Questions tagged [arbitrage]
The simultaneous purchase and sale of a financial security in order to profit from the difference in the security price during the trading activity.
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Does arbitrage theory actually help in practice? If so, how?
Am wondering if arbitrage theory (the ones defined "classically" with stochastic processes, martingales, etc.) is actually helpful in practice for an actual trader beyond simply having an ...
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Determining bet sizes given odds
Recently, I was asked the following question in an interview with a prop trading firm.
You are given the opportunity to make money by betting a total of 100 bucks on the outcome of two simultaneous ...
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Statistical Arbitrage, Avellaneda & Lee - Estimation of the Residual Process
I am trying to calculate the trade signal outlined in Avellaneda & Lee paper "Statistical Arbitrage in the US Equities Market".
They describe their approach in appendix. Here is my ...
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FX FORWARDS Calculating funding cost and wether funding will be expensive or not
Lets say for example my TN for USDHKD point per day spot is -1.9467 and for 1mnth it is -1.4142 and the notional is 100m HKD dollars.
Would you say more or less I would be flat in terms of funding ? ...
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Arbitrage Opportunities in a Two-Zero Coupon Bond Market
Question:
Suppose we are in a market where there are only two zero coupon bonds, both with a face value of 100: the first one with a maturity of one year and a price of 90, and the second one with a ...
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Stock clustering for Statistical Arbitrage Trading
Has ML based stock-clustering been practically adapted by the industry in arbitrage trading strategies like pairs trading for forming pairs instead of other traditional techniques like cointegration?
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Show discrete market is arbitrage free if and only if there exist no admissible arbitrage portfolios
Problem: Let S be a discrete market. Show S is arbitrage free if and only if there exist no admissible arbitrage portfolios.
Definition of Discrete Market: Let $T$ be a positive real number and
$N$ ...
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Arbitrage with two puts and definition of convexity
This is concerning a common interview style question which has me confused; it has been discussed here:
How to Take Advantage of Arbitrage Opportunity of Two Options
and
Arbitrage opportunity ...
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Filipovic: Where is it used that the world is deterministic
In this text (Damir Filipovic, Term-Structure Models, Springer, 2009) $P(t,T)$ denotes the price of a zero-coupon bond at time $t$ with maturity $T$. I cannot see where the proof uses the ...
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For which interest rates r is the model arbitrage-free?
Given $\Omega=\{\omega_1,...,\omega_4\}$ and a probability measure
$\mathbb{P}$ on $(\Omega, \mathcal{P}(\Omega))$ where
$\mathbb{P}(\{\omega_i\})>0$ for all $i$. Let, furthermore, $r\geq 0$,
$S_0=...
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Counterexample for the Second fundamental theorem of Asset Pricing
so the The Second Fundamental Theorem of Asset Pricing says:
An arbitrage-free market (S,B) consisting of a collection of stocks S and a risk-free bond B is complete if and only if there exists a ...
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Determine Dependent Variable Product
Let's say I have three products that are correlated (e.g. AAPL, MSFT, and AMZN). I would like to construct a spread between these products and trade the mean-reverting spread. Specifically, sell the ...
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is there some arbitrage relation one can show between a short term vanilla , a cliquet , and a long term vanilla?
suppose all 3 are calls and have same strike moneyness.
The cliquet (V12) pays off S2-S1-K12
The short vanilla (V1) pays S1-K1
The long vanilla (V2) pays S2-K2.
All are floored at zero ofcourse.
K1,K2 ...
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Question about proving the existence of an arbitrage opportunity
I am having a hard time understanding the reasoning behind a statement in the proof of the following lemma from page 14 (228) of the paper "Martingales and stochastic integrals in the theory of ...
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How to price a derivative security in a trinomial asset pricing model
I am reading the first two chapters of Shreve's book "Stochastic Calculus for finance 1". The author discusses the question of how to price a derivative security assuming a binomial asset ...
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Is negative forward variance an arbitrage?
I believe that having a negative forward variance on a ATMF implied volatility curve of a volatility surface could imply the existence of a static arbitrage (for example, a calendar arbitrage). ...
