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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64 views

If arbitrage can happen exactly at one moment, is it really arbitrage?

There are many "interpretations" of what no-arbitrage means in mathematical finance, the most well known is no free lunch with vanishing risk: If $S=\left(S_{t}\right)_{t=0}^{T}$ is a ...
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475 views

When looking for arbitrage among a LARGE amount of assets, is there an optimal way?

Looking for arbitrage opportunities when looking at 3 pairs of related currencies is easy. However if we assume that we have a large amount of currencies, is there an optimal way to swipe through them ...
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51 views

Self-financing condition and funding, collateral and discounting

I'm reading "Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting" paper. Is it just me or authors have a typo in their main ...
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Spot-Futures arbitrage profit calculation

My question is about spot-futures arbitrage. Lets say, t=0 , Spot Price=1.38 , ArbFree Theoretical Fwd Price= 1.40 and Real Futures Market Price = 1.38. So we see that there's arbitrage. I take a long ...
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286 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
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30 views

How to compute the yield to maturity on a zero-coupon 3 year bond in this case?

Suppose I have the following problem: We have data on three bonds: a one-year zero-coupon bond (bond A), a twoyear zero-coupon bond (bond B), and a three-year bond with an annual coupon equal to 5% ...
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84 views

Can we observe smile arbitrage from the implied and local volatility?

Here are graphs of implied volatility and local volatility. Our prof mentioned that we can observe that the short end low strike region has some smile arbitrage. I would like to know how? Thanks
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Arbitrage portfolio example

Can you give me a concrete example of a self financing portfolio which gives arbitrage opportunity in the two-dimensional Black-Scholes model? By the two-dimensional Black-Scholes model I mean $$dS_{1}...
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1answer
129 views

Does CRR Model lose completeness if we add another instrument?

Consider the multiperiod binomial/CRR model with one risky asset $S^{1}$ and a numeraire $S^{0}$. By seeing that the equivalent martingale measure is uniquely determined, we obtain that the market is ...
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1answer
92 views

Arbitrage in a Single Index Model

Simple question really, but I'm very confused by the starting point. Let's assume that we have a portfolio whose excess returns can be described by the following equation from the single index model: ...
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521 views

How to prove no-arbitrage when a long butterfly is strictly positive?

I want to prove why there are no arbitrage opportunities when a long butterfly is strictly positive. I know there is a similar topic out there, but it seems it doesn't solve my question: Prove that ...
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126 views

Clean noisy data from arbitrage

My problem is that I have a surface of implied black volatilites that is supposed to represent market data. However, the surface contains some slight arbitrage. More precisely, the graph contains ...
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1answer
118 views

What is the interpretation if the real world measure $\mathbb P$ is equal to the martingale measure $\mathbb Q$

Out of interest, is there anything noteworthy about a market when its real world measure $\mathbb P$ is actually also its martingale measure. In other words the real world measure $\mathbb P$ is equal ...
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Is there a forward contract the underlying of which is another forward contract?

Is there a forward contract on a forward contract? Let us take a simple example: Persons $A$ and $B$ agree that $A$ sells $B$ some asset tomorrow at the fixed price $K_1$. This is a normal forward ...
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283 views

Why did investors believe that Volkswagen's preference and ordinary shares would converge in price?

The second para. below confirms that "Porsche's takeover demand would target the latter [ordinaries] rather than the former [preference]." Then why did investors like Albert Bridge Capital &...
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ETF Market Making - Locking profits via hedging

I am interested in deeply understanding the way ETF market makers operate to profit. I already know that market makers profit from buying at the bid price and selling at the ask price, and I am also ...
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1answer
74 views

Swap Spread Arbitrage & Rates/STIRT Vol

Concerning the classic swap spread arbitrage trade where you (as far as I understand it): Buy a treasury and borrow in GC repo, paying repo rate and funding the haircut in short term unsecured ...
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Options Arbitrage

I have a basic question regarding the BSM formula, would be thankful for any assistance. As far as I understand $N(d2)$ and $N(-d2)$ stand for the probability of a Call and Put respectively being ...
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126 views

Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging

Need some expert advice and suggestions: I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–...
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170 views

No-arbitrage arguments: how do additional fees affect futures on an index?

