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.
318
questions
8
votes
2answers
200 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 ...
0
votes
0answers
62 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 ...
0
votes
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 ...
0
votes
0answers
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}\...
0
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0answers
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 $...
-2
votes
1answer
93 views
Option Arbitrage Opportunity [closed]
Could you please explain me whether there is an arbitrage opportunity in this situation (added below)?
0
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0answers
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 &...
2
votes
0answers
81 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 ...
0
votes
0answers
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 ...
5
votes
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 ...
2
votes
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 ...
1
vote
0answers
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|=\...
2
votes
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)...
1
vote
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 ...
2
votes
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(...
1
vote
0answers
53 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 ...
0
votes
0answers
52 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 ...
0
votes
0answers
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 ...
0
votes
0answers
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}\...
0
votes
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:
...
0
votes
0answers
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(\...
1
vote
0answers
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 ...
1
vote
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 ...
0
votes
1answer
48 views
How does $1 + R = q_u · u + q_d · d $ follow from $d ā¤ (1 + R) ā¤u$ in the Binomial Pricing Model?
I've been reading Tomas Bjork's 'Arbitrage theory' and it says:
To say that $d ā¤ (1 + R) ā¤u$ holds is equivalent to saying that $1 + R$ is a
convex combination of u and d, i.e. $1 + R = q_u Ā· u + q_d ...
0
votes
0answers
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 ...
1
vote
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, ...
2
votes
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 ...
0
votes
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 / ...
0
votes
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, Ornsteinā...
-1
votes
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 ...
2
votes
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=...
2
votes
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 ...
2
votes
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):
$$\...
0
votes
0answers
87 views
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 ...
1
vote
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 ...
1
vote
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: ...
1
vote
0answers
44 views
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 ...
0
votes
0answers
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 ...
1
vote
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 ...
0
votes
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 ...
1
vote
0answers
43 views
Modelling considerations for a jump model
The Problem:
Suppose I have a simple jump model for an asset price
$$ dS = S(t-)[\mu dt + YdN(t)] $$
where $N(t)$ is a Poisson process and $Y_i$ are the jump sizes (assume independece of $N(t)$ and ...
1
vote
1answer
37 views
Hedging/Arbitrage with multiple period binomial tree
Plenty of material is written on how to hedge/arbitrage option price in one period binomial model, but I cannot find anything about hedging in multiple periods. If one to use multiple periods binomial ...
1
vote
1answer
93 views
Put-Call parity arbitrage relationship
I would like to know what the relationship is between the time value of call/puts. From the put call parity formula
$$C-P = S_{t} - PV(K)$$
and that value of call/put options is simply the sum of ...
0
votes
0answers
27 views
No unique no-arbitrage price when the stock price can remain unchanged
In a 1-period binomial model, with initial stock price 100, if the stock price is either 50,100, or 150 after 1 period then how can I show there is no longer a unique no-arbitrage price for a European ...
-3
votes
2answers
89 views
Tips on building an automated trading system in python [closed]
I have an trading API that allows me to send/cancel/update orders.
I have marketdata that I can use through another API that gives me orderbook data.
Now let's say I want to build a simple arbitrage ...
1
vote
2answers
219 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 ...
1
vote
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 ...
1
vote
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 ...
