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.
384
questions
1
vote
1
answer
104
views
Basic question/clarification about the LOOP
This is a very basic question/comment regarding the way that the LOOP is stated in the book "Dan Stefanica - A Primer for the Mathematics of Financial Engineering". The proposition goes as ...
- 121
1
vote
0
answers
47
views
Forward price of dividend paying asset and IV skew asymptotics as $T\to\infty$
Assuming for simplicity deterministic interest rate and dividend yield, then the forward price of an asset is
$$
F = Se^{(r-q)T}
$$
where $T$ is maturity date.
In studying IV skew asymptotics, the ...
- 323
-1
votes
1
answer
120
views
What is the arbitrage opportunity and strategy here? [closed]
Suppose that the current stock price is $€100$, the exercise price is $€100$, the annually compounded interest rate is 5 percent, the stock pays a $€1$ dividend in the next instant, and the quoted ...
1
vote
2
answers
188
views
Role of Intercept In OLS Beta Estimation
I am constructing a classic pairs trading strategy in which I use a linear estimator to model the spread of two assets opening a long-short market neutral position during times of divergence. I am ...
2
votes
1
answer
212
views
W-shaped Event Vol and Butterfly Arbitrage
I came across the Vola Dynamics page about the W-shaped vol before an event: https://voladynamics.com/marketEquityUS_AMZN.html
I'm a bit confused by "this term does not have any butterfly ...
- 131
0
votes
0
answers
147
views
Combining two orderbooks
Consider two different pairs of currencies traded in the same exchange. We will call these pairs A/B and A/C.
Each market comes ...
- 193
2
votes
1
answer
106
views
Can I replicate an option with time to expiry $t$ by trading in another with expiry $T > t$?
Suppose there's a salesman who will always sell me an option expiring in two weeks. His options trade at a steep discount, but I can't directly arb it because the closest exchange-traded contract ...
- 177
0
votes
2
answers
101
views
Are risk-free-rate bonds and cash fungible?
I had a thought experiment: suppose you wanted to borrow an equity security from me (perhaps to short sell it). I ask you for collateral and a borrow fee, and in exchange you get the stock.
If you ...
- 177
1
vote
2
answers
110
views
Bond forward arbitrage relationships
I am trying to see if the following statement is true or not and I would really appreciate your help.
The statement is as follows:
$\forall $ Tradable Asset $V(t)$,
$$ E[\frac{P(t,T_{i})P(T_{i},T_{i+1}...
- 237
0
votes
0
answers
43
views
Asymmetry in cash and carry arbitrage with carry costs?
I'm a bit confused on the effect of carry in the cash-and-carry arbitrage scenario.
Assume we have a commodity $C$. The spot price is \$100. Assume a 2% risk-free rate. Assume a 1% carry cost, no ...
- 113
1
vote
0
answers
141
views
StatArb : Fourier transform to find the perfect factor?
We have a basic mean reverting strategy. Given a bench of assets, we are looking for the best linear combination of them such as the resulting normalized time series would be noisy at high frequencies ...
- 111
0
votes
0
answers
39
views
Pricing Leveraged ETF option based on base ETF
I am following along with the paper linked here: https://math.nyu.edu/~avellane/thesis_Zhang.pdf .
In section 4.4, equation (4.4.2) makes the claim:
$$\sigma(k) = |\beta|\sigma_s(S_0k^*)$$
where:
$$...
- 929
3
votes
1
answer
178
views
Convergence of crypto perpetual futures
Perpetual contracts are supposed to track the spot prices through the funding mechanism. Typically, if the future has traded above the spot in the last averaging period used to compute the funding, ...
- 31
0
votes
0
answers
266
views
Does Put-Call parity have influence over American Option pricing in practice?
I am learning my options and from what I read it seems that put-call parity is regarded as only being applicable to European options because the time to exercise is known. American options, on the ...
- 1
2
votes
1
answer
331
views
Why is this inequality strict for arbitrage argument for European call?
in the notes about arbitrage arguments I am reading, I notice the statement
We can also see that
$$C^E_t>(S_t-K\mathrm{e}^{-r(T-t)})^+$$
Notice that the inequality holds STRICTLY!
I don't ...
- 175
1
vote
1
answer
135
views
How do I extract the arbitrage?
You are looking at a particular stock ticker and its options. You can go long or short on any quantity of the following instruments:
Each unit of stock is priced at \$10.
A call on the stock with ...
- 13
0
votes
0
answers
79
views
Short term implied fx rate
For context, I'm working towards constructing a FX implied rate curve based on the fwd points market. As you know, most of the spot rates usually settle in t+2. We can group fwd points in two types, ...