I am considering a fund that replicates the returns of an index minus a fee, using the following case-study my lecturer used regarding SPY: In practice, futures and forwards can be written on assets ...
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Example of one-period model that satisfies law of one price but is not free of arbitrage

We know that by the law of one price: in a one-period model $(\overline{\pi},\overline{S})$ for an arbitrage-free market model it follows that for two strategies $\overline{\rho}$ and $\overline{\xi}\...
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102 views

For one-period model, construct a risk-neutral measure $\mathbb P^{*}$ such that the density is constant on $\{S^{1} (<,>,=)c\}$

Consider a one-period arbitrage-free model, it has one risky asset $(\pi^{1},S^{1})$ such that $\pi^{1}>0$, with interest rate on the risk-free asset $(\pi^{0},S^{0})$ at $r > -1$.Furthermore $...
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Why do transaction costs increase the range of the no-arbitrage bounds for an option's price?

I am reading this book by Mark S. Joshi. Can you help me make sense of one of the exercise questions? Here is the question (from page 40 of the book): Exercise 2.5 Suppose no-arbitrage bounds for an ...
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Given the density function of $S^{1}$ in one-period model, find the risk-neutral measure

Consider the one period market model $\left(\overline{\pi},\overline{S}\right)$ consisting of a risk-free asset $\left(\pi^{0},S^{0}\right)=(1,1+r)$ and a risky $\left(\pi^{1},S^{1}\right)$ Let $ r &...
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Option Arbitrage Opportunity [closed]

Could you please explain me whether there is an arbitrage opportunity in this situation (added below)?
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How to price a forward-rate agreement?

I don't understand how the formula on page 24 of Joshi: Concepts and Practice of MF is derived. Here is the paragraph I don't understand: A forward-rate agreement is simply an agreement to take some ...
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54 views

$\epsilon$-arbitrage model

In the model here described, Bertsimas says that we can use the Robust Optimization to find the replicating portfolio the value of which is such that minimize the difference $|P(\widetilde{S},K)-W_T|=\...
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173 views

How to detect price anomalies in HFT?

Let's say I'm developing an HFT application and seeking arbitrage in futures markets between MAY contract(M) and JUNE contract(J). In this strategy, my spread is ...
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835 views

Can someone explain rigorously Taleb's criticism of Nate Silver's election forecasting?

Taleb makes the claim in this paper (and others) that there exists some sort of bound on the variance of a binary forecast such that if a forecaster's binary predictions exceed the bounds on variance ...
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1answer
67 views

Is this actual example of calendar arb in quotes?

From my understanding total implied variance has to be a monotonic function of time for there to be no calendar arbitrage. Stumbled upon quotes for this Monday with apparent arb (NKE Dec expiry vs Jan)...
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60 views

How can the face value of a bond not be a round number?

I'm reading Bruce tuckman's "fixed income securities" and I'm at the section that is explaining arbitrage. In the chart below, the cash flows are based off the biannual interest rates * the ...
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1answer
105 views

Market price of risk of different maturities

T. Bjork Arbitrage Theory in Continuous Time Proposition 23.1 "Assume that the bond market is free of arbitrage. Then there exists a process $\lambda$ such that the relation $\frac{\alpha_T(t)-r(...
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Replicating portfolio

I have a doubt about the replicating portfolio methodology. Example - Consider an European Call with $K=21$ and underlying with current price $S_0=20$. We assume that, at the maturity, the underlying ...
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56 views

Determining Presence of Arbitrage

I am slightly confused by part (b) of this question. My understanding is that the easiest way to determine if there is arbitrage is to compute the state prices and then look at their sign: if one or ...
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Binomial Model Strike Price Assumption

Let us have the standard single-period binomial pricing model, and denote the up and down states of the underlying by $S_u$,$S_d$ respectively. Let us say we have a call option on the underlying with ...
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Proof of existence of one only martingale measure

