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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322 views

What are the essential characteristics of asset prices?

I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., ...
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199 views

Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time $T$...
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383 views

Show that in an arbitrage-free and non-redundant market a certain set is compact

Some notation: We consider a financial market with $d+1$ assets, the $0$-th asset is considered the risk-free asset, the others are the risky ones. The vector $\overline \pi \in \mathbb R^{d+1}$ ...
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382 views

Calculating index arbitrage

I have a days-worth of level 2 market data. I am calculating S&P500 index arbitrage. I have a few questions about the calculation: 1) Should I be summing all the bids and asks from the stocks ...
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67 views

Law of one Price and Cointegration relationship

I have a question on the relationship between the law of one price and cointegration of (financial) time series. To set things clear I start with something simple: Suppose there is an unobserved "...
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229 views

Volatility surface fitting, interpolation and extension from sparse data

There are some nice papers about constrained spline fitting essentially giving you a smoothing and arb free surface. I am focusing on the oil market here: The market is essentially split in a very ...
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111 views

Equivalent martingale measure in time changed Levy models

I am investigating time changed Levy models. As far as I have seen, these models are usually directly described under the risk neutral measure $\mathbb{Q}$. However, I'm interested in first modelling ...
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287 views

Binomial model's Radon-Nikodym derivative

Related: Dumb question: is risk-neutral pricing taking conditional expectation? In the one-step binomial model... For $\frac{d \mathbb Q}{d \mathbb P}$, I think it's $\frac{d \mathbb Q}{d \mathbb P}...
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625 views

When is implied volatility greater than realized volatility?

Assume it to be known that the volatility of a stock at any point in time is $\sigma(t)$. My question is, if we have a number of options priced using some implied volatilities $\sigma_1, ..., \...
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70 views

FTAP in the model independent case, paper by Schachermayer

I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions ...
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1answer
68 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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94 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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143 views

Prove unique arbitrage-free price implies attainable

I just read a Corollary in a finance course note: Suppose the market is arbitrage free and $C$ is a contingent claim. Then $C$ is attainable if and only if it admits a unique arbitrage-free price. ...
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230 views

Arbitrage from ATM option trading?

So I was testing out a collar options strategy (long put, short call, and long shares of the underlying stock) in a backtest for a school finance project, and the profits & losses are given by the ...
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163 views

Checking arbitrage for the SABR model - analytical vs numerical approach

I wish to check if the fitted volatility smile/surface from the SABR model for a fixed time period is arbitrage free. Through my research, I've learnt the following need to be checked: The RND (risk ...
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106 views

Piterbarg's Rates Squared - Quadratic Models and Arbitrage

I am trying to follow Piterbarg's formulation in "Rates Squared" paper for QG model. It looks like he is ignoring the third Riccati equation in favour of an arbitrage condition in $T$ forward measure. ...
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278 views

Frequency Arbitrage

We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit ...
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88 views

An arbitrage strategy involving forward contracts to show that LIBOR rates are martingales

I note $L_{t}^{[T_s, T_e]}$ the forward rate at time $t$ for the period $[T_s, T_e]$. Recall it is the strike making equal to $0$ the value at time $t$ of a forward contract for the period $[T_s, T_e]$...
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92 views

What is a standard model of convergence when looking at negative stub values?

I am trying to understand whether or not there is a standard model of convergence in the arbitrage scenario of negative stub models, i.e. when the market value of a company is valued less than its ...
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65 views

How to optimize an arbitrage portfolio when taking into account different speeds of mean reversion?

In portfolio optimization, it is insufficient to just note the size of price deviation - that only tells the amount of profit if held to maturity. One also needs to take into account reversion speed - ...
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239 views

Are there alternatives to the Box-Tiao decomposition in identifying mean reverting portfolios?

As documented in this paper, Box-Tiao decomposition (a way to decompose multiple time series into components with different speeds of mean reversion) can be used to identify mean reverting portfolios. ...
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37 views

Helpful references for fully understanding the mechanics of NASDAQ's auction system?

