Questions tagged [no-arbitrage-theory]
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191 questions
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Has there been any research that allows utility maximization with arbitrage?
I have read the paper "Pricing without no-arbitrage condition in discrete time" by Carassus and Lépinette (2022) that explains how to price under arbitrage. They introduced a weak assumption ...
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Equivalent formulations of the No-Arbitrage Principle
Let us consider two definitions of the arbitrage opportunity, for simplicity focusing on the one-step binomial model with one risk-free and one risky asset.
We define an arbitrage opportunity to be ...
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Violation of No Free Lunch with Vanishing Risk
In this question I construct a very simple violation of the No Free Lunch with Vanishing Risk property (NFLVR). This should not be possible. Have I made a mistake? To be as detailed as possible, I ...
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Proof of Durrleman's condition for the implied volatility surface to eliminate butterfly spread arbitrage
I have seen many papers mention the Durrleman condition for an implied volatility surface as a means to eliminate butterfly spread arbitrage, yet none provide a rigorous proof that fully convinces me. ...
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Expected return of the underlying not an explicit input in the binomial options pricing formula, but volatility is?
I'm new to options (finance in general) and am trying to learn the theory.
I have read that the argument for why the underlying expected growth doesn't matter is that we're pricing the options ...
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Single and daily recalibration, arbitrage and stochastic volatility
Local volatility models such as Dupiré's are arbitrage free if used as single calibration models during the lifetime of a pricing task. But in practice they are recalibrated daily (or possibly intra-...
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