# Tagged Questions

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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### 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 ...
128 views

### 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 ...
1k views

### How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic intereset rates, a stock paying no dividends, no repo rates etc. Let C(T,K) be the price of a call with expiry ...
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### 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 ...
3k views

### SPX options vs VIX futures trading

Forward volatility implied by SPX options, and that of VIX futures get out of line. If there existed VIX SQUARED futures they could easily be replicated (and arbitraged) with a strip of SPX options. ...
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### 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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### 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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### 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 ...
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### 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): ...
56 views

### 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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### 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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### 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 flag? What kind of strategies are toxic and why? Below is an article ...
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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 ...
83 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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### Is this an arbitrage opportunity? [closed]

The 6 months risk free rate is $0.0809\%$ the 12 month rate is $0.1415%$ today. The forward rate for 6 months in 6 months is $0.0913\%$ Is there an arbitrage opportunity?
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### Do you know any CFD broker with super cheap stock CFD that pays out dividends?

Do you think, it would be possible to buy stock prior its dividend date at some very cheap CFD broker, then wait 1 day, get dividend compensation credited and then sell the CFD back and end up in ...
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### Market with exponentially distributed random variable

Consider a market consisting of a stock with $S_0^1=1$ and $\log(S_1^1)=Z$, where $Z$ is an exponentially distributed random variable. $S_0^1$ denoted the prices of the stock $1$ at time $t=0$ and ...
48 views

### method/technique for finding arbitrage

I was able to solve this 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 the ...
33 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 = ...
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### Does presence of arbitrage necessarily make all derivatives have zero value?

Spin-off from: Pricing when arbitrage is possible through Negative Probabilities or something else I mean in a theoretical sense: If we have a particular market model with some fancy assumptions such ...
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### market change, correlation and estimation bias

I hear many quants sating that markets change very slowly. This "fact" is even presented as a justification of statistical arbitrage, for example, by affirming that correlations remain roughly the ...
234 views

### Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
439 views

### Arbitrage opportunity interview question

I have seen this interview question mentioned in a couple of places: There are three call options on the market, with the same expiry and with strikes 10, 20, and 30. Suppose the call option with ...
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### Bond's bid-ask spread with no arbitrage assumption

Suppose I have a bond with unknown bid-ask spread, and a portfolio, containing it and also other bonds, all with known bid-ask spreads. How can the unknown spread be inferred? I assume there should ...
272 views

### How to check that an interest rate curve is arbitrage free

I have 2 interest rate curves (LIBOR 3M and OIS). I want to create stress scenarios for those two curves. Is it possible that some scenarios will make my term structure arbitrageable? How can I test ...
87 views

### Triangular Arbitrage with CFD

I cannot understand how the triangular arbitrage fits with CFD. Assuming there is an arbitrage opportunity: EUR/USD < USD/GBP * GBP/EUR If I do this strategy: 1 Long on EUR/USD at Ask price 1 ...
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### Calculating PnL from log prices

I'm backtesting a statistical arbitrage strategy. To calculate the PnL I simply use $Y(t)-Y(t+n)$ for the profit on the first leg and $\beta*X(t) - \beta*X(t+n)$ for the profit on the second leg, ...
29 views

### Helpful references for fully understanding the mechanics of NASDAQ's auction system?

I've read about this before on their website directly and via this ITG paper. nasdaq site itg paper But I was wondering if there are any other good references I can supplement my understanding ...
1k views

### Why isn't the Nelson-Siegel model arbitrage-free?

Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e. $$dX_t=\sigma dB_t-AX_tdt$$ and the spot interest rate evolves by the following equation: $$r_t=a+b\cdot X_t.$$ After solving for $X_t$ ...
131 views

### Finding Arbitrage in two Puts

A European Put Option on a non-dividend paying stock with strike price 80 is currently priced at 8 and a put option on the same stock with strike price 90 is priced at 9. Is there an arbitrage ...
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### Portfolio Strategies Project

My first assignment for my Quantitative Finance Masters is to design a portfolio that theoretically makes money under any market movement. I am also asked to state all necessary assumptions. What ...
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### Self-Frontrunning Arbitrage

If I have a large order to fill, shouldn't I always buy a derivative in the same direction to profit from the market impact? E.g. I sell 1 million shares and so I buy a put, which will hence almost ...
282 views

### What‘s the definition of static arbitrage?

Could someone give the strict definition of static arbitrage? I know what the arbitrage means but have no idea about the term "Static". Thanks in advance!
172 views

### Forward Curves and Par Yield Curves

I'm recently reading a research paper on the yield curve by Salomon brothers and in it it states that when the forward curve is above the par yield curve, it is seen as cheaper. If for example, the ...
121 views

### Capital gains and dividends tax arbitrage

There is a statement in Paul Wimott Introduce Quantitative Finance: Often capital gains due to the rise in a stock price are taxed differently from a dividend, which is often treated as income. ...
827 views

### Calculating most profitable arbitrage orders on multiple market with fixed and variable fees

If I have multiple markets (let's say 5, but the solution should be generic) trading the same stock/commodity/whatever, and the markets differ in both variable fees (which are in % of the trade order) ...
292 views

### Option arbitrage with dividends?

If a stock pays a discrete dividend, the stock price falls by the amount of the dividend. There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of ...
46 views

### Show that in an arbitrage-free and non-redundant market a certain set is compact

Some notation: We consider a financial market with $d+1$ assets, the $0$-th asset is considered the risk-free asset, the others are the risky ones. The vector $\overline \pi \in \mathbb R^{d+1}$ ...
252 views

### References on Statistical Arbitrages

Is there any basic materials (books, papers) to read on Statistical Arbitrage? I certainly understand much of the useful information is in the industry. I just want to get some understanding on the ...
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### 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 $B_1 = 1+r$, ...
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### 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 ...
The solution of the Black-scholes equation is the price of a European call. And the option price assumes the underlying stock is a geometric Brownian motion with volatility $\sigma_{1}>0$. ...