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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18 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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22 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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40 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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167 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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29 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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123 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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82 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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191 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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38 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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50 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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42 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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191 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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78 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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57 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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45 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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49 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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69 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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226 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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79 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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135 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
109 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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69 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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95 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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311 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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58 views

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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48 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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78 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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47 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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124 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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63 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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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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61 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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120 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 $\...
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1answer
164 views

Risk neutral valuation formula

I am totally new to Finance and Arbitrage theory and I have started reading Björk (2018) Arbitrage theory in continuous time. Can anyone please explain to me what is the risk-neutral valuation formula ...
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150 views

Arbitrage from ATM option trading?

So I was testing out a collar options strategy (long put, short call, and long shares of the underlying stock) in a backtest for a school finance project, and the profits & losses are given by the ...
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115 views

How to calculate riskless profit out of call options?

I'm having trouble with working out a question that I can't currently ask my lecturer as they're away. Hoping for some help here with why the answer is (a). A stock price is currently \$40. It is ...
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326 views

Prove that a market is arbitrage free

The question is based on a one period model. Let a market be arbitrage free, and then let a security $X$ be added to it. Denote $P(X)$ as the price of this security at $t=0$. The security has the ...
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Checking arbitrage for the SABR model - analytical vs numerical approach

I wish to check if the fitted volatility smile/surface from the SABR model for a fixed time period is arbitrage free. Through my research, I've learnt the following need to be checked: The RND (risk ...
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514 views

Does Black Scholes need to assume no arbitrage?

Since Girsanov's theorem guarantees a risk neutral measure for Geometric Brownian motion, by the fundamental theorem of asset pricing there can be no arbitrage. So, why does the model assume no ...
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120 views

“Dusty Corners of the Market” and Limits-to-Arbitrage

In his 21 November 2014 blog post, Dusty Corners of the Market, John Cochrane seems to imply that certain areas of the market tend to be more resilient to the forces of arbitrage and efficiency. The ...
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Definition of Arbitrage

Definition. An arbitrage is a portfolio $H$ ∈ $R^n$ such that • $H⋅P_0≤0≤H⋅P_1$ almost surely, and • $P(H⋅P_0=0=H⋅P_1)<1$. where $P_0$ and $P_1$ ∈ $R^n$ represent the prices at time $t=0,1$ ...
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Equivalent martingale measure in time changed Levy models

I am investigating time changed Levy models. As far as I have seen, these models are usually directly described under the risk neutral measure $\mathbb{Q}$. However, I'm interested in first modelling ...
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79 views

Piterbarg's Rates Squared - Quadratic Models and Arbitrage

I am trying to follow Piterbarg's formulation in "Rates Squared" paper for QG model. It looks like he is ignoring the third Riccati equation in favour of an arbitrage condition in $T$ forward measure. ...
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198 views

Understanding Forex HFT Arbitrage with different counter parties/ Brokers/ ECN

I came across this in a online lecture. But couldn't wrap my head around it. Lets say I have accounts with two brokers/ECN/STP. Now consider the following scenario for currency pair USD/JPY Broker1: ...
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138 views

Risk of Put-Call-Parity in practice

When $C+PV(K) \ne P + S_0$, it's an opportunity for risk-free arbitrage (excluding cost). In practice, what potential risk could make the arbitrage fail? I know that failure to build complete ...
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75 views

Adding a new strategy to an existing portfolio

I wanted some help in looking for suitable articles/literature. Suppose an investor has a bunch (bouquet?) of quantitative strategies already generating trading signals for him. If he comes up with a ...
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200 views

Please explain this proof for me: (arbitrage and bounded set) [closed]

Consider this problem and subsequent proposition: Part of the proof of this proposition is given here: Could somebody please explain to me why the existence of the "associative ray" (which I have ...
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228 views

European Call price for an asset with mean reverting (Vasicek model) dynamics

Let's look at a stock with a mean reverting price dynamics: $$dS_t = a(S-S_0)dt + \sigma dW_t$$ If we let $\sigma=0.25$ and $a=-0.5$ then the variance of this process is: $$Var(S_t) = 0.199\sim0.2$$ ...