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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2answers
809 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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710 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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1answer
940 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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1k 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 ...
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290 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
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132 views

Best strategy to maximize Profit if no transaction cost?

I was recently in a competition which simulated real time currency trading. Teams were supposed to build bots that could request current prices of currencies, buy, or sell currencies using HTTP ...
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235 views

Do price approximations lead to arbitrage opportunities?

Do price approximations lead to arbitrage opportunities against a price computed using the exact formula? For instance, dirty bond price uses a linear approximation to compute the accrual interest: $$...
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1answer
250 views

Taking advantage of mispricing in forwards [duplicate]

Suppose gold futures are selling at 360 in February, and 370 in April. Interest is 9% annually. Note that 360*(1+0.09*2/12)=365.4, so the April futures is overpriced. Then we can sell April and buy ...
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1answer
1k views

Why does arbitrage free imply complete market?

Proposition 2.10 of Tomas Bjork's "Arbitrage Theory in Continuous Time" states that if the general binomial model is free of arbitrage then it is also complete i.e. every contingent claim has a ...
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127 views

How does volatility affect price arbitrage?

Suppose I'm running automated classic price arbitrage on 3 currencies (let's ignore the unfeasibility of this in our day and age). We have currency pairs Gold/Silver, Silver/Bronze, and Gold/Bronze. ...
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189 views

What are recommended recovery techniques in arbitrage when one order doesn't fill?

Let's say you are running an arbitrage strategy in the Forex market. You see an opportunity to buy USD/JPY at 100 on exchange A, and sell USD/JPY at 105 on exchange B. You submit the buy and sell ...
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What are the essential characteristics of asset prices?

I think the question has already been asked about stylized facts of asset returns; this question regards the essential characteristics and normative assumptions used to evaluate asset prices. I.e., ...
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822 views

Finding arbitrage opportunity

Find an arbitrage opportunity in this market. Can anyone explain how to mathematically solve this exercise with for example solving a system of linear equations?
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Reference that states that the price of an option is not the expected present value of the payoffs under Black and Scholes?

I recently met an options trader that said to me that the price of an option is the expected present value of the payoffs of an option (present value as in discount by the risk free rate and expected ...
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386 views

Equivalent martingale measure price dynamics

Assume $S_0(t)=\exp(\int_0^t r(s) ds)$. Then $\mathbb{Q}\sim \mathbb P$ is a martingale measure $\iff$ every asset price process $S_i$ has price dynamics under $\mathbb Q$ of the form $dS_i(t)...
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How realistic are the scenarios outlined in my course?

I am currently taking a course in Financial Mathematics as part of my Maths degree. Many of the covered topics are quite basic, and revolve around potential arbitrage opportunities. For example, ...
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Arbitrage free option prices: real life example

I would like to be sure of my correct understanding of some basic principles. I have following example, data from Euronext: 1 Month maturity, future and options are same day expiry. Strike 5400. ...
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1answer
699 views

FX forward rates

FX forward rate should reflect the difference in the interate in the two currencies. At the moment GBP USD is trading near 1.29. The 5 year yield for US treasuries is about 1.87% and the UK 5 year ...
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1k views

Arbitrage free smoothing of implied volatility surface, by Fengler

I'm reading this paper link and have came across the below statement. Can someone shed some light on it. "The approach we propose here builds on smoothing rather than interpolation. Therefore, the ...
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An arbitrage strategy involving forward contracts to show that LIBOR rates are martingales

I note $L_{t}^{[T_s, T_e]}$ the forward rate at time $t$ for the period $[T_s, T_e]$. Recall it is the strike making equal to $0$ the value at time $t$ of a forward contract for the period $[T_s, T_e]$...
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167 views

Isn't this modified stop-loss strategy an arbitrage?

In John Hull's The Book, section 18.3 he briefly discussed a stop-loss strategy for writing a call option: buy one share of stock whenever $S_t>K$ and sell it otherwise (except at time $0$: if $S_0\...
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212 views

How would you arbitrage this?

Assume it to be true that $dS = S\mu dt + \sigma(t)S dW$ where $\sigma$(t) is known. Consider a call option with expiry $T$, currently $t = 0$. For all $t \in [0,T]$, $\sigma(t) < \sigma_{impv}$ ...
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638 views

When is implied volatility greater than realized volatility?

Assume it to be known that the volatility of a stock at any point in time is $\sigma(t)$. My question is, if we have a number of options priced using some implied volatilities $\sigma_1, ..., \...
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1answer
75 views

Valuation functional

Consider an economy with $J = 2$ assets and $S = 3$ states. The $J\times S$ payoff matrix for the two assets is $$X = \begin{pmatrix} 0 & 3 & 3\\ 1 & 1 & 0\\ \end{pmatrix}$$ and the ...
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How to make the arbitrage if intrinsic value is greater than European call value

It always says if the intrinsic value is greater than European call value, there will be a arbitrage opportunity,but how to construct the portfolio $(S_t - K)^+$ or how to make this arbitrage. By the ...
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129 views

Do all assets satisfy the “black scholes type PDE”, or just the stocks?

I am reading Bjork. In it, he says that the martingale measure $Q$ is characterized by the property that all stocks have the short rate as their local rate of return under the $Q$-dynamics. Is it ...
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1answer
2k views

Why must a riskless portfolio earn the risk-free rate?