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Check for arbitrage - European calls with same strike price, different duration and price
I tried a lot of different things to check for arbitrage on the following calls but didn't succeed.
Let's suppose we have a stock that is currently valued at 40. The interest rate is 0.05 and the ...
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SABR, Stochastic collocation and calendar arbitrage
Ok, this is a bit of a long read, so be warned..
I am currently learning about the so called "Stochastic collocation" technique which seem to have been quite popular during recent years for ...
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When the market is volatile, relatively fewer factors suffice for a productive stat -arb signal. Have you noticed it, and why would that be? [closed]
In volatile markets only a small number of factor are sufficient for factor based statistical arbitrage to work well. This is an empirical observation. Why would this be? Have others noticed it as ...
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Futures basis (Bond) optimal delivery
i have a confusion regarding how the basis converges in a couple of scenarios. Lets assume I am long UST CTD Basis
Say the curve is upward sloping:
optimally, i would choose to make delivery of the ...
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Joint SPX and VIX calibration - volatility surfaces construction
I am currently researching the joint calibration problem of SPX options and VIX options. A question that comes to mind is the construction of each assets respective volatility surface.
In the articles ...
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Basic question/clarification about the LOOP
This is a very basic question/comment regarding the way that the LOOP is stated in the book "Dan Stefanica - A Primer for the Mathematics of Financial Engineering". The proposition goes as ...
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Forward price of dividend paying asset and IV skew asymptotics as $T\to\infty$
Assuming for simplicity deterministic interest rate and dividend yield, then the forward price of an asset is
$$
F = Se^{(r-q)T}
$$
where $T$ is maturity date.
In studying IV skew asymptotics, the ...
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What is the arbitrage opportunity and strategy here? [closed]
Suppose that the current stock price is $€100$, the exercise price is $€100$, the annually compounded interest rate is 5 percent, the stock pays a $€1$ dividend in the next instant, and the quoted ...
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Role of Intercept In OLS Beta Estimation
I am constructing a classic pairs trading strategy in which I use a linear estimator to model the spread of two assets opening a long-short market neutral position during times of divergence. I am ...
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W-shaped Event Vol and Butterfly Arbitrage
I came across the Vola Dynamics page about the W-shaped vol before an event: https://voladynamics.com/marketEquityUS_AMZN.html
I'm a bit confused by "this term does not have any butterfly ...
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Combining two orderbooks
Consider two different pairs of currencies traded in the same exchange. We will call these pairs A/B and A/C.
Each market comes ...
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Can I replicate an option with time to expiry $t$ by trading in another with expiry $T > t$?
Suppose there's a salesman who will always sell me an option expiring in two weeks. His options trade at a steep discount, but I can't directly arb it because the closest exchange-traded contract ...
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Are risk-free-rate bonds and cash fungible?
I had a thought experiment: suppose you wanted to borrow an equity security from me (perhaps to short sell it). I ask you for collateral and a borrow fee, and in exchange you get the stock.
If you ...
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Bond forward arbitrage relationships
I am trying to see if the following statement is true or not and I would really appreciate your help.
The statement is as follows:
$\forall $ Tradable Asset $V(t)$,
$$ E[\frac{P(t,T_{i})P(T_{i},T_{i+1}...
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StatArb : Fourier transform to find the perfect factor?
We have a basic mean reverting strategy. Given a bench of assets, we are looking for the best linear combination of them such as the resulting normalized time series would be noisy at high frequencies ...
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Convergence of crypto perpetual futures
Perpetual contracts are supposed to track the spot prices through the funding mechanism. Typically, if the future has traded above the spot in the last averaging period used to compute the funding, ...
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Why is this inequality strict for arbitrage argument for European call?
in the notes about arbitrage arguments I am reading, I notice the statement
We can also see that
$$C^E_t>(S_t-K\mathrm{e}^{-r(T-t)})^+$$
Notice that the inequality holds STRICTLY!
I don't ...
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How do I extract the arbitrage?
