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Confusion about how price of a contingent claim at time 1 could give arbitrage

I have been reading the book Tomas Bjork's Arbitrage Theory in Continuous Time and could not understand how there could be arbitrage if the price of a contingent claim is not $X$. To give some ...
KMR's user avatar
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1 vote
1 answer
52 views

Showing a basic market admits no arbitrage

I'm learning the fundamentals of financial mathematics and came across the following problem I cannot solve Setting We work in $\left(\Omega, \mathcal{F},\left(\mathcal{F}_t\right)_{t=0}^1, \mathbb{P}\...
portero's user avatar
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2 answers
109 views

Shape of Yield curve of ZCB under no-arbitrage

Sorry if the question is somewhat elementary, but I have thought about it for a while and I cannot figure out where my mistake is. Suppose we are in are in an arbitrage-free market in which risk-free ...
Cirdan's user avatar
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1 vote
2 answers
144 views

Is this arbitrage? Infinite payoff / infinite loss (energy generation investment problem)

I'm a student using stochastic optimization in energy systems and I have a particular phenomena in an optimization problem that I think must occur in finance aswell, so I have been trying to find ...
waxcomb's user avatar
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1 answer
189 views

filtering implied Vol surface for butterfly arbitrage

Suppose I have a volatility surface (matrix in time and strike) but it might have butterfly arbitrage in it. I want to remove nodes from the surface so that the Vol surface is butterfly arbitrage free....
Madhuresh's user avatar
4 votes
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127 views

Decomposing a bond's excess returns into duration, volatility, and market-price-of-risk. Discrepancy/confusion with Rebonato text

I am working on deriving the formula for the market price of risk for zero-coupon bonds and the associated formula for the excess returns. I am following the derivation in Appendix 12.6 of Rebonato's ...
Alex Lapanowski's user avatar
0 votes
1 answer
209 views

Understanding completeness in this simple one-period exercise

Let's consider a one period model (t=0, 1) with one risk-free asset that yields r, and one risky asset. $S_t^j$ will be the value of the asset j=0,1 at time t=0,1, where j=0 is the risk-free asset and ...
Confused Quant's user avatar
1 vote
1 answer
104 views

The relationship between no-arbitrage and the law of one price

If no-arbitrage exists, then the law of one price holds, but the existence of the law of one price does not always imply that no-arbitrage exists." To prove this, what is an example where the law ...
FSH's user avatar
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66 views

Does arbitrage theory actually help in practice? If so, how?

Am wondering if arbitrage theory (the ones defined "classically" with stochastic processes, martingales, etc.) is actually helpful in practice for an actual trader beyond simply having an ...
lokett33's user avatar
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0 answers
39 views

Implementations of stochastic collocation for Arbitrage Free SABR

I am currently reading this paper (link) on fitting arbitrage free parameters for SABR using stochastic collocation. Are there any publicly available github repos that implement solutions that are ...
user85127's user avatar
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73 views

Binomial option pricing model for American options on assets paying a continuous dividend yield

Let's say an asset has a continuous dividend yield of 5% (and assume interest rate is 0%). If I want to price an American call option on such an asset, I take each time step individually and construct ...
artemars's user avatar
2 votes
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80 views

Filipovic: Where is it used that the world is deterministic

In this text (Damir Filipovic, Term-Structure Models, Springer, 2009) $P(t,T)$ denotes the price of a zero-coupon bond at time $t$ with maturity $T$. I cannot see where the proof uses the ...
Landscape's user avatar
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2 votes
0 answers
51 views

No arbitrage principle in Counterparty Credit Risk

I think this is a fairly basic question but I'm struggling to understand the no-arbitrage principle applied to CCR. Imagine that we want to calculate the exposure evolution in an IR derivative, ...
vsa's user avatar
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3 votes
1 answer
384 views

Is negative forward variance an arbitrage?

