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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8
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2answers
232 views

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
72 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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1answer
61 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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63 views

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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1answer
100 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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1answer
168 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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82 views

Self-financing strategy, arbitrage and martingale pricing

Let us start with the following definition: $H_t$ is a simple predictable process if $$H_t=H_01_0(t)+\sum_{i=0}^nH_i1_{(t_i,t_{i+1})}(t)$$ where $0=t_0<t_1<...<t_{n+1}<\infty$ and $H_i$ is ...
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15 views

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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94 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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3answers
386 views

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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44 views

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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1answer
93 views

Option Arbitrage Opportunity [closed]

Could you please explain me whether there is an arbitrage opportunity in this situation (added below)?
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57 views

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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1answer
252 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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52 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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2answers
169 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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2answers
796 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
64 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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1answer
57 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
100 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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54 views

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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53 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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31 views

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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43 views

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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38 views

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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92 views

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
51 views

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
48 views

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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41 views

Carr and Madan algorithm to avoid arbitrage in oprion prices

Hey in this text (https://arxiv.org/abs/1107.1834) in section 7 is described an algorithm which can delete options which generate an arbitrage. $C_ij$ is call option price with strike $K_i$ and ...
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1answer
93 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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1answer
72 views

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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0answers
79 views

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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1answer
92 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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31 views

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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52 views

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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1answer
78 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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0answers
83 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
182 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
198 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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4answers
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Is statistical arbitrage on FX possible?

Do you know of any papers which consider pairs trading (or statistical arbitrage) on foreign exchange? I couldn't find any. I asked this question on several forums and got no reply. Thus, I guess ...
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How do trading firms that pay for order flow make money from “arbitrage”?

I understand that retail brokers pass their customers' trades on to trading firms, and receive a payment for order flow in return. These trading firms carry out the trades and presumably also have to ...
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1answer
84 views

Arbitrage strategy using binomial tree

Suppose that we have a one step binomial tree model for a company. Lets say that the time per step is T, and that price of the stock can go up to $p_1$ or go down to $p_2$. Suppose a T-month European ...
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0answers
59 views

The distribution of mean reversion time from the OU process

I was reading the paper Statistical Arbitrage in the US Equity Market and I couldn't understand the figure that plots the histogram of the empirical distribution of characteristic time to mean ...
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1answer
90 views

How to compute portfolio returns when constructing a dollar-neutral portfolio

I am trying to wrap my head around this statement: dollar-neutral portfolios are built: dollar amounts of both long and short positions are equal. Furthermore, it is also true at the stock level: ...
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0answers
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Replicating portfolio of an option and to find inital price

I am very new to financial math so I am not sure how to do with this question. A friend sent me this question to practice but I am unsure how to begin. I read about call option . Can that be used for ...
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37 views

Black-Scholes pricing of european call option

I am really confused on the usage of the greeks and the Black-Scholes model for option pricing. To gain some more understanding I am attempting to see if I can price a european call option under the ...
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1answer
155 views

Boundary for European Put Option

As an entry level financial engineer, I'm learning about call-put parity, which helps us to get the boundary for call option: $S-Ke^{-rT}\leq c\leq S$, what about put option? Should its upper bound be ...
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1answer
65 views

Hedging With Zero Coupon Bonds from The Concepts and Practice of Mathematical Finance by Mark Joshi

In section 2.5 he describes an example of arbitrage-free pricing (attached below). I have a pretty solid understanding of how we arrived at $K' = K\frac{1+d}{1+r}$, but I got a little lost when he ...
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1answer
87 views

What market conditions are attributable to prolonged instances of triangular arbitrage opportunities?

I am investigating the potential for intra-exchange triangular arbitrage opportunities for the Cryptocurrency market. I believe that due its immaturity, relatively low volume and high volatility that ...
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2answers
222 views

Would C++'s speed over Python make it a more applicable language for scalping arbitrage opportunities?

I am using the Bittrex exchange API to ping markets to poll whether there are triangular arbitrage opportunities available for USD/BTC/LTC/USD. Note that I am not trading but rather synthesising them ...

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