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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600 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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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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124 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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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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201 views

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
120 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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302 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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395 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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704 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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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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495 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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129 views

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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56 views

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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657 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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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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177 views

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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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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256 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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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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352 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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352 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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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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What is the pseudo code for a pairs trading strategy?

I am trying to learn about pairs trading strategy. I know that we have to long and short cointegrated assests simultaneously. But I still have some confusion in how the strategy works. I wrote the ...
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European vs American derivative securities, interesting question

Let us denote by $c^A(t, S(t))$ the price, at time $t$ of a certain American-style derivative security, whose instrinsic value, at time $t$ is denoted by $V(t)$.From the no-arbitrage principle, we ...
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645 views

Questions on arbitrage

I have the following questions about arbitrage that I am unsure of. Will an inverse term structure rate imply arbitrage possibilities? Will negative zero coupon rates imply arbitrage possibilities? ...
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Arbitrage and completeness in multiperiod model?

Given a 2-period market with above stock price process along with a riskfree stock with a return of 5%, how do I determine whether the market is arbitrage-free and complete when I only have knowledge ...
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164 views

Two definitions of arbitrage in finite markets

I have read two definitions of the term an arbitrage opportunity in the literature*. Are they equivalent? Consider a single period market model over the measurable space $\Omega = \{\omega_1, \dots, \...
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441 views

Solving for r in the Black Scholes equation

Could you please correct which parts of my reasoning are wrong? Let's suppose that I know for sure that my estimate for a stock volatility is right (I have a crystal ball) and that it will be for ...
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1answer
186 views

What are the answers to these questions on card deck and option pricing?

here are 3 questions I have some trouble dealing with. Your help will be greatly appreciated! 1 - We have a deck card: 26 red, 26 black. we play a game: you draw a card from the deck without putting ...
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1answer
325 views

arbitrage proof question

prove the condition $D<R<U$ is equivalent to the absence of arbitrage: R = risk free investment rate of return. U and D are returns corresponding to the upward/downward price movements of a ...
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1answer
140 views

Arbitrage opportunity in discrete time

Say we have the following binary option $B$ on asset $S$ with strike K and expiration time T, assume also that the following relation holds at time $0$: $B > N*C(K,T)-N*C(K+1/N,T)$ Where $N$ is ...
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FX Statistical Arbitrage Strategy [closed]

I have had experience creating stat arb strategies for equities and etfs, but haven't dabbled much into FX trading. I was wondering if anyone knew any resources online they would suggest, or could ...
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1answer
714 views

Swaption Volatility Cube arbitrage

How can I exploit an arbitrage by violating the following no-arbitrage condition (taken from the paper "Arbitrage-Free Construction of the Swaption Cube" by Simon Johnson and Bereshad Nonas): Swptn(K,...
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335 views

What is the arbitrage opportunity in this simple one-period market?

I have a single period market, and three states, and I have 3 risky assets. I assume no interest. So I have three states $\Omega=\{\omega_1,\omega_2,\omega_3\}$. All assets start with the value 1, ...
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How do most arbitrage opportunities account for unknown volume at a ticker price?

So, from a conceptual level, arbitrage seems quite forward... buy at one place at one price, and sell somewhere at a higher price. However, after doing some initial digging it appears to be not quite ...
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Calendar Arbitrage in a Vol Surface

I am trying to determine the condition such that my implied vol surface doesn't have calendar arbitrage. I have done research and found that one such condition is that total variance should increase ...
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What is Toxic FX Flow debate?

So, basically I want to debate and find out the real reason behind being flag by ECNs and venues as "toxic". How to avoid being flagged? What kind of strategies are toxic and why? Below is an article ...
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1answer
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Higher moments arbitrage

Is there concrete evidence that statistical arbitrage (historical vs. implied) on higher moments, specifically skewness and kurtosis, can be (significantly) done? Working from this source, the author ...
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414 views

Prove arbitrage opportunity

The continuously compounded interest rate is $r$. The current price of the underlying asset is $S(0)$ and the forward price with delivery time in 1 year is $F(0,1)$. Short selling of the stock ...
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Latency Arbitrage in forex [closed]

(I've been downgraded on this question, and it's because most people don't understand what I mean. If you ever did hft arb, you will understand what I mean. If not, please do not answer) Everybody ...
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What is a standard model of convergence when looking at negative stub values?

I am trying to understand whether or not there is a standard model of convergence in the arbitrage scenario of negative stub models, i.e. when the market value of a company is valued less than its ...
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How to optimize an arbitrage portfolio when taking into account different speeds of mean reversion?

In portfolio optimization, it is insufficient to just note the size of price deviation - that only tells the amount of profit if held to maturity. One also needs to take into account reversion speed - ...
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251 views

Is there an efficient method or technique to find an arbitrage between two FX dealers?

I was able to solve the following problem and find the arbitrage but only after spending a long time on it and trying out different possibilites. Is there a method or technique that can help me find ...
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233 views

Are there alternatives to the Box-Tiao decomposition in identifying mean reverting portfolios?

As documented in this paper, Box-Tiao decomposition (a way to decompose multiple time series into components with different speeds of mean reversion) can be used to identify mean reverting portfolios. ...
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HJM model, existence of arbitrage:

The Setup: Suppose I know the yield curve of a Bond satisfies: f (0, t) = 0.04 for t ≥ 0 and f (ω, 1, t) = 0.06, t ≥ 1, ω = ω 1 , 0.02, t ≥ 1, ω = ω 2 , where Ω = {ω 1 , ω 2 } with P[ω i ] > 0, i = 1,...

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