I believe that having a negative forward variance on a ATMF implied volatility curve of a volatility surface could imply the existence of a static arbitrage (for example, a calendar arbitrage). ...
fwd_T's user avatar
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Finding upper bound for portfolio made from European call / put options

I tried finding upper bounds for each component in terms of E_1 using the put call parity but couldn’t get the correct answer.
Alex Seitzy's user avatar
2 votes
1 answer
81 views

Mean level of the state variables under the risk-neutral measure in Arbitrage-free Nelson Siegel

I do not understand why mean levels of the state variables under the risk-neutral measure, $\theta^{\mathbb{Q}}$, in Arbitrage-free Nelson-Siegel is set to zero. It should follow from the following ...
Martin N.'s user avatar
0 votes
1 answer
222 views

Finding latest market price of market portfolio according to No Arbitrage

In Excel, I have the monthly stock price data for the past few years for Asset A and Asset B. I have calculated the monthly returns, mean returns, variances, and standard deviations for both stocks as ...
Red's user avatar
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1 vote
1 answer
115 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 ...
user_12345's user avatar
2 votes
0 answers
37 views

Properties of the American derivative security price process

$$ \newcommand{\cbkt}[1]{\left\{{#1}\right\}} \newcommand{\rbkt}[1]{\left({#1}\right)} \newcommand{\sqbkt}[1]{\left[{#1}\right]} $$ Shreve volume I, defines an American derivative security as follows: ...
Quasar's user avatar
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0 answers
35 views

No-arbitrage framework and the coordinate process

In the paper by Beiglböck et al, I encountered the following description of the no-arbitrage framework (see screenshot below). What is the meaning of this coordinate process $S_i$? How does it relate ...
qarabala's user avatar
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3 votes
0 answers
420 views

Understanding the asset pricing theory and numeraire

While reading about asset pricing theory and numeraire, I had faced some confusion. Short summary of asset pricing theory from my book We start our journey with a risky asset $S_t=\mu S_tdt+\sigma ...
emonhossain's user avatar
2 votes
1 answer
346 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 ...
Ice Tea's user avatar
  • 185
1 vote
0 answers
128 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 ...
Devtons's user avatar
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2 votes
1 answer
195 views

Payoff of a Butterfly spread under risk neutral measure is always positive for any t<T

In a situation where $$K_3-K_2=K_2-K_1=h>0$$ and $$K_1\le S_t\le K_3$$ where $$S_T=S_t.e^{[(r-\sigma^2/2)(T-t)+\sigma(W_T-W_t)]}$$ (i.e. Stock process follows GBM under the risk neutral measure). I ...
user43534's user avatar
1 vote
0 answers
183 views

Market models of implied volatility and no arbitrage

Something has been bugging me for a while, and I can't really find an answer to it in papers. Maybe somebody can help me out. In addition to modelling the instantaneous vol, or modelling forward ...
user avatar
0 votes
1 answer
1k views

How to find state prices?

I am trying to find out how to solve state prices, but I do not know what I am supposed to do, my professor has given a solution to this problem as being (0.060 0.417 0.476), but I can't figure out ...
Emil's user avatar
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6 votes
0 answers
124 views

What are the requirements for no arbitrage to exist in a chaotic/dynamical system?

Consider the continuous dynamical system $$\alpha\ddot{S}+\dot{S}=\mathcal{F}(S,t),$$ such that $\alpha\in\mathbb{R}$ and $\mathcal{F}$ is real and analytic. We assume that if a solution for $S$ ...
UNOwen's user avatar
  • 128
7 votes
0 answers
141 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 ...
user avatar
0 votes
1 answer
189 views

Risk-neutral pricing to determine no-arbitrage price

We are asked to consider a derivative with payoff $C_t = S_{T}^{1/3}$ at maturity $T > 0$ and to use risk neutral pricing to derve the no-arbitrage price process $C_{t}$. Some context: Let $W$ be a ...
George's user avatar
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0 votes
1 answer
466 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 ...
Hasek's user avatar
  • 814
3 votes
2 answers
2k views

How to derive forward price on stock with continuous dividend

Let $F_{t,T}$ be the forward price of a stock $S$ at time $T$ and $t$ be the current time. The stock pays a proportional continuous dividend at a rate of $q$ and the risk-free rate is $r$. How can I ...
BaroqueFreak's user avatar
4 votes
0 answers
62 views

How to compute this current value using no arbitrage condition?

