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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67 views

A financial market is complete if and only iff there exists a unique equivalent martingale measure

Do you have any intuition behind the following theorem : A financial market is complete if and only iff there exists a unique equivalent martingale measure. I understand the easier version of ...
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44 views

theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
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50 views

One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$ S_t= 120 \, \text{with probability}\, 0.5 $$ $$ S_t= 60\, \text{with probability}\, 0.5 $$...
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Binomial Model - completeness in presence of arbitrage

Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is $$ V_0 = B_0 + hS_0, $$ ...
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163 views

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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Law of one Price and Cointegration relationship

I have a question on the relationship between the law of one price and cointegration of (financial) time series. To set things clear I start with something simple: Suppose there is an unobserved "...
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98 views

A relatively useless but fun question for quants and physicists

Suppose I am a trader travelling in a very fast spaceship. What kind of SDE and corresponding PDE should I jot down and work with in order to ensure that there is no arbitrage (or if there is ...
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45 views

Option arbitrage on two correlated or cointegrated underlying assets

If two indices are highly cointegrated, does it allow for some set of statistical arbitrage strategies for european options for which those indices are single underlyings ? Does answer change if ...
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1answer
66 views

Arbitrage-free IV surface definition vs. real arbitrage process

In the context of BS implied volatility surface fitting. In the literature, it seems that conditions for arbitrage are defined in a way that assumes that options can be traded at the same price for ...
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29 views

Arbitrage free volatility smile and delta

If we have a (parametric) volatility surface which has arbitrage, then consider the delta of the options, i.e. $N(d_1)$, where $d_1 = \frac{1}{\sqrt{t}\sigma(K)}\log(F/K) + \frac{1}{2}\sigma(K)\sqrt{...
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113 views

Using cumulative returns to hedge against the overall trend

I am curious about a hypothetical strategy where you are long for a given period (like a year), and at the same time you hedge against the overall trend by going short everyday and accumulating the ...
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Binomial model arbitrage

I've recently started studying math finance from Shreve's Stochastic calculus text. In the binomial model, there is no arbitrage $\iff d<1+r<u$. To show that no arbitrage implies $1+r<u$, ...
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55 views

Arbitrage pricing models

I have been reading Wu's Interest rate modeling and in his chapter on the HJM model he says that With arbitrage pricing models, the prices of the basic instruments are treated as model inputs ...
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27 views

Non-redundant asset?

I've been solving many exercises with three assets that have two possible payoffs each, one payoff per possible future state. The question is always the same, i.e. is any asset redundant. After ...
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31 views

Factor model alternative? [closed]

Suppose there is a Fama-French model estimated for a stock of Shoemaker Ltd.: $α = 0.01$ $β_M = 0.9$ $r_M = 0.12$ $β_S = 0.3$ $S = 0.05$ $β_H = 0.2$ $H = 0.06$ $r_F = 0.03$ How would you ...
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26 views

Arbitrage bounds on volatility of price of binary option?

What are the arbitrage bounds on the volatility of the price of a binary option? If the binary price moves too much (such that it violates the arbitrage bounds) what trades would you actually execute ...
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24 views

Possible interference of Cross-Rate inaccuracy and CIP Deviations

I am currently attempting to calculate historical deviations from covered interest rate parity between 2013 and 2018. I recently read that: "Unlike the interbank spot market, in the interbank ...
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58 views

Definition Of A Portfolio

I have very recently started studying quantitative finance on my own through a book called An Introduction To Quantitative Finance by Stephen Blythe. In chapter 6 of his book, he sets out to prove ...
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185 views

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

Taleb makes the claim in this paper (and others) that there exists some sort of bound on the variance of a binary forecast such that if a forecaster's binary predictions exceed the bounds on variance ...
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49 views

Generalisation of calendar arbitrage condition to options on futures

This question has discussed the condition on which calendar arbitrage opportunities arise for European call options on a stock. Do similar criteria exist for European options on futures? The most ...
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2answers
157 views

Does high levels of vol-of-vol parameter in SABR lead to Arbitrage? (Something seems wrong with Hagans formula)

Main question: Do we need to restrict the vol-of-vol parameter in SABR further than $\text{vol-of-vol}>0$ and how do we determine the interval of vol-vol which the model is arbitragefree? ...
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2answers
116 views

Find arbitrage opportunity in the given market model

Consider the following 3-period-market-model: The discounted price of the risky asset $S$: How can I find an arbitrage opportunity in this model? I know that there would be no arbitrage if we ...
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192 views

How would one sell a security that they don't own?

I am reading an article about arbitrage and it gives an example where "If you buy one unit of security B for £11 and sell two units of security A for £6 each you make a profit of £1 at t = 0$. As ...
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41 views

Price at equilibrium in a market with arbitrage opportunities

I have a fragmented market with multiple assets which are traded with each other and some times triangular arbitrage can occur. The question is how to predict the price of those assets once the ...
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51 views

Arbitrage strategy one-period model

Consider a one-period model with a stock $S_0=1$ and $S_1>0$. Introduce call options with strikes $K_1<K_2<K_3$ maturing at $T=1$. Assume further that $$ C(K_2)>\frac12(C(K_1)+C(K_3)) $$ ...
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43 views

Issue involving arbitrage conditions

In my book it's written that if one of these two conditions is verified then you can make an arbitrage. The two conditions are: $$1) \left\{ \begin{array}{c} \mathbf{q} \bullet\mathbf{n} \le0 \\ \...
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202 views

Are there any quant strategies which do not involve simultaneous buying and selling of two or more assets?

