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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183 views

arbitrage opportunity in a two period model

I have a little problem evaluating an european call. I Suppose the following: in $$t=0 : S_0 = 10$$ $$t = 1 : S_1 = \{10,11\}~with ~p=0.5$$ riskless rate : $(1+r)=\beta=1.049$ Strike ...
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59 views

Self-financing condition and funding, collateral and discounting

I'm reading "Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting" paper. Is it just me or authors have a typo in their main ...
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67 views

Law of one Price and Cointegration relationship

I have a question on the relationship between the law of one price and cointegration of (financial) time series. To set things clear I start with something simple: Suppose there is an unobserved "...
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254 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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112 views

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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295 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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642 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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2answers
671 views

Arbitrage and dominant strategies

If there is no arbitrage there is no dominant trading strategy, but there may be arbitrage opportunities even if there are no dominant trading strategies. Could you explain this statement and bring ...
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70 views

FTAP in the model independent case, paper by Schachermayer

I have a question about the following paper by Beatrice Acciaio, Mathias Beiglböck, Friedrich Penkner, Walter Schachermayer. At the very beginning of the paper, on page 3, there are two definitions ...
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2answers
220 views

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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2answers
127 views

Using cumulative returns to hedge against the overall trend

I am curious about a hypothetical strategy where you are long for a given period (like a year), and at the same time you hedge against the overall trend by going short everyday and accumulating the ...
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2answers
381 views

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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1answer
287 views

Boundary for European Put Option

As an entry level financial engineer, I'm learning about call-put parity, which helps us to get the boundary for call option: $S-Ke^{-rT}\leq c\leq S$, what about put option? Should its upper bound be ...
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3answers
218 views

Arbitrage Condition and Identity in Black-Scholes

After I went through the derivation to get the skew in Backus et al., I had two questions: In the proof, it mentioned the application of the arbitrage condition and then obtained equation (31): $$\...
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2answers
169 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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1k views

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
591 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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2answers
232 views

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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2answers
1k views

Index arbitrage with Options when not all underlyings have options listed?

One arbitrage strategy involves looking at the price of the Index Futures price compared with the prices of the options contracts for the underlyings. My question is, can this arbitrage strategy ...
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2answers
1k views

main arbitrage & statistical arbitrage concepts

Can we please sumarise here some of the basic concepts, tools used in arbitrage and statistical arbitrage in real life? ARB: benefit from price difference on same asset ARB: difference between stock ...
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1answer
81 views

Martingale proof: Call-prices must be increasing in maturity

I have observed that IV is increasing with time to maturity by using market prices and plotting IV (from Black-Scholes) against log-moneyness, $\log(S_t/K)$. $S_t$ being the price of the stock at time ...
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1answer
110 views

Setting up arbitrage strategy in R

I am trying to construct an arbitrage portfolio $\textbf{x}$ such that $S^T\textbf{x} = 0$ and $A\textbf{x} \geq \textbf{0}$, where $A$ is the payoff matrix at $t=1$ and $S$ is the price at $t=0$. I ...
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2answers
202 views

Strike Arbitrage

In Stochastic Volatility Modelling, Chapter 2, the author derived the Dupire equation $$\mathbb{E}[\sigma_T^2|S_T = K] = 2\frac{\frac{dC}{dT} + qC +(r-q)K\frac{dC}{dK}}{K^2 \frac{d^2C}{dK^2}}.$$ The ...
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1answer
129 views

Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

Question: Given two call options $c_1$ and $c_2$ with strike price $30$ and $40$ respectively. If $c_1$ costs \$3 and $c_2$ costs \$4, is there an arbitrage opportunity? My attempt: Short $c_2$ and ...
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1answer
195 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
955 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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1answer
1k views

Derivation of the Nelson-Siegel model and proof of arbitrage

1. I am looking for a derivation of the Nelson-Siegel model $y(m)=a+b\left( \frac{1-e^{-\lambda m}}{\lambda m}\right)+c\left( \frac{1-e^{-\lambda m}}{\lambda m} -e^{-\lambda m} \right)$ It is ...
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1answer
2k views

Multiple (linear) regression

I am looking for some inputs on a pair trading strategy that I am trying to improve with some semi-fundamental input. The basic idea is to use multiple linear regression to estimate the price of a ...
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1answer
440 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 ...
2
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1answer
224 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
190 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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2answers
540 views

Which distribution do I get?

Let's assume the stock moves according to a classic Black-Scholes model, and makes a proportional jump with an unknown proportion. Say, it is either +1% or -3% of the stock value, and we know for sure ...
2
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1answer
303 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, where ...
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2answers
198 views

Pricing Principle 1

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this Pricing Principle. Is the one in red supposed to be the proof of the Pricing Principle 1? Or merely an intuitive ...
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1answer
544 views

How Much Capital is Needed to Start an Arbitrage Strategy?

I'm trying to experiment with a simulated simple arbitrage strategy. I'm not doing this to actually invest, I'm just curious if the market is inefficient enough for this to be feasible. Every ...
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1answer
390 views

interest rate in cost of carry

What interest rates are used in practice in a stock index / futures arbitrage? I've seen cases, when the assumed rate is 3 months LIBOR, but does it mean, that everyone who does the arbitrage can ...
2
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1answer
104 views

How to price complex corporate actions with spinoffs

Let's look at below UTX/RTN merger as an example: https://www.fool.com/investing/2020/03/30/raytheon-united-technologies-merger-gets-green-lig.aspx The merged companies will from that moment ...
2
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1answer
142 views

theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
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1answer
129 views

Arbitrage-free IV surface definition vs. real arbitrage process

In the context of BS implied volatility surface fitting. In the literature, it seems that conditions for arbitrage are defined in a way that assumes that options can be traded at the same price for ...
2
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1answer
238 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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1answer
94 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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2answers
146 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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1answer
292 views

Relationship between ADR in USD and original stock in GBP - Drift in price

For tax reasons, I switched a position I had in the HSBC London GBP listing into the USD ADR. The ADR represents 5 shares of the GBP listing. My understanding was that since at all times 1 ADR = 5 UK ...
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2answers
1k views

Arbirtage free price process question in Bjork's Arbitrage Theory in Continuous Time

I am currently working through questions in Bjork's Arbitrage Theory in Continuous Time. However, I am unable to solve the following question, 7.2 in the book. A solution would be greatly appreciated. ...
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107 views

Why is it called the No-Arbitrage Theorem if it’s really “arbitrage exists but only briefly”? [closed]

Why is it called the No-Arbitrage Theorem if it’s really “arbitrage exists but only briefly”? Is it just because all opportunities revert to equilibrium so fast that there’s no ultimate arbitrage, or ...
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60 views

Arbitrage portfolio example

Can you give me a concrete example of a self financing portfolio which gives arbitrage opportunity in the two-dimensional Black-Scholes model? By the two-dimensional Black-Scholes model I mean $$dS_{1}...
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1answer
83 views

Swap Spread Arbitrage & Rates/STIRT Vol

Concerning the classic swap spread arbitrage trade where you (as far as I understand it): Buy a treasury and borrow in GC repo, paying repo rate and funding the haircut in short term unsecured ...
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111 views

Linear factor representation Pricing kernel APT

following Cochrane (2005) and other insights, we know that under Arbitrage Pricing Theory (Ross, 1976), if investors believe returns follow a linear multifactor structure of the form $x^i=r^f+\sum_{j=...
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177 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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242 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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