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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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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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37 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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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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How to check if arbitrage is possibile in a recombining Binomial tree

Consider the recombining Binomial tree below; knowing that: $S_0 = 100$ is the cost of an asset at $t=0$ (now), $∆t$ is the distance between two time points, e.g. $∆t = 0.5 =$ six months, $...
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51 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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93 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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35 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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91 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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102 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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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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205 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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Calibration of financial models when only pricing PIDE is known

This is a rather general question but I have not found much on it on the internet. Suppose I describe the stock price dynamics under the risk neutral measure by some SDE. Suppose that I don't have any ...
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223 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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“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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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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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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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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54 views

Why is it called Linear Multi-factor models (APT)?

In what way are no arbitrage sentral for the APT model? The model is derived from maximizing a von Neumann-Morgenstern utility function subject to a budget constrant. Where does the no arbitrage ...
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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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111 views

Price Series vs Returns series for pairs trading

Consider two stocks A and B. Suppose we regress their price series and find a coefficient β. Specifically, Pi = βQi + Ei And we find that the Error is mean reverting. So the strategy ...
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145 views

Arbitrage Strategy Long American Call and Short European Call

We know for the fact that the holder of an American call option has all the same rights as the holder of a European call option and more. This also results in American call option always worth at ...
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96 views

How to deal with no-arbitrage violations to fit the volatility smile?

I have a database of options for single stocks, with a lot of aggregated data. I noticed that sometimes (especially for stocks with few points) I have a concave volatility smile because of an outlier ...
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54 views

Is it possible to construct a leveraged position at the risk-free rate?

Looking online at brokers who offer spread betting accounts, traders are able to enter into hugely leveraged positions on certain assets (say, currencies). For example, FXCM allows new traders to use ...
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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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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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Arbitrage opportunity with call options? [duplicate]

Call options with strikes 100, 120, and 130 on the same underlying asset and with the same maturity are trading for 8, 5, and 3, respectively (there is no bid-ask spread). Is there an arbitrage ...
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Question on forward market arbitrage involving exchange rates

I am totally new to these type of questions on arbitrage. I tried the following question. Some answers need to be cross-checked and some, I don't know at all. $(a)$ Suppose the $6$-month interest ...
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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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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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Rounding or trimming stock prices

I have created a vwap timeseries. The values in the timeseries have 14 decimal places. I would like to reformat to 5 decimal places. My question is should I trim the price to 5 decimals or round to 5 ...
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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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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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206 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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Arbitrage-free quotations FRA

The rates for a FRA 3x9 are 0.95 %/1.08 %. However, according to the interest rates, the calculated forward rates should be 1.010%/1.170%. The question is whether it is arbitrage-free, and they ...
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70 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 ...
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2answers
96 views

Are there any papers about cointegration consisting of time series of more than two assets?

Are there any papers about cointegration consisting of time series of more than two assets ? I wonder if there could be any trading strategy for three assets case.
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188 views

Violation of the call-put parity

The last price of Wells Fargo (Ticker: WFC) on Thursday, 10/26/17, was $55.62. Options with expiration 11/17/17 had following last prices: Options with expiration 11/17/17 had following last prices: ...
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660 views

What is model-free finance?

I have run across the term "model-free finance" (e.g. there was a Thalesian talk in London recently), yet haven't found any real definition of it nor anything really substantial. Could you point me ...
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291 views

Extrapolation of the volatility smile

Are there any market practices to extrapolate the volatility smile for equities? I already have an arbitrage free interpolated call prices data and I'm looking for a method to extrapolate beyond the ...
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statistical arbitrage vs factor trading

I've recently read Avellaneda & Lee which seems to be widely recommended as an introduction to Statistical Arbitrage methods in trading. For those who aren't familiar with the paper, the method in ...
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283 views

Positive base arbitrage CDS vs Asset Swap

While I completely understand the negative base arbitrage when the base is defined as : $$Base = CDS - ASW$$ I am stuck on the possible arbitrage when the base is positive. Let's think with an easy ...
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413 views

Slight confusion regarding arbitrage opportunities in ETFs as mentioned by investopedia

On the "how ETF arbitrage works" page, investopedia says The arbitrage opportunity happens when demand for the ETF increases or decreases the market price, or when liquidity concerns cause ...