Whenever I read about quant strategies it leads me to stratergies which involve simultaneous buying and selling of two or more assets. Pairs trading, arbitrage, market neurtal or headging all these ...
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2answers
89 views

Gold forward price

In the Hull book, i saw the following exercice and its answer : Suppose the one-year gold lease rate is 1,5% and the one-year risk-free rate is 5%. Both rates are compounded annually. Calculate the ...
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1answer
64 views

Achieving desired fx exposure with using minimum pairs possible

Let say my algorithm tells me to get the following positions through opening fx positions: CUR NET POSITIONS GBP 236.96379 USD -310.58000 CHF 0.02000 There are 2 ways to achieve this: Long ...
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1answer
60 views

Determine the maximum arbitrage profit from the given contracts

I really have tough time trying to figure this out. An investor observes the following prices in the market: Euro-Stoxx-Future DEC 148.02-148.03; Euro-Stoxx-Future Call-Option DEC 148.00 1.13-1.15; ...
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53 views

How to optimize a series of equations whose outputs are a variable of the subsequent equatinos

The basic question is, given $f(x) = y$ and $f(y) = z$, how can you find $x$ such that $z$ is at its maximum? I can optimize each equation independently, but I do not know how to optimize when ...
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93 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
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1answer
232 views

Probability and statistics in Quantitative Finance

Certain types of traders attempt to repeatedly buy and sell the same asset for a profit over a short time period, such as high-frequency “market makers”. For example, if you can repeatedly sell a ...
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1answer
80 views

How can I calculate the amount of volume to use to ensure highest profit on an arbitrage trade of two Constant Product Market Making exchanges? [closed]

If there exists an arbitrage opportunity between two Constant Product Market Making exchanges, how can you confidently determine the maximum volume to use in order to ensure highest profit? I can ...
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1answer
150 views

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). ...
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3answers
116 views

Put Call Parity Arbitrage Question [closed]

I am incredibly stuck on the following question... Any help would be greatly appreciated. According to your binomial model, the price of YMH in 3 months will be either USD 55 or USD 45, with ...
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77 views

value of forward contract at inception

I am reading a derivation of the forward price $F$ of a forward contract. I think the author uses a circular argument to assume that "the value of the forward at inception is equal to 0" because the ...
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109 views

Pairs trading strategy: Portfolio returns and NAV

Currently trying a pairs trading approach using cointegration. Tried both formations: $$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$ $$P_t^A=P_t^B \hat{\gamma}+\hat{\...
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365 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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When does funding cost of a portfolio enter into the portfolio's present value?

This question comes from some confusion when reading Hull's book and from the general concept of no-arbitrage/self-financing portfolios in stochastic finance books. I am not fully seeing the ...
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50 views

Arbitrage argument and Market Quotes [closed]

Good day, I wanted to ask for help with a question from one of my exercise sheets. For a share S the market quotes a given strike K in both european and american styles. Use an arbitrage ...
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1answer
81 views

What do I call the combination of two or more prices when doing arbitrage?

Suppose that I’m doing forex arbitrage between multiple currencies. A possible arbitrage strategy is to combine the currency prices in pairs and then evaluate if there is a chance to make a profit. ...
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53 views

Short sale and zero investmest strategy

Suppose I want to build a pairs trading strategy. Theory says that we can create a zero-investment portfolio by going long stock A and short-selling stock B, given a certain hedge ratio. My question ...
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142 views

Volatility surface fitting, interpolation and extension from sparse data

There are some nice papers about constrained spline fitting essentially giving you a smoothing and arb free surface. I am focusing on the oil market here: The market is essentially split in a very ...
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1answer
67 views

How to determine the cross rate in a triangular arbitrage

I am very confused about what two currencies are to be chosen as the cross rate in a triangular arbitrage. For example, when the bank quotes are ¥180/£ $1.5/£ ¥130/$ Does the cross rate have to be ¥...
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1answer
54 views

How to match future price from the market with the one computed with a model?

I have a future quoted in the market. Let's say $50 price. The price model of this future is : S * Exp (rate + storage - convenience - yield) How can I be sure that the model gives exactly the ...
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1answer
101 views

Most profitable? High % but low probability or Low % but high probability

I have identified a pattern in different assets where a quick spike/flash crash often occurs, dropping the price between -5% and -15% for a few seconds and then going back to previous average. I am ...
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72 views

Prove unique arbitrage-free price implies attainable

I just read a Corollary in a finance course note: Suppose the market is arbitrage free and $C$ is a contingent claim. Then $C$ is attainable if and only if it admits a unique arbitrage-free price. ...
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Arbitrage possible with negative rate of interest?

Given a security having price $1$ at time $t=0$, and price $1+r$ in all world states at $t=T$, i.e., a risk-free bond with interest rate $r$. At $t=0$, short this and also buy an other risk-free bond. ...
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1answer
137 views

Showing that a market model has arbitrage and describing martingales

This is an exercise which I came upon while studying an introduction to financial mathematics. Exercise : Consider the finite sample space $\Omega = \{\omega_1,\omega_2,\omega_3\}$ and let $\...