I know that: Hypothesis 1 (Girsanov Theorem) Let $\theta=\begin{Bmatrix} \theta_t \end{Bmatrix}_{t\in [0,T]}$ be a square-integrable and $\Im_t$-adapted process such that $\mathbb{E}[e^{\frac{1}{2}\...
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Replicating a derivative

Assume an underlying random variable $S_T$ which satisfies that $S_T > 0$ and that $\mathbb{P}\{S_T \neq 100 \} > 0$. Let $X_0$ be the time-0 price of a contract that pays $X_T: -2\log\left(\...
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Where could I get a mathematical background on circular arbitrage?

I am particularly interested in the dependence of profit on the path length (the number of intermediate currencies) and graphical models / algorithms. More specifically: How can we model currency ...
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1answer
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Risk-Neutrality: Discount factors of the $P$ world according to risk preferences?

I am coming to terms with the connections between the so-called $P$ world and the $Q$ world. In my understanding, the risk-neutral measure $Q$ induces a probability space under which investors are ...
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1answer
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How does $1 + R = q_u · u + q_d · d $ follow from $d ≤ (1 + R) ≤u$ in the Binomial Pricing Model?

I've been reading Tomas Bjork's 'Arbitrage theory' and it says: To say that $d ≤ (1 + R) ≤u$ holds is equivalent to saying that $1 + R$ is a convex combination of u and d, i.e. $1 + R = q_u · u + q_d ...
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1answer
103 views

Setting up arbitrage strategy in R

I am trying to construct an arbitrage portfolio $\textbf{x}$ such that $S^T\textbf{x} = 0$ and $A\textbf{x} \geq \textbf{0}$, where $A$ is the payoff matrix at $t=1$ and $S$ is the price at $t=0$. I ...
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Is there a reason why futures and options have more substitutes than other financial instruments?

This is somewhat non-technical question, but it seems like this forum is still the best place for it. I'm reading Shleifer's Inefficient Markets, where he points out that [...] for futures and ...
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Can arbitrage arguments be rearranged to avoid selling? (Hull, Chapter 5)

Suppose forward contracts are traded on a consumption asset, so there aren't necessarily people ready and willing to sell the asset to jump on an arbitrage opportunity. Suppose the asset has no yield, ...
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95 views

Is there arbitrage in this market?

I have an incomplete market (rows are states and columns are securities) and I need to determine if there is arbitrage, and if so, construct an arbitrage strategy. A is the payoff matrix (payoffs at ...
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Fitting a Spread into ARIMA AR(1) process

I'm a newbie to econometrics. I've simply ran a regression and have coefficient values of the variables. I'm running a regression for a crypto data, and I've gotten the Spread of the variables. To ...
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Managing a portfolio of pair trades

When arbitraging ETF holdings against the ETF, how does one manage the portfolio over time? Assume the strategy creates a long signal in pair A (stock X/ ETF) and a short signal in pair B ( stock Y / ...
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114 views

Options conversion/reversion arbitrage [closed]

I'm trading bitcoin option and i'm trying to find arbitrage opportunity with a synthetic short/long and a long/short future position. The options are europeans style and settled in BTC. The contracts ...
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104 views

Linear factor representation Pricing kernel APT

following Cochrane (2005) and other insights, we know that under Arbitrage Pricing Theory (Ross, 1976), if investors believe returns follow a linear multifactor structure of the form $x^i=r^f+\sum_{j=...
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2answers
193 views

Strike Arbitrage

In Stochastic Volatility Modelling, Chapter 2, the author derived the Dupire equation $$\mathbb{E}[\sigma_T^2|S_T = K] = 2\frac{\frac{dC}{dT} + qC +(r-q)K\frac{dC}{dK}}{K^2 \frac{d^2C}{dK^2}}.$$ The ...
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3answers
207 views

Arbitrage Condition and Identity in Black-Scholes

After I went through the derivation to get the skew in Backus et al., I had two questions: In the proof, it mentioned the application of the arbitrage condition and then obtained equation (31): $$\...

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