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13 votes
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How to exploit calendar arbitrage?

The answer by @HenriK is certainly correct. However, for justification, technique such as the Jensen inequality is needed. For example, since $x^+$ is a convex function, assuming zero interest and ...
Gordon's user avatar
  • 21.1k
13 votes
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statistical arbitrage vs factor trading

1) Why would you trade the error on the residual instead of creating a long/short factor model and trade expected returns? I would posit that the biggest reason people do this is for orthogonality of ...
mperlow's user avatar
  • 456
11 votes
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What is the pseudo code for a pairs trading strategy?

The following link has a good summary of a typical pair trading strategy: https://www.quantstart.com/articles/Backtesting-An-Intraday-Mean-Reversion-Pairs-Strategy-Between-SPY-And-IWM It actually ...
KarolisR's user avatar
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10 votes
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Can someone explain rigorously Taleb's criticism of Nate Silver's election forecasting?

hope I am not too late to the party. tl;dr Taleb's paper draws incorrect conclusions from a set of wrong assumptions. In practice, the movements of the forecast at 538 are very much in line with what ...
Gabriele Bonomi's user avatar
10 votes

When looking for arbitrage among a LARGE amount of assets, is there an optimal way?

For example, Thomas H. Cormen, Charles E. Leiserson, Ronald Rivest, Clifford Stein. Introduction to Algorithms, problem 24-3 says: 24-3 Arbitrage Arbitrage is the use of discrepancies in currency ...
Dimitri Vulis's user avatar
9 votes

Calendar Arbitrage in a Vol Surface

In a pure diffusion setting, you can equivalently write no calendar arbitrage constraints: In terms of implied volatility: total implied variance should be non decreasing in time, and that, for any ...
Quantuple's user avatar
  • 14.7k
9 votes

Arbitrage possible with negative rate of interest?

As a practical aside on a large scale, I have heard the rumours of European banks and even a consortium of banks considering plans to build an ultra secure deposit facility for cash, and also the ECBs ...
Attack68's user avatar
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9 votes
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Making a beeline to statistical arbitrage

I get this question frequently from academic types, and happily for you, the path does not involve any of those books. The major gaps in your knowledge, from the point of view of statistical arbitrage,...
Brian B's user avatar
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8 votes
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Why must a riskless portfolio earn the risk-free rate?

If you imagine you have two risk-less assets that have a unit payoff at maturity $V_1(T) = V_2(T) = 1$ but their present value is not equal, e.g. $V_1(t) < V_2(t)$. You buy the cheaper, sell the ...
LocalVolatility's user avatar
8 votes
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Finding arbitrage opportunity

Generally speaking, let us consider a problem where you have a series of simple payoffs $f_{K_i}(S_T)$ of strike $K_i$, $i \in I$, that depend on the value of $S_T$ at time $T$, as well as a more ...
Daneel Olivaw's user avatar
8 votes
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Do price approximations lead to arbitrage opportunities?

No. The dirty price is the market's estimate of fair value for the bond. The clean price is just a quoting convention (so that the price doesn't jump when you pass over a coupon date). The market ...
Chris Taylor's user avatar
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8 votes

Can someone explain rigorously Taleb's criticism of Nate Silver's election forecasting?

Taleb argues that under uncertainty, election forecasts should be seen as a Binary option. A similar thought is presented by De Finetti's principle that probability should be treated like a two-way "...
alexbougias's user avatar
  • 1,416
8 votes

Why isn't the Vasicek model arbitrage-free?

Short rate models are broadly divided into equilibrium models and no-arbitrage models. The models from Vasicek, Dothan and Cox, Ingersoll and Ross are examples of equilibrium short rate models. The ...
Kevin's user avatar
  • 16k
8 votes

Boundary for European Put Option

Let's carefully distinguish which exercise type we consider. European-style call option $$ \max\{S_0-Ke^{-rT},0\}\leq C_E \leq S_0.$$ European-style put option $$\max\{Ke^{-rT}-S_0,0\}\leq P_E\leq ...
Kevin's user avatar
  • 16k
8 votes
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Why do transaction costs increase the range of the no-arbitrage bounds for an option's price?

Assume a store is fairly pricing a bottle of water at \$1. Now another store is pricing the same bottle of water for \$1.2. Assuming it is possible, you can buy the water at the first store, end sell ...
Pontus Hultkrantz's user avatar
7 votes

Why was CDS-bond basis close to zero before the financial crisis?

