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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Strike arbitrage in discrete implied volatility grid

I need to test strike (butterfly) arbitrage on a discrete implied volatility grid. I know that the traditional procedure for continuous case is (for a given maturity T): See the Dupire formula in ...
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How to exploit calendar arbitrage in the continuous dividends case

In this paper (Arbitrage-free SVI volatility surfaces. Jim Gatheral, Antoine Jacquier), on page 4, it is stated that $$\frac{\tilde{C}_2}{K_2}>\frac{\tilde{C}_1}{K_1}$$ where $\tilde{C}_i = \tilde{...
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Calendar arbitrage in implied vol grid with discrete and proportional dividends

I have an implied vol discrete grid, obtained from market data. To obtain prices from these implied vols, a dividend model with discrete and proportional dividends is used. How can I verify if there ...
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Why do VIX spot and futures converge if there is no cash and carry arbitrage?

Since VIX spot is not tradable, why do the futures and spot converge @ expiration? By what mechanism does this occur if arbitrage is not one of them?
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Equivalent martingale measure and derivative pricing [duplicate]

So I just recently saw in class that to price a derivative you use what is called an equivalent martingale measure which allows you to compute the price of the contract which then will be the expected ...
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What is the P-probability of an unhedged call-arbitrage to lose money at expiration

Assume that the Risk Neutral Price (under the $\mathbb{Q}$-measure) of an European Call Option with expiration date $T$ has a price of $F(S_0,0)$ at time $t=0$ in the single asset Black-Scholes model ...
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Analytical evaluation of the following caplet-type product under lognormal assumptions

Let $n \geq 2$, and consider a tenor discretization: $0 = T_{0} < T_{1} < ... < T_{n}$ and associated forward rates evaluated at time $t$, as $L_{i}(t):=L(T_{i},T_{i+1};t)$ for any $i = 0,...,...
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How am I supposed to understand the following statement on the convexity adjusted rate

Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays $$V_{N}(T):=X(T)N(T) \...
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Extrinsic value larger than strike distance [closed]

Let a stock trade at 50\$. Would it be possible for a call at the 55\$ Strike to trade a a price greater than 5$? I'm pretty sure that there has to be an arbitrage opportunity, I'm just not seeing it. ...
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How to exactly calculate lag between 2 exchanges

Let's assume that there are two exchanges. One exchange is slow for various reasons.(for eg it is an open outcry versus electronic exchange) Even when there is no lag the prices will not match exactly ...
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Why would valuation for a swap be the same on the backward and forward rate but not a caplet

Consider for time discretization $0 = T_{0} < T_{1} <... < S < T < T_{n}$, and the corresponding forward rates and backward rate: $\text{Forward rate: }L(S,T;t)$ $\text{Backward Rate: }...
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Basis Trade- Long/Short vs Short/Long

I understand the long-short basis trade quite well, especially in the context of crypto. Say BTC is worth \$100. For example, buy \$100 of BTC, and short \$100 of a perpetual futures BTC-USD contract. ...
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Implied vol bounded if and only if instantaneous vol bounded

I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form $$ dS_u = \sigma_u S_u ...
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Triangular Arbitrage In FX Volatility

If I know the price of $GBPUSD$ and $EURUSD$, I can retrive the $EURGBP$ price simple by $EURGBP = \frac{GBPUSD}{EURUSD}$. Is there something equivalent to FX Volatility? Knowing the $\sigma_{GBPUSD}$,...
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Is it true that interest rates options with different maturities are free of calendar arbitrage because of the different underlying rates dynamics?

The title says it all - is it true that European style interest rates options (lets say on LIBOR 3M for the sake of simplicity) with different maturities are free of calendar arbitrage because ...
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Understanding arbitrage, defined as a series of cash flows

I'm currently catching up on material presented in the edX-MIT course Foundations of Mondern Finance 1, in which they present a definition of arbitrage that doesn't quite make sense to me. Informally, ...
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No-arbitrage conditions on a caps/floors volatility surface

Suppose that one has a caps/floors volatility surface and wants to check whether this surface admits arbitrage. What is the theoretical and practical way to do it? Lets talk only about caps for ...
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Rates arbitrage - practical trade example, is it actually risk free or can it burn?

The trade: Imagine a bank balance sheet as follows: One liability: GBP 100m deposit fixed term 6 month One asset: JPY 153m government bond maturing in 1 year (£100m equivalent, spot rate 153) ...
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Simple hedging technique comparison question: forward market vs money market

I am trying to do some self studying and came across this question. I am not sure how I would analyze these hedging strategies to figure out which is better. Could you give me any help on how I could ...
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Simple cross-rate table question

I am trying to self-study and came across this question, I am not sure how to answer this. I think I should transform all of the product's quoted prices to USD then compare them, is that correct? The ...
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Simple three-pair triangulation question

I have a question I came across whilst self-studying and I need to use cross-currency triangulation. I am not too sure how to apply the cross-rate formula, and was hoping someone could show me how to ...
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Is it fair in an introductory stochastic calculus/derivatives pricing class to ask for the price when absence of arbitrage is violated? [closed]

Re close votes: I believe this is a fair kind of opinion-based question because it's like those ethics questions in academia se or workplace se or because it's pedagogical. Context: I'm actually ...
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How to price a set of cashflows from which the buyer can choose one?

Lets consider an arbitrage free and complete Model.Let also focus the analysis on the discrete time setting.Assume you have a finite set of random Cashflows $\mathcal{A}$. That means all elements of ...
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Should the Libor Market Model using spot measure as numeraire simulate an arbitrage free forward curve?