- 282
0
votes
0
answers
76
views
Modeling intraday futures-spot basis
I'm looking at futures-spot arbitrage trading. Futures-spot basis changes in the exchange during the day. And I wonder how it can be modeled... I mean intraday futures-spot basis modeling...
I'm ...
- 321
2
votes
1
answer
316
views
Understanding FX forward points and market usage
I've been trying to make sense of how the FX forward market works.
Let's say today is June 13, 2022. And we have the next market info as seen in Bloomberg for the FX cross between USDMXN, assuming mid ...
- 282
1
vote
1
answer
68
views
ETF structure's effect on premium to NAV
The GBTC (Grayscale Bitcoin) ETF is known for historically having a premium to net asset value (NAV). This led crypto funds to buy bitcoin, deposit their bitcoin into the trust to obtain GBTC, then ...
- 113
1
vote
0
answers
81
views
Deviation between spot price and implied spot price of S&P500 mini-futures
From Derivatives Markets (McDonald) it is stated that we may price a financial forward and, equivalently, get an implied spot price from a given futures price:
$$
F_{0, T}=S_0e^{(r-\delta)T} \implies ...
- 11
0
votes
0
answers
72
views
Strike arbitrage in discrete implied volatility grid
I need to test strike (butterfly) arbitrage on a discrete implied volatility grid.
I know that the traditional procedure for continuous case is (for a given maturity T):
See the Dupire formula in ...
- 773
0
votes
0
answers
38
views
How to exploit calendar arbitrage in the continuous dividends case
In this paper (Arbitrage-free SVI volatility surfaces. Jim Gatheral, Antoine Jacquier), on page 4, it is stated that
$$\frac{\tilde{C}_2}{K_2}>\frac{\tilde{C}_1}{K_1}$$
where $\tilde{C}_i = \tilde{...
- 773
1
vote
2
answers
145
views
Calendar arbitrage in implied vol grid with discrete and proportional dividends
I have an implied vol discrete grid, obtained from market data.
To obtain prices from these implied vols, a dividend model with discrete and proportional dividends is used.
How can I verify if there ...
- 773
1
vote
1
answer
155
views
Why do VIX spot and futures converge if there is no cash and carry arbitrage?
Since VIX spot is not tradable, why do the futures and spot converge @ expiration? By what mechanism does this occur if arbitrage is not one of them?
- 21
0
votes
0
answers
44
views
Equivalent martingale measure and derivative pricing [duplicate]
So I just recently saw in class that to price a derivative you use what is called an equivalent martingale measure which allows you to compute the price of the contract which then will be the expected ...
0
votes
0
answers
58
views
What is the P-probability of an unhedged call-arbitrage to lose money at expiration
Assume that the Risk Neutral Price (under the $\mathbb{Q}$-measure) of an European Call Option with expiration date $T$ has a price of $F(S_0,0)$ at time $t=0$ in the single asset Black-Scholes model ...
- 388
2
votes
1
answer
140
views
Analytical evaluation of the following caplet-type product under lognormal assumptions
Let $n \geq 2$, and consider a tenor discretization: $0 = T_{0} < T_{1} < ... < T_{n}$ and associated forward rates evaluated at time $t$, as $L_{i}(t):=L(T_{i},T_{i+1};t)$ for any $i = 0,...,...
- 73
4
votes
1
answer
253
views
How am I supposed to understand the following statement on the convexity adjusted rate
Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays
$$V_{N}(T):=X(T)N(T) \...
- 73
-1
votes
1
answer
112
views
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 ...
- 1
0
votes
1
answer
94
views
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: }...
- 73
7
votes
0
answers
130
views
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 ...
user34971
1
vote
1
answer
315
views
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}$,...
1
vote
0
answers
45
views
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 ...
- 636
0
votes
0
answers
91
views
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, ...
- 101
0
votes
1
answer
269
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 ...
- 636
1
vote
1
answer
58
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 ...
- 115
0
votes
1
answer
120
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 ...
- 115
0
votes
1
answer
217
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 ...
- 901
1
vote
1
answer
46
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 ...
- 151
2
votes
1
answer
227
views
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^...
- 123
3
votes
0
answers
99
views
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 (...
- 151
2
votes
0
answers
42
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 ...
- 45
2
votes
1
answer
219
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 ...
- 165
2
votes
1
answer
288
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 ...
- 165
0
votes
1
answer
179
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 ...
- 171
2
votes
0
answers
70
views
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 ...
- 773
5
votes
1
answer
353
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 $...
- 373
-1
votes
1
answer
447
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) ...
- 3
2
votes
0
answers
72
views
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 ...
- 1,634