You and the paper are both correct. Funding was not free before the GFC, but the funding cost of both positions then was almost equal, generating almost-zero basis. Since then, holding physical bonds ...
demully's user avatar
  • 5,071
6 votes
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Violation of the call-put parity

On 10/24/17, Wells Fargo announced that they would pay a dividend of 0.39 to holders of record on 11/3/17. Thus, if you buy the stock after this date (through the exercise of the call) you do not get ...
dm63's user avatar
  • 17.2k
6 votes
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Definition of Arbitrage

Conceptually, an arbitrage gives you something for nothing. This is a different idea than making or losing money almost surely. A risk free bond allows you to make money almost surely, but it isn't an ...
Matthew Gunn's user avatar
  • 6,954
6 votes
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Do *all* non-dividend paying assets have the risk-free instantaneous return rate under the risk-neutral measure?

Under the assumption that the market is complete, any discounted contingent claim can be replicated as a stochastic integral against the discounted stock price, therefore the discounted contingent ...
Antoine Conze's user avatar
6 votes
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Risk-Neutrality: Discount factors of the $P$ world according to risk preferences?

You're right. Euler's equation states $$p_t=\mathbb E^\mathbb P_t[M_{t+1}X_{t+1}],$$ that is pricing under $\mathbb P$ requires you to know the stochastic discount factor (SDF, aka pricing kernel) $M$....
Kevin's user avatar
  • 16k
6 votes
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Are risk-free-rate bonds and cash fungible?

First of all your statement is not quite correct. If you receive cash as collateral, you have to pay me interest at whatever rate we have agreed to (probably Fed Funds). If you receive bonds as ...
dm63's user avatar
  • 17.2k
5 votes
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What is the arbitrage opportunity in this simple one-period market?

Sell 1 unit of S1,2,3 respectively, gain 3; buy 2 units of risk-free asset, cost 2. No matter which state appears, the future payoff/loss is 0 for sure, while you will gain 1 at the beginning.
Brownian3's user avatar
  • 121
5 votes

What is Toxic FX Flow debate?

The primary way ECNs determine if a liquidity taker's flow is 'toxic' or not is by looking at aftermath charts. The aftermath chart shows the average mark-to-market profit of trades done by the ...
mpeac's user avatar
  • 415
5 votes
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Does Black Scholes need to assume no arbitrage?

This is a far subtler and deeper rabbit hole than appears. Harrisson, Kreps and Pliska’s papers explain the completeness, uniqueness and risk-neutral aspects. With regards to the BS framework, it ...
Ivan's user avatar
  • 1,396
5 votes

Arbitrage possible with negative rate of interest?

Indeed, interest rates have been below zero and your logic appears sound. My conclusion: safe mattresses that are large enough don’t exist.
Bob Jansen's user avatar
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5 votes
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How to prove no-arbitrage when a long butterfly is strictly positive?

I am not sure why the question you link to does not provide an answer. I’ll try to answer it but it is really similar to what has already been said there. Bottom line is: if the value $K$ is reachable ...
Daneel Olivaw's user avatar
5 votes
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Does CRR Model lose completeness if we add another instrument?

I answer from a general discrete time/discrete state model point of view. This includes the binomial tree model as a special case. In finite dimensions, you can interpret asset payoffs and returns as ...
Kevin's user avatar
  • 16k
5 votes
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Risk-neutral Probability, Risk-Adjusted Returns & Risk Aversion

It would make total sense for you to quote the price of a financial instrument by discounting its future cash flows according to your own risk aversion ($\Bbb{P}$ measure, stochastic discount factor). ...
Quantuple's user avatar
  • 14.7k
5 votes

Risk-neutral Probability, Risk-Adjusted Returns & Risk Aversion

My thoughts: Risk-neutral probability measure ${Q}$ is a convenient mathematical tool that is used primarily for pricing derivatives The price of a derivative is essentially the price of the ...
Jan Stuller's user avatar
  • 6,118
5 votes
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No free Lunch and weak-star topology

The context of weak$^*$ topologies and no free lunch is often the proof of the first fundamental theorem of asset pricing. All the ideas below are from Delbaen and Schachermayer (1994). Notation ...
Kevin's user avatar
  • 16k

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