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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1answer
183 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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436 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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216 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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556 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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155 views

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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1k 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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127 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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277 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
176 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
87 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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239 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
352 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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50 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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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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1answer
302 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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274 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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515 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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567 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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79 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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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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516 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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775 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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606 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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785 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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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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231 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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129 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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223 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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196 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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870 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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122 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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180 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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727 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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339 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
677 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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946 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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155 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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181 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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599 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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