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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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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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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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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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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
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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
55 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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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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46 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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1answer
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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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219 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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74 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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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
108 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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63 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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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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1answer
275 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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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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77 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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42 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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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
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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
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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
99 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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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
113 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
153 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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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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1answer
102 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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1answer
311 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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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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1answer
119 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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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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1answer
170 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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1answer
123 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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1answer
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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1answer
194 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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1answer
207 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: $$Var(S_t) = 0.199\sim0.2$$ ...
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1answer
47 views

Price of a risk arbitrage call

Let’s say I know that the probability of a merger-acquisition happening is p=1/4, the payoff i’d get in 6M (the time of the merger announcement) is 30. If the merger fails (q=1-p=3/4), my payoff is -...
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213 views

Frequency Arbitrage

We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit ...
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197 views

option call question

i have a question regarding a call option exercise i cant get my head around The price of a stock is 100, the continuously compounded risk free rate is 5%. The strike price of an european call option ...
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204 views

Binomial model's Radon-Nikodym derivative

Related: Dumb question: is risk-neutral pricing taking conditional expectation? In the one-step binomial model... For $\frac{d \mathbb Q}{d \mathbb P}$, I think it's $\frac{d \mathbb Q}{d \mathbb P}...
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358 views

Dumb question: is risk-neutral pricing taking conditional expectation?

Dumb question: is risk-neutral pricing taking conditional expectation? $\tag{1}$ In trying to recall intuition for risk-neutral pricing, I think I read that we should price derivatives risk-neutrally ...
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Interpretation of drift parameter $\mu$ in GBM

Currently studying Ito's calculus. Looking on the GBM model: $ \frac{d S_t}{S_t} = μ dt + \sigma d B_t$ we end up on the expected stock price at time t: $E[S_t]=s_0 e^{\mu t}$.What does actually $\mu$ ...
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295 views

Arbitrage strategies in Rubinstein's binomial tree one-step

Suppose that the current stock price is $S_0=20$ and the call option price with no arbitrage is $c=0.633$. Knowing that the expiry stock price can be $S_T=22$ with call option price $1$ or $S_T=18$ ...
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1answer
76 views

What is arbitraging without moving assets called?

I am currently trying to arbitrage across two markets A and B. My trading strategy is as follows: if the price between A and B differs by more than X%, then go long on the lower priced market, and ...