts changes with measure which affects convergence. There is also the problem in the terminal measure that the numeraire can get very small and so some paths can ...


3

I would say the financial- and the art market is very different, only the roots of the market / auctions is the same. As the art market is unique and very illiquid, alot of the strategies from the modern financial market simply does not apply. I have been building (and still maintains) a toolbox of models, which mostly try to find trends based on multiple ...


3

The only way you can use limit orders to provide liquidity is to post prices that are the same as the prices of the limit orders, and then you will not be earning any spread. In other words, what you are asking is not possible, since to earn spread you would have to quote a bid that is lower than the price of your client's limit buy order, or an offer that ...


3

Whereas when you marketmake on a last-look basis: - You, the marketmaker, are sending indicative prices to the ECN - The ECN sends orders to you and is at risk (since you have the option to reject, hopefully rarely) When you marketmake on a no-last-look (NLL) basis: - the ECN is sending indicative prices - You, the marketmaker, send orders to the ECN and ...


3

To answer your question: I mean in a theoretical sense: If we have a particular market model (which I guess we may assume is complete or frictionless if need be) where shorting and fractional purchases are allowed, does presence of arbitrage necessarily make all kinds of derivatives have zero value? The answer is no. See example below. Went over your ...


3

You should make your borrow cost sufficient to dissuade unlimited short selling. In practice, each short would require you to borrow shares from your broker. This is usually handled when computing transaction cost. You should account for this in your trading algorithm or in the factor model itself. A simple method would make shorts some N% more expensive ...


3

The general effect of quantitative analysis of the markets is to enforce randomness. Suppose a strategic quant finds a predictable pattern where a stock always rises on Tuesdays. His institution will commence buying the stock every Monday, and selling on Tuesday. The trading itself pushes the stock price up on Monday and down on Tuesday (in general), so if ...


3

For Q1, the function $a(t)$ is the instantaneous correlation. The form given by (2) is basically the Cholesky decomposition. Of course, you may directly show, uisng Levy's characterization, that $$ \widetilde{W}(t) = \int_0^t\bigg[\frac{1}{\sqrt{1-||a(t)||^2}} dZ(t) -\frac{a(t)^T}{\sqrt{1-||a(t)||^2}} dW^B(t) \bigg] $$ is a standard scalar Brownian motion ...


3

Q1: $$(1)\rightarrow(2)$$ (1): $a(t)$ is the instantaneous correlation of $\rho(Z_t,W_t)$ because: $$\rho(dZ_t,dW_t)=\dfrac{Cov(dZ_t,dW_t)}{\sigma_{dZ_t}\sigma_{dW_t}}=\dfrac{E(dZ_t\cdot dW_t)}{\sqrt{dt} \sqrt{dt}}=\dfrac{\langle dZ_t, dW_t\rangle}{t}=a(t)$$ $\Rightarrow$ (2) holds as following, in the 1-dim case: $dZ_t\sim N(0,dt),$ $dW_t,\tilde{dW_t}\...


3

I have asked myself the very same question when I first read the book. As far as I can tell, the "scalability" condition is only imposed for technical reasons. It simplifies the subsequent proof of the Fundemental Theorem of Asset Pricing in constrained markets. There are several papers that have shown that the theorem is valid for conic constraints. ...


3

The terminal condition for the HJB equation implies that you can factor the value function into \begin{equation*} u(s, x, q, t) = \exp(-\gamma x)\exp(-\gamma \theta(s,q,t)): \end{equation*} and a direct substitution using this ansatz allows you to factor out $\exp(-\gamma x)$ from the equation. This is because of the exponential utility function used, which ...


3

OK, your framework on this is right. Long-term yields embed "expectations" about future short rates. That is: what do I think I'll get if I sat for T years with cash in the bank for swaps, or the same rolling Govvie Bills with respect to Bonds? Plus a cherry-on-top called "term premium". One can rationalise the existence of this in lots of intuitive ways, ...


2

Calibrating to swaption prices would give you the right volatilities for your model, but you have to use the floating notes (or similar instruments, as swaps) in order to get the right drifts. In any case, your model have to be able to exactly replicate the floating notes prices in order to be considered a valid model, and you can feel comfortable to use it ...


2

Idiosyncratic volatility is NOT included in the regressors, so it should not be and actually cannot be part of your matrix X. Idiosyncratic volatility is the volatility (of Y) your matrix X (explanatory variables) cannot explain (i.e. remaining unexplained part), so it is the error term of your regression equation. Just compute the standard deviation of ...


2

For LMM I thing the Rebonato's book 2002 is a good reference. He has explained the condition of vol quotation that allow existence of calibration solution. LMM parameters and inputs are quite complexe, calibrator not work maybe caused by your implementation's bugs but not only data input. I think it is better if you calibrate virtually before true market ...


2

With a resting order the market maker's client takes (buys) at the offer, or gives (sells) at the bid. The market maker prices the deal that way as with any other order type. A resting order is simply another type of order and the client pays the market maker's spread like with any order type. I am not sure I agree with @CPL593H if you're a market maker and ...


2

it's difficult to say that they are not popular. Some people definitely use them for live pricing. I'd say the real question is "why are they not popular in the academic literature"? One answer would simply be that most the questions that arise in their use are ones of fiddliness which do not make good papers.


2

In practice, most derivatives traded on Fed Funds rates are linear(i.e. Forwards) rather than non-linear (options and exotics). As such, there has not been a strong case for precise modeling of the full distribution of a Fed Funds rate for a particular day. In contrast , there is a large market for derivatives on 3month USD Libor , which is less sensitive ...


2

Yes I used one in the early 2000s. At the time, US interest rates were quite high (5 or 6pct) and the market skew was such that -100bp receivers were more expensive than +100 payers. The lognormal model is very inappropriate for this skew regime , but the normal model is much closer, having symmetric skew. As a byproduct of this we noticed that the model ...


2

As a starting point I would make the assumption that your new orders are negligibly small, in order that their market impact does not affect the trajectory of the price. This will provide a reasonable way to test strategies that do not possess any forward looking or snooping data. When you are in the position that your actions are believed to impact the ...


2

A simple model would be the double exponential model from Kou (2002). It is very similar to the jump-diffusion model from Merton (1976) but instead of modelling the jump size by a normal distribution, Kou employs an asymmetric double exponential distribution (aka Laplace distribution). The corresponding density is $$f_X(x) = p\zeta e^{-\zeta x}\mathbb{1}_{\...


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