I've read about this before on their website directly and via this ITG paper. nasdaq site itg paper But I was wondering if there are any other good references I can supplement my understanding ...
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127 views

Risks Associated with Option Arbitrage Portfolio

If my math is correct, if I construct the following portfolio of options the worst that I can do regardless of what the underlying does is profit $1.74 (less commissions). Is this correct? Are there ...
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86 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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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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62 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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97 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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80 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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60 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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45 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 ...
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44 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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66 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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64 views

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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59 views

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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51 views

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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111 views

A relatively useless but fun question for quants and physicists

Suppose I am a trader travelling in a very fast spaceship. What kind of SDE and corresponding PDE should I jot down and work with in order to ensure that there is no arbitrage (or if there is ...
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63 views

Arbitrage pricing models

I have been reading Wu's Interest rate modeling and in his chapter on the HJM model he says that With arbitrage pricing models, the prices of the basic instruments are treated as model inputs ...
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44 views

Non-redundant asset?

I've been solving many exercises with three assets that have two possible payoffs each, one payoff per possible future state. The question is always the same, i.e. is any asset redundant. After ...
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26 views

Possible interference of Cross-Rate inaccuracy and CIP Deviations

I am currently attempting to calculate historical deviations from covered interest rate parity between 2013 and 2018. I recently read that: "Unlike the interbank spot market, in the interbank ...
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143 views

Generalisation of calendar arbitrage condition to options on futures

This question has discussed the condition on which calendar arbitrage opportunities arise for European call options on a stock. Do similar criteria exist for European options on futures? The most ...
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51 views

Price at equilibrium in a market with arbitrage opportunities

I have a fragmented market with multiple assets which are traded with each other and some times triangular arbitrage can occur. The question is how to predict the price of those assets once the ...
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135 views

Pairs trading strategy: Portfolio returns and NAV

Currently trying a pairs trading approach using cointegration. Tried both formations: $$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$ $$P_t^A=P_t^B \hat{\gamma}+\hat{\...
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66 views

When does funding cost of a portfolio enter into the portfolio's present value?

This question comes from some confusion when reading Hull's book and from the general concept of no-arbitrage/self-financing portfolios in stochastic finance books. I am not fully seeing the ...
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132 views

Best strategy to maximize Profit if no transaction cost?

I was recently in a competition which simulated real time currency trading. Teams were supposed to build bots that could request current prices of currencies, buy, or sell currencies using HTTP ...
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126 views

How does volatility affect price arbitrage?

Suppose I'm running automated classic price arbitrage on 3 currencies (let's ignore the unfeasibility of this in our day and age). We have currency pairs Gold/Silver, Silver/Bronze, and Gold/Bronze. ...
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200 views

How would you arbitrage this?

Assume it to be true that $dS = S\mu dt + \sigma(t)S dW$ where $\sigma$(t) is known. Consider a call option with expiry $T$, currently $t = 0$. For all $t \in [0,T]$, $\sigma(t) < \sigma_{impv}$ ...
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317 views

Fair price and no arbitrage

The market is arbitrage-free iff there exists an equivalent martingale measure for the discounted price process of the stock. So in a world with a finite amount of possible outcomes $\Omega$ that ...
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425 views

Different definitions of arbitrage

Consider the following setup: Let $S=\left(S_1,\ldots,S_n\right)$ be a $n$-dimensional price process and denote by $V$ its value process defined by $V_t=\phi_t\dot\ S_t$ for $t=0,\ldots,T$. In "...
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52 views

Arbitrage and completeness in multiperiod model?

Given a 2-period market with above stock price process along with a riskfree stock with a return of 5%, how do I determine whether the market is arbitrage-free and complete when I only have knowledge ...
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90 views

How do most arbitrage opportunities account for unknown volume at a ticker price?

So, from a conceptual level, arbitrage seems quite forward... buy at one place at one price, and sell somewhere at a higher price. However, after doing some initial digging it appears to be not quite ...