# 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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4answers
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### risk-neutral valuation implies no arbitrage?

It is known that in an arbitrage-free continuous time market, the price of every asset is evaluated as the corresponding price in the replicating strategy using risk-neutral valuation. I want to ...
1answer
84 views

### Law of one price in continuous time

The law of one price (i.e. for assets $S^{(i)}$ and $S^{(j)}$, $S^{(i)}_T = S^{(j)}_T$ almost surely implies that $S^{(i)}_t = S^{(j)}_t$ almost surely for all $0 \leq t \leq T$) is known to hold ...
2answers
679 views

### arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy \begin{equation} dB_t = B_t r dt \end{equation} \begin{equation} \quad \quad \quad \quad \, ...
2answers
810 views

### 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% ...
1answer
91 views

### Pricing rule shall be a martingale measure

In the book "Financial Modelling with jump processes" by Cont and Tankov there is a chapter that explains martingale pricing principles. It is not extremely formal, but gives the idea underlying the ...
1answer
238 views

### Replicate by Arbitrage price of a forward

Given market(Mid): 1- USD Swap market (fixed for float). Float leg pays 3MLibor quarterly, act360. Fixed Leg pays annually, act360. Market is trading mid at 1.125%. 2- TIIE market. Fixed for ...
1answer
1k views

### What is the difference between market efficiency, market equilibrium, and no-arbitrage?

Aaron Brown (in the book, The Poker Face of Wall Street, p. 196), discusses four approaches to deriving the same Black-Scholes-Merton option-pricing formula: Ed Thorp, Myron Scholes, Robert Merton, ...
1answer
69 views

### Risk-free arbitrage given a volume oracle?

Given a magical oracle who can correctly predict the volume, but not the price, of a given security, does there exist a risk-free arbitrage to capitalize on this information?
3answers
8k views

### How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc... Let $C(T,K)$ be the price of a call with ...
1answer
406 views

### If I am very fast (less than 10 microseconds latency) what would be the first strategy to execute? [closed]

Let's assume I found the holy grail of low-latency trading (which I didn't). For educational purposes, what would be the first strategy I would direct my trading code?
1answer
2k views

### 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?
1answer
2k views

### Calibrating an Ornstein Uhlenbeck process on residuals of regression

I am trying a basic statistical arbitrage strategy as follows: Perform PCA on a log return series of a basket of stocks Regress returns against top principal components identified Calculate the ...
2answers
2k views

### What software should I use for forex arbitrage?

These are my requirements: Speed of lookup & update Speed of crunching large numbers and combinations The exchanges I want to connect to will mostly provide json feeds to their orderbooks & ...
2answers
531 views

### How does this follow from the separating hyperplane theorem?

This is from Pliskas book in mathematical finance. I do not know what was best to write the question so I included the pages from the book. He has not written what form of the separating hyperplane ...
1answer
196 views

### ADR vs Foriegn Stock Price Arbitraguers

So I am sure you all know about the whole Argentina default that has been in the papers lately, no need to delve into it. This so called "technical" default has lead some interesting investment ...
2answers
248 views

### M&A hedging an equity portfolio against an index

Quick Note This question was already posted under the userID user8170. Reason being I could not access my account. Now I am able to login to my account I am reposting the question here and will ...
3answers
466 views

### Is this arbitrage?

Assume the stockprice as in the Black-Scholes model (Geometric Brownian Motion): $$S_t=S_0e^{(\mu-\sigma^2/2)\cdot t+\sigma W_t}$$ Wouldn't there be an immediate arbitrage opportunity, to just buy ...
2answers
2k views

### law of one price, understanding

I am reading about mathematical finance, and I was tipsed to ask the quesiton on this site. It is about the "law of one price". Just first I'll make precise the model my book uses: I have a single ...
2answers
281 views

### Non-Negativity of up-factor and down-factor in Binomial No-Arbitrage Pricing Model

Consider a stock which is trading at $S_0$ at time $t=0$ and is expected to be trading at price $uS_0$ or $dS_0$ at time t=1 where $u$ and $d$ are up-factor and down-factor. The theory says that to ...
3answers
2k views

### Arbitrage free implies complete market?

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition It seems that to show that the model is complete, we must show that the claims are reachable. That is, we ...
2answers
195 views

### Pricing Principle 1

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this Pricing Principle. Is the one in red supposed to be the proof of the Pricing Principle 1? Or merely an intuitive ...
1answer
423 views

### Prove that the binomial algorithm implies the arbitrage free price at t=0 of a T-claim

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ these propositions How does the first formula follow from from the algorithm? I get that $\Pi(0;X) = V_0(0)$, but I don't ...
2answers
677 views

### 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 ...
2answers
398 views

### 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 ...
1answer
539 views

### How Much Capital is Needed to Start an Arbitrage Strategy?

I'm trying to experiment with a simulated simple arbitrage strategy. I'm not doing this to actually invest, I'm just curious if the market is inefficient enough for this to be feasible. Every ...
1answer
212 views

### In a Black-Scholes world, why must volatility be strictly increasing in time-to-expiration?

This question is from Rebonato's Volatility and Correlation 2nd Edition. Rebonato states that if $\sigma_T^2T$ is not strictly increasing, it would be simple to set up an arbitrage. Unfortunately (...
1answer
2k views

### Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
1answer
327 views

### Arbitrage Strategy Proof in Bjork

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition Proposition 2.9 Suppose that a claim X is reachable with replicating portfolio h. Then any price at t=0 of ...
3answers
11k views

### Volatility arbitrage - how is the profit extracted?

Is there any paper that describes in detail how the profit is extracted in directional volatility bet (vol arb)? I mean in the case that I bet the realized volatility will be lower than currently ...
1answer
275 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 ...
2answers
396 views

### Why is the LIBOR-market model free of arbitrage?

Recently I have been reading a lot on the market models. One thing that keeps escaping me - why is the Libor-market model (LMM) assumed to e free of aritrage in continuous time ? To me this means ...
2answers
198 views

### Harnessing small correlations for reliable profit

It is said that Edward O. Thorp was able to harness small correlations for reliable financial gain. I've seen some strategies based on strong correlations which did not seem particularly reliable. ...
1answer
119 views

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### main arbitrage & statistical arbitrage concepts

Can we please sumarise here some of the basic concepts, tools used in arbitrage and statistical arbitrage in real life? ARB: benefit from price difference on same asset ARB: difference between stock ...