Suppose $X_t$ is a geometric Brownian motion with drift $\mu$ and volatility $\sigma$. $X_0$ is known. You have a machine that produces something worth $X_t$ at random times $t$ generated by a Poisson ...
cxxu96's user avatar
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1 answer
243 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 ...
BCLC's user avatar
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0 answers
69 views

Does zero cost arbitrage imply the existence of negative cost arbitrage?

I've been wondering, if there exists a zero-cost arbitrage trading strategy in some market, does that also mean that there also has to be a negative-cost arbitrage trading strategy in the same market? ...
wasabiwaffles's user avatar
2 votes
0 answers
98 views

Pricing formula under a new risk-neutral pricing measure:

From the fundamental asset pricing theorem, we know that in the absence of arbitrage opportunities, the present value of an asset paying $\Psi(X)$ at maturity time $T$ is given by: \begin{equation} ...
user53249's user avatar
  • 419
2 votes
1 answer
282 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 ...
abc's user avatar
  • 165
2 votes
1 answer
528 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 ...
abc's user avatar
  • 165
2 votes
1 answer
402 views

Proving the discounted stock price is martingale

Let $\mathcal{K}_s$ be $$ \mathcal{K}_s=\{\tilde{V}_t(\theta):0\leq t<\infty,\,\theta\text{ a simple strategy}\},$$ where $\tilde{V}_t(\theta)$ is the discounted value process of the self financing ...
abc's user avatar
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0 votes
0 answers
93 views

Is the initial value of the portfolio replicating a forward zero?

This is from the book Financial Calculus: An Introduction to Derivative Pricing by Martin Baxter. By choosing appropriate weights in a portfolio of a stock and cash bond you can replicate the payoff ...
Danial Adibi's user avatar
0 votes
1 answer
123 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 ...
user54908's user avatar
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1 vote
0 answers
25 views

Additional requirement for the asset price and payoff to ensure the market is arbitrage-free

Suppose we have two risky assets and one risk-free asset in the market. The market is incomplete in that there are three assets and four states. The price vector at $t_0$ is: $\boldsymbol{p_0}=[p^s_{1}...
Xuan's user avatar
  • 11
1 vote
2 answers
295 views

Free Arbitrage conditions in ATM swaption surfaces

I'm wondering how can we check free arbitrage conditions in ATM swaptions surfaces since we only have access to Expiry, Tenor and volatility? Can someone help me please, i didn't find any article ...
toto's user avatar
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2 votes
2 answers
846 views

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 ...
Cybernetic's user avatar
2 votes
0 answers
122 views

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 ...
Cybernetic's user avatar
1 vote
1 answer
675 views

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 ...
user926034's user avatar
0 votes
1 answer
164 views

No-arbitrage bounds on Implied Volatility under Black-Scholes

Suppose the overnight (1-day) at-the-money implied volatility is X% and the two week (14-day) at-the-money implied volatility is also X%. How would I go about finding the upper and lower no-arbitrage ...
quantoad's user avatar
2 votes
1 answer
122 views

Single period risk-neutral probability derivation

Let $S_u$ be the price of stock in the up-state one period from now. Let $S_d$ be the price of the stock in the down state. Let $C_u$ be the payoff of a call option at time $1$ in the up-state and ...
James's user avatar
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0 votes
1 answer
210 views

No-arbitrage arguments: how do additional fees affect futures on an index?

I am considering a fund that replicates the returns of an index minus a fee, using the following case-study my lecturer used regarding SPY: In practice, futures and forwards can be written on assets ...
user107224's user avatar
3 votes
2 answers
1k views

Question About SVI and SSVI Tradeoff between Fitness and No-Arbitrage

I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...
Dovie Chu's user avatar
  • 121
0 votes
1 answer
110 views

Futures and Forwards in Relation to No-Arbitrage Axiom

Is it possible to make an arbitrage profit by taking a long position in the futures contract and a short position in the forward contract when Forward Contract F(0,0) > Futures Contract G(0,0)? ...
UnevenMango's user avatar