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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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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127 views
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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36 views
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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42 views
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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77 views
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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134 views
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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40 views
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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47 views
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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38 views
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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169 views
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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102 views
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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116 views
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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204 views
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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102 views
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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39 views
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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128 views
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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1answer
74 views
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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1answer
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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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72 views
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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517 views
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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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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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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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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If arbitrage can happen exactly at one moment, is it really arbitrage?
There are many "interpretations" of what no-arbitrage means in mathematical finance, the most well known is no free lunch with vanishing risk:
If $S=\left(S_{t}\right)_{t=0}^{T}$ is a ...
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When looking for arbitrage among a LARGE amount of assets, is there an optimal way?
Looking for arbitrage opportunities when looking at 3 pairs of related currencies is easy. However if we assume that we have a large amount of currencies, is there an optimal way to swipe through them ...
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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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Spot-Futures arbitrage profit calculation
My question is about spot-futures arbitrage.
Lets say, t=0 , Spot Price=1.38 , ArbFree Theoretical Fwd Price= 1.40 and Real Futures Market Price = 1.38. So we see that there's arbitrage. I take a long ...
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How to compute the yield to maturity on a zero-coupon 3 year bond in this case?
Suppose I have the following problem:
We have data on three bonds: a one-year zero-coupon bond (bond A), a twoyear zero-coupon bond (bond B), and a three-year bond with an annual coupon equal to 5% ...
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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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Can we observe smile arbitrage from the implied and local volatility?
Here are graphs of implied volatility and local volatility. Our prof mentioned that we can observe that the short end low strike region has some smile arbitrage. I would like to know how?
Thanks
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Does CRR Model lose completeness if we add another instrument?
Consider the multiperiod binomial/CRR model with one risky asset $S^{1}$ and a numeraire $S^{0}$. By seeing that the equivalent martingale measure is uniquely determined, we obtain that the market is ...
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Clean noisy data from arbitrage
My problem is that I have a surface of implied black volatilites that is supposed to represent market data. However, the surface contains some slight arbitrage.
More precisely, the graph contains ...
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723 views
How to prove no-arbitrage when a long butterfly is strictly positive?
I want to prove why there are no arbitrage opportunities when a long butterfly is strictly positive. I know there is a similar topic out there, but it seems it doesn't solve my question: Prove that ...
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Is there a forward contract the underlying of which is another forward contract?
Is there a forward contract on a forward contract?
Let us take a simple example: Persons $A$ and $B$ agree that $A$ sells $B$ some asset tomorrow at the fixed price $K_1$. This is a normal forward ...
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What is the interpretation if the real world measure $\mathbb P$ is equal to the martingale measure $\mathbb Q$
Out of interest, is there anything noteworthy about a market when its real world measure $\mathbb P$ is actually also its martingale measure. In other words the real world measure $\mathbb P$ is equal ...
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Why did investors believe that Volkswagen's preference and ordinary shares would converge in price?
The second para. below confirms that "Porsche's takeover demand would target the latter [ordinaries] rather than the former [preference]." Then why did investors like Albert Bridge Capital &...
