# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### What literature (books, articles, etc.) should someone hoping to learn basic HFT / arbitrage strategies read first? [closed]

I am not looking for your winning strategies. Just the basic stuff from where to start. Can anyone share their opinions about what should I read to hit the ground running?
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### 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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### 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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### 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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### 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 ...
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,... 1answer 106 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 ... 2answers 90 views ### 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 ...
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 ...