You are looking at a particular stock ticker and its options. You can go long or short on any quantity of the following instruments:
Each unit of stock is priced at \$10.
A call on the stock with ...
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Understanding FX forward points and market usage
I've been trying to make sense of how the FX forward market works.
Let's say today is June 13, 2022. And we have the next market info as seen in Bloomberg for the FX cross between USDMXN, assuming mid ...
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ETF structure's effect on premium to NAV
The GBTC (Grayscale Bitcoin) ETF is known for historically having a premium to net asset value (NAV). This led crypto funds to buy bitcoin, deposit their bitcoin into the trust to obtain GBTC, then ...
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Deviation between spot price and implied spot price of S&P500 mini-futures
From Derivatives Markets (McDonald) it is stated that we may price a financial forward and, equivalently, get an implied spot price from a given futures price:
$$
F_{0, T}=S_0e^{(r-\delta)T} \implies ...
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Strike arbitrage in discrete implied volatility grid
I need to test strike (butterfly) arbitrage on a discrete implied volatility grid.
I know that the traditional procedure for continuous case is (for a given maturity T):
See the Dupire formula in ...
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Calendar arbitrage in implied vol grid with discrete and proportional dividends
I have an implied vol discrete grid, obtained from market data.
To obtain prices from these implied vols, a dividend model with discrete and proportional dividends is used.
How can I verify if there ...
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Why do VIX spot and futures converge if there is no cash and carry arbitrage?
Since VIX spot is not tradable, why do the futures and spot converge @ expiration? By what mechanism does this occur if arbitrage is not one of them?
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What is the P-probability of an unhedged call-arbitrage to lose money at expiration
Assume that the Risk Neutral Price (under the $\mathbb{Q}$-measure) of an European Call Option with expiration date $T$ has a price of $F(S_0,0)$ at time $t=0$ in the single asset Black-Scholes model ...
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Analytical evaluation of the following caplet-type product under lognormal assumptions
Let $n \geq 2$, and consider a tenor discretization: $0 = T_{0} < T_{1} < ... < T_{n}$ and associated forward rates evaluated at time $t$, as $L_{i}(t):=L(T_{i},T_{i+1};t)$ for any $i = 0,...,...
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How am I supposed to understand the following statement on the convexity adjusted rate
Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays
$$V_{N}(T):=X(T)N(T) \...
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How to exactly calculate lag between 2 exchanges
Let's assume that there are two exchanges. One exchange is slow for various reasons.(for eg it is an open outcry versus electronic exchange) Even when there is no lag the prices will not match exactly ...
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Why would valuation for a swap be the same on the backward and forward rate but not a caplet
Consider for time discretization $0 = T_{0} < T_{1} <... < S < T < T_{n}$, and the corresponding forward rates and backward rate:
$\text{Forward rate: }L(S,T;t)$
$\text{Backward Rate: }...
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Implied vol bounded if and only if instantaneous vol bounded
I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form
$$
dS_u = \sigma_u S_u ...
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Triangular Arbitrage In FX Volatility
If I know the price of $GBPUSD$ and $EURUSD$, I can retrive the $EURGBP$ price simple by $EURGBP = \frac{GBPUSD}{EURUSD}$.
Is there something equivalent to FX Volatility? Knowing the $\sigma_{GBPUSD}$,...
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Is it true that interest rates options with different maturities are free of calendar arbitrage because of the different underlying rates dynamics?
The title says it all - is it true that European style interest rates options (lets say on LIBOR 3M for the sake of simplicity) with different maturities are free of calendar arbitrage because ...
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Understanding arbitrage, defined as a series of cash flows
I'm currently catching up on material presented in the edX-MIT course Foundations of Mondern Finance 1, in which they present a definition of arbitrage that doesn't quite make sense to me. Informally, ...
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No-arbitrage conditions on a caps/floors volatility surface
Suppose that one has a caps/floors volatility surface and wants to check whether this surface admits arbitrage. What is the theoretical and practical way to do it?
Lets talk only about caps for ...
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