28 votes
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Arbitrage opportunity interview question

A similar question for put option has been discussed in this question: Finding Arbitrage in two Puts. Basically, the call option payoff is a convex function of the strike. Then the call option price ...
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16 votes
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Volatility arbitrage - how is the profit extracted?

Setting aside, that it's not pure riskless arbitrage, but rather statistical arbitrage: You can extract the profit by performing continuous delta hedging. If you constantly adjust your hedge position ...
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  • 683
12 votes
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Arbitragefree Pricing: Q vs. P

In the derivatives context, "arbitrage free" means almost surely for the probability measure under consideration. This is in opposition with statistical arbitrage used at high frequencies for example. ...
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12 votes
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Why doesn't Black-Scholes assume the absence of statistical arbitrage?

Neither. Black--Scholes says nothing about the parameter values: $\mu$ and $\sigma.$ A very large $\mu$ and very small $\sigma$ is very unlikely to actually occur in the market and if it did you ...
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11 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 ...
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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 ...
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  • 693
11 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 ...
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  • 406
10 votes
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Finding Arbitrage in two Puts

Let $K_1=0$, $K_2=80$, and $K_3=90$. Then \begin{align*} K_2 = 1/9 \, K_1 + 8/9 \, K_3. \end{align*} Moreover, \begin{align*} Put(K_2) &= Put(1/9 \, K_1 + 8/9 \, K_3)\\ &< 1/9 \, Put (K_1)...
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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 ...
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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 ...
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9 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 ...
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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,...
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  • 14.4k
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 ...
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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 ...
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  • 5,603
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 "...
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  • 1,346
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 ...
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7 votes

Pricing when arbitrage is possible through Negative Probabilities or something else

You cannot use negative probabilities in this context. When there is no unique probability measure, there can be no unique price. You only know that it is in [0, 0.6] range, if you want to tighten ...
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  • 346
7 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 ...
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7 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 ...
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7 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 ...
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7 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 ...
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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 ...
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  • 4,896
6 votes

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

In three bullet points: Efficiency: the obtained prices maximize assumed utilities of different agents. In their paper "The Valuation of Option Contracts and a Test of Market Efficiency", Cohen, ...
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6 votes
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Pricing when arbitrage is possible through Negative Probabilities or something else

I believe there is not a unique price if you can't short. Say, instead of buying the option you spent 0.5 on a half a unit of the asset $S^2_1$ This asset pays out $[0.4, 0.6, 0.8]$ which first order ...
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  • 226
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 ...
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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 ...
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  • 6,294
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 ...
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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) $M$....
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5 votes

How to exploit calendar arbitrage?

You should always think: I buy the one which is too cheap and sell the one that is too expensive and figure it out. The figuring out in this case is noting that: $C\geq 0$ since it will never cost ...
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