In Options, Futures and Other Derivatives when Hull introduces the risk-neutral approach to pricing European options in the one-step binomial model, he claims that Riskless portfolio must, in the ...
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Arbitrage problem [closed]

Question A share of non-dividend paying stock is trading at USD 30. The maturity of both options is 1 year from now. A put with a strike of USD 28 is trading at USD 1 and call with a strike of USD 29 ...
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31 views

Best strategy for generating floats with minimum amount of risk

I'm looking for a way to get cash-in-hand in exchange for future obligation. For example, I can sell deep-in-the-money puts and buy out-of-the-money puts (for hedge) with expiration of 2 years, The ...
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1answer
126 views

Black Scholes: two assets, same $W$-process

Consider a Black Scholes model with two risky assets that are driven by the same $W$-process, and then 1 risk-free asset. When is this model arbitrage-free and complete? We have only 1 driving ...
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328 views

Fair price and no arbitrage

The market is arbitrage-free iff there exists an equivalent martingale measure for the discounted price process of the stock. So in a world with a finite amount of possible outcomes $\Omega$ that ...
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444 views

Different definitions of arbitrage

Consider the following setup: Let $S=\left(S_1,\ldots,S_n\right)$ be a $n$-dimensional price process and denote by $V$ its value process defined by $V_t=\phi_t\dot\ S_t$ for $t=0,\ldots,T$. In "...
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Why is $Y(t)V^h(t)$ a martingale?

Let $\lambda$ be the market price of risk: $\frac{a - r}{\sigma}$, and define $Y(t) = e^{-\lambda W(t) - (r + \frac{\lambda^2}{2})t}$. Let $V^h(t)$ be the value process of any self-financing portfolio....
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Why won't Bjork ever show that the integrability condition is satisfied?

A major technique employed throughout Bjork's "Arbitrage theory in Continuous Time" is that when taking the expectation of a stochastic integral, the result is 0. This is based on a result presented ...
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769 views

Options Arbitrage strategy

Supposed we have 1-year call option with a strike of 90 and it costs 10. We also have 1-year put on the same stock with a strike of 100. The risk free rate is 5% per annum. the stock is currently ...
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1answer
169 views

Is this the same as the conditial expectation in risk neutral pricing formula?

Let the dynamic of underlying asset $S_t$ under objective probability measure $\mathbb{P}$ be as follow $$dS = \mu Sdt + \sigma S dW_t^{\mathbb{P}}.$$ We now define another probability measure $\...
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1answer
566 views

Black-Scholes evaluating the squared of the stock price

Consider a Black-Scholes model $S_t = 5\exp{(\sigma W_t + \mu t)}$, $B_t = \exp{(rt)}$, where $W_t$ is Brownian motion with respect to a given measure $\mathbb{P}$. Suppose you hold a forward contract ...
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For equity options, why sometimes ATM vol of shorter expiration is higher than that of longer expiration?

Basically a negative forward vol in the ATM vol term structure. For index options, it's probably rare. But for single name options, I've seen a bunch of examples on Bloomberg. Does this relationship ...
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1answer
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For discrete models, the existence of strong arbitrage is equivalent to a particular self-financing strategy

Background Information: This question is from Lectures on Financial Mathematics: Discrete Asset Pricing. Question: Prove that for discrete models, the existence of a strong arbitrage is also ...
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708 views

What is the difference between state prices and stochastic discount factor?

I was reading a paper on arbitrage and it was mentioned that a positive SDF implies no arbitrage and later on it said that positive state prices imply no arbitrage. I am new to this topic and i am ...
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1answer
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If there is an inconsistent pricing strategy then by defintion we have strong arbitrage

Background Information: An Inconsistent pricing strategy is a self financing strategy $\phi$ with $V_T(\phi)= 0$ and $V_0(\phi) \neq 0$ A strong arbitrage is a self-financing strategy $\phi$ with $...
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1answer
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Law of One price and the Inconcistent pricing strategy

Background Information: A market satisfies the Law of One Price if every two self-financing strategies that replicate the same claim have the same initial value. An inconsistent pricing strategy is ...
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1answer
38 views

Price of every asset in discrete market model strictly increasing

If the price of every asset in a discrete model is strictly increasing, with probability one, then does the market admit arbitrage? Thoughts: I believe this is true but I am not sure how to give an ...
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1answer
290 views

How do you decide what time frame you're going to use when testing for cointegration?

I've been fiddling around with different time frames when doing tests for cointegration between two timeseries, and I've realized that the dates that you use for your start/stop of the test will ...
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398 views

How to calculate an option porfolio cost and payoff function?

There are call and put options on the same underlying asset, with the same expiry, $T$, and with strikes $K_c=(k_c^1, k_c^2, \ldots, k_c^m)$ and $K_p=(k_p^1, k_p^2, \ldots, k_p^m)$, $S_t$ is a price ...
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1answer
403 views

How can I apply error correction model in pairs trading?

I have read Vidyamurthy and others, but did not find clear example of error correction model (ECM) application in pairs trading. How should I use the ECM model in the pairs trading? How to use ECM ...
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1answer
2k views

Latency arbitrage: what exactly is the arbitrage mechanism?

I'm reading about latency arbitrage in regards to direct exchange feeds vs. SIP feeds. SIP feeds are on average 1 millisecond slower than direct feeds, which allows HFTs to see an NBBO update before ...
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1answer
430 views

How buying/selling pairs and entering/exiting trade works in pairs trading?

Lets say I have two stocks x and y and their corresponding stock price p(x) and p(y). consider HR as hedge ratio. Then we can calculate the spread using this equation. $spread=p(x)-HR*p(y)$ from ...
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333 views

Triangular arbitrage formula error

I am struggling with a formula for calculating the above. I have been using the following example: https://www.youtube.com/watch?v=lKu2LAgEcpU ...

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