I have been looking at the following resource: Reference Paper Using equation [4] for the discretized version of the forward libor rate: $\tilde{L}^i_{T_{j+1}} = \tilde{L}^i_{T_{j}} exp[\sigma^i(\sum^...
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Is this term structure model valid? (Modeling the Zerobonds directly)

Let us define the dynamics of the discounted Zerobonds as $$ \tilde{P}(t,T) = \int \sigma(t,T) dW_t + \tilde{P}(0,T)$$ Lets assume $\sigma(t,T)$ is s.t. $\tilde{P}(t,T) $ is a martingale and positive (...
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How the swap curve moves if fed fund rate decrease?

I am currently reading the book "Interest Rate Swap and other Derivatives by Howard Corb", in Chapter 8.2 Curve Trades, it mentioned: "Investors believes Fed is going to lowering the ...
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Equivalence of expectation condition for contingent claims attainable and contingent claims super replicable

We have the following definitions for set of contingent claims attainable and contingent claims super replicable I want to prove the following result How do I show iii $\implies $ ii.I understand ...
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No free Lunch and weak-star topology

The no free lunch is stated as follows What is the significance of the weak-star topology here .Also as far as I understand the weak-star topology is defined on the dual of a Banach space.So what is ...
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No free lunch with bounded and vanishing risk

I am reading a book which states 'No free lunch with bounded risk as follows where $\tilde{V}_t$ is the discounted value of the portfolio.Then it states the following theorem EMM is the equivalent ...
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How do you hedge your inventory when doing arbitrage?

Say I want to do arbitrage between Exchange A and Exchange B on USD/AAPL. This requires that I hold equal parts USD and AAPL. I don't want exposure to the movement in AAPL. How do I hedge my AAPL ...
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Speculation with quanto option - how to see the realized correlation

From this question, on vanilla option vol speculation, we can gain intuition on the impact of realized vol on the gamma, and consequently on the efficiency of the speculation trade. Asuming long ...
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Show a model is complete but not free of arbitrage

Let $\mathcal{F}=\{\Omega, \emptyset\}$ be the trivial $\sigma$ -algebra, and consider the deterministic financial market model with zero interest rates, $S_{0} \equiv 1$, and $n=1$ additional asset $...
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Model for allocating capital between statistical arbitrage opportunities?

Dear users of quantstackexchange, I am currently creating a model with my team to look for the best (the highest returns) statistical arbitrage opportunity. This model will scan a significant amount ...
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Question in convex arbitrage [closed]

In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance, $$ C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
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Arbitrage the commodities market

Assume $F_0$ is the delivery price of a forward contract on a commodity, say oil. Let $S_0$ be the spot price and $U$ be the present value of all storage costs net income. Also let $r$ be the risk-...
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Model independent (or reasonable assumption) bounds on OTM put price given an ATM call price

I am looking for model independent (or weak/reasonable assumption) bounds on price of a OTM vanilla put on strike $k1$, conditional on an observable price for a ATM call at some strike $k2$. I ...
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How can we argue that the "economic" risk-neutral argument doesn't introduce arbitrage?

I am wondering why when use the "economic" risk neutral argument, we don't introduce arbitrage. By "economic" I mean an argument that doesn't use stochastic calculus or equivalent ...
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Calendar arbitrage with dividends

In this question, it is shown: i) the definition of calendar arbitrage for Call options; ii) the financial/mathematical rationale. Nevertheless, in that question, one assumes that there are no ...
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SPACs - How can IPO investors incur losses?

I'm trying to understand the role of the initial IPO investors of a SPAC. From the Beginner's Guide of r/SPACs: When the IPO occurs, a SPAC generally offers Units – generally at \$10 per Unit. These ...
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Is there any data sources for historical arbitrage basis (e.g. on-the-run/off-the-run basis)?

I hope to get data going back as far as possible. Someone must have computed these things, but not sure if anyone has shared these data online? If not, if you know how I can get the data for the ...
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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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When are parameters calibrated using one option type applicable to price other option types on the same underlying?

I am coding up some basic models to show prospective employers, but I am forced to guess "what is done in practice" since I don't yet work in the industry. I am implementing various ...
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Why was CDS-bond basis close to zero before the financial crisis?

For instance, see the evidence here: This paper claims that this arises from the fact that cash bond and CDS have different margins, and thus it is cheaper (funding wise) to hold CDS positions. ...
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Making a beeline to statistical arbitrage

This question is somewhat related to my previous question here but has not been addressed in any other thread. The answer in that thread hit the nail right on the head with that one line "...
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5 votes
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Why were cross-currency swap basis so close to zero before the financial crisis?

For instance, see the graphs below. Before the 2008 financial crisis, they were extremely close to zero. Why is that so? (https://www.sr-sv.com/wp-content/uploads/2019/02/CIP_01.png)
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What exactly are the “bounds” in arbitrage bounds?

Wikipedia’s article on arbitrage bounds is loaded with jargon, and thus requires a lot of prerequisite knowledge to understand what should be a basic definition. What exactly are the “bounds” in ...
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2 votes
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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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Arbitrage optimal size model that accounts for slippage given a specific path?

I'm interested in any model that helps calculating the optimal size to maximize PnL given the liquidity of an asset (or the slippage that I would incurr per unit of asset traded). For instance, let's ...
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Replicating Portfolio / Complete Market / Attainable Claim

Attempt So Far: 1) First Part: I have shown that the market is arbitrage-free since the only possible portfolio for which $V_1^h\geq0 \ $ given that $V_0^h=0 \ $ is $h=(0,0,0)$ and this clearly ...
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3 votes
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Risk-neutral Probability, Risk-Adjusted Returns & Risk Aversion

When we employ the Fundamental Theorem of Asset Pricing and the existence of an equivalent probability measure, say $Q$ with respect to the historical probability $P$, we often say the expectation ...
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