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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41 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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37 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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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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76 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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83 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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30 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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40 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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62 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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66 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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68 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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153 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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189 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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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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53 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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62 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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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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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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72 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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62 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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42 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 ...
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27 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 ...
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81 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 ...
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23 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 ...
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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 ...
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189 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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83 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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93 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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1answer
105 views

Relation of risk-neutral probability measures to arbitrage opportunities

Could someone describe how risk-neutral probability measures are linked to arbitrage opportunities and also to whether or not a market is complete? I've been asked this question and am unsure how to ...
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57 views

Arbitrage between American and European put options on the same underlying asset

Suppose there exist both American-style and European-style put options on the same underlying asset, at the same strike price, and with the same expiry date. Suppose the European put is selling below ...
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70 views

How to find an arbitrage when the solution is not obvious (2 assets in a market)?

I am struggling to find an arbitrage in the following configuration. I know how to prove that there is an arbitrage (using the fundamental theorem of asset pricing). So I ve proven there is an ...
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48 views

Are statistical arb and relative value arb strategies implicitly short volatility?

I obviously don't want to generalise here, but my initial impression of stat arb and relative value arb is that these strategies earn stable pennies during bull markets when volatility is depressed ...
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Arbitrage and dominant strategies : Linear Pricing measure

Given a monoperiodic setting, my professor defines that if there is no arbitrage opportunity, it means that there is no dominant strategy. This is clear. However he defines that if there is NO ...
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71 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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81 views

How to price complex corporate actions with spinoffs

Let's look at below UTX/RTN merger as an example: https://www.fool.com/investing/2020/03/30/raytheon-united-technologies-merger-gets-green-lig.aspx The merged companies will from that moment ...
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49 views

Arbitrage argument with bonds

Let $B(t,T)$ denote the cost at time t of a risk-free 1 euro bond, at time T. Assume that the interest rate is a deterministic function. Show that the absence of arbitrage requires that: $ B(0,1) B(1,...
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104 views

Advantages of pathwise calculus over stochastic calculus in continuous self-financing trading models

I am new to stochastic calculus but the statement below confuses me: Beside the issue of the impossible consensus on a probability measure, the representation of the gain from trading lacks a ...
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How to model the different returns of agents with different information information

For a seminar, I would like to graphically represent the returns made by agents of different information standpoints. In other words, say I have a market tuple $(\Omega, \mathbb{F}, P,S)$ where $S$ is ...
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How to calculate the interest rate under no arbitrage condition

We have two forwards with the same IBM share as the underlying asset. 1) The delivery date is two months from now, the forward price is 1.1 2) The delivery date is seven months from now, the forward ...
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European Call option combined with Short selling

How would I calculate the abitrage profit from a combination of buying the $10 European call option and short selling X number of shares at t=0 and the coming out with a profit at expiry no matter ...
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109 views

Zero Volatility Options Pricing

Suppose an asset evolves in time according to the SDE $$ dS = \mu S dt + \sigma S dW, $$ where $\mu>0,\sigma>0$ are fixed constants and $dW$ is a Wiener process. To price options for this ...
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103 views

Basic arbitrage exercise

In the exercise we are given, possible contracts to buy/sell and possibility to take credits / make deposits money with current market rates. We are asked if its possible to make profit at time T=0 ...
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100 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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72 views

Nonlinear dependency between prices

Can you help me with pricing theory? There are three assets: $A$, $B$ and $C$ with prices $P_A$, $P_B$ and $P_C$ respectively. There are two processes (production, transportation, etc.) that ...
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76 views

Bond arbitrage in practice

If we have the following term structure for riskless bonds: \begin{array} {|c|c|} \hline \text{Maturity} & \text{\$1 Zero-Bond price}\\ \hline \text{0 years} & \$ 1.00 \\ \hline \text{1 years}...
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Relationship between Calendar Spread Arbitrage and Probability Density Function (pdf)

We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $\partial ^2C/\partial K^2 \geq 0$, which also means the ...
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Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

Question: Given two call options $c_1$ and $c_2$ with strike price $30$ and $40$ respectively. If $c_1$ costs \$3 and $c_2$ costs \$4, is there an arbitrage opportunity? My attempt: Short $c_2$ and ...
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120 views

A financial market is complete if and only iff there exists a unique equivalent martingale measure

Do you have any intuition behind the following theorem : A financial market is complete if and only iff there exists a unique equivalent martingale measure. I understand the easier version of ...
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theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
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One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$ S_t= 120 \, \text{with probability}\, 0.5 $$ $$ S_t= 60\, \text{with probability}\, 0.5 $$...
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Binomial Model - completeness in presence of arbitrage

Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is $$ V_0 = B_0 + hS_0, $$ ...

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