# 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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### 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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### Why doesn't Black-Scholes assume the absence of statistical arbitrage?

Both Black-Scholes and binomial model assume that there's no risk-free arbitrage in the market. But that sounds like a very weak condition. If a trading scheme makes you gain 100 dollars with 99% ...
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### Finding Arbitrage in two Puts

A European Put Option on a non-dividend paying stock with strike price 80 is currently priced at 8 and a put option on the same stock with strike price 90 is priced at 9. Is there an arbitrage ...
827 views

### Finding arbitrage opportunity

Find an arbitrage opportunity in this market. Can anyone explain how to mathematically solve this exercise with for example solving a system of linear equations?
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I am reading a paper that very briefly talks about some volatility arbitrage strategies. It's so brief that I do not exactly understand how it works. It says one of the strategy is based on "short ...
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### Calendar Arbitrage in a Vol Surface

I am trying to determine the condition such that my implied vol surface doesn't have calendar arbitrage. I have done research and found that one such condition is that total variance should increase ...
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### Why isn't the Vasicek model arbitrage-free?

Could anyone explain why the Vasicek model isn't an arbitrage-free model? Additionally, which interest rate model is arbitrage-free and why?
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### Do *all* non-dividend paying assets have the risk-free instantaneous return rate under the risk-neutral measure?

For simplicity let's consider a 1D BS world. The only source of randomness comes from the Brownian motion dynamics $dB_t$. The risk-free rate is $r$ (one may assume it as constant for the time being). ...
399 views

### What is the arbitrage opportunity in this simple one-period market?

I have a single period market, and three states, and I have 3 risky assets. I assume no interest. So I have three states $\Omega=\{\omega_1,\omega_2,\omega_3\}$. All assets start with the value 1, ...
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### European Call price for an asset with mean reverting (Vasicek model) dynamics

Let's look at a stock with a mean reverting price dynamics: $$dS_t = a(S-S_0)dt + \sigma dW_t$$ If we let $\sigma=0.25$ and $a=-0.5$ then the variance of this process is: $$Var(S_t) = 0.199\sim0.2$$ ...
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### Slight confusion regarding arbitrage opportunities in ETFs as mentioned by investopedia

On the "how ETF arbitrage works" page, investopedia says The arbitrage opportunity happens when demand for the ETF increases or decreases the market price, or when liquidity concerns cause ...
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### Which is the correct definition of arbitrage?

Spin-off from here. In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ 2 inconsistent definitions of arbitrage, which is correct? The first definition is for the single period ...
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### Risk neutral valuation formula

I am totally new to Finance and Arbitrage theory and I have started reading Björk (2018) Arbitrage theory in continuous time. Can anyone please explain to me what is the risk-neutral valuation formula ...
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### “Dusty Corners of the Market” and Limits-to-Arbitrage

In his 21 November 2014 blog post, Dusty Corners of the Market, John Cochrane seems to imply that certain areas of the market tend to be more resilient to the forces of arbitrage and efficiency. The ...
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### 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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### References on Statistical Arbitrages

Is there any basic materials (books, papers) to read on Statistical Arbitrage? I certainly understand much of the useful information is in the industry. I just want to get some understanding on the ...
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### Inconsistent Definition of Arbitrage in Bjork?

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ what seems to be 2 inconsistent definitions of arbitrage: The first definition is for the single period Binomial model The ...
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### 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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### Swaption Volatility Cube arbitrage

How can I exploit an arbitrage by violating the following no-arbitrage condition (taken from the paper "Arbitrage-Free Construction of the Swaption Cube" by Simon Johnson and Bereshad Nonas): Swptn(K,...
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### What is the difference between state prices and stochastic discount factor?

I was reading a paper on arbitrage and it was mentioned that a positive SDF implies no arbitrage and later on it said that positive state prices imply no arbitrage. I am new to this topic and i am ...
276 views

### Pricing of a simple contingent claim

Earlier I had the question (5.11 Tomas Bjork): $$\frac{\partial F}{\partial t}+\frac{1}{2}x^2\frac{\partial^2 F}{\partial t^2}+x = 0$$ $$F(T,x) = ln(x^2)$$ And solve it using Feynman-Kac. The ...
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### 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 ...
642 views

### statistical arbitrage using PCA

While reading the paper Statistical Arbitrage in the U.S. Equities Market by Marco Avellaneda and Jeong-Hyun Lee on statistical arbitrage using PCA I realized that the author sums the residuals of ...
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### Dumb question: is risk-neutral pricing taking conditional expectation?

Dumb question: is risk-neutral pricing taking conditional expectation? $\tag{1}$ In trying to recall intuition for risk-neutral pricing, I think I read that we should price derivatives risk-neutrally ...
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### Is there an efficient method or technique to find an arbitrage between two FX dealers?

I was able to solve the following problem and find the arbitrage but only after spending a long time on it and trying out different possibilites. Is there a method or technique that can help me find ...
686 views

### Prove that a market is arbitrage free

The question is based on a one period model. Let a market be arbitrage free, and then let a security $X$ be added to it. Denote $P(X)$ as the price of this security at $t=0$. The security has the ...
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### How do you decide what time frame you're going to use when testing for cointegration?

I've been fiddling around with different time frames when doing tests for cointegration between two timeseries, and I've realized that the dates that you use for your start/stop of the test will ...
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### Latency arbitrage: what exactly is the arbitrage mechanism?

I'm reading about latency arbitrage in regards to direct exchange feeds vs. SIP feeds. SIP feeds are on average 1 millisecond slower than direct feeds, which allows HFTs to see an NBBO update before ...
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### What are the answers to these questions on card deck and option pricing?

here are 3 questions I have some trouble dealing with. Your help will be greatly appreciated! 1 - We have a deck card: 26 red, 26 black. we play a game: you draw a card from the deck without putting ...
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### Self-Frontrunning Arbitrage

If I have a large order to fill, shouldn't I always buy a derivative in the same direction to profit from the market impact? E.g. I sell 1 million shares and so I buy a put, which will hence almost ...
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### arbitrage opportunity in a two period model

I have a little problem evaluating an european call. I Suppose the following: in $$t=0 : S_0 = 10$$ $$t = 1 : S_1 = \{10,11\}~with ~p=0.5$$ riskless rate : $(1+r)=\beta=1.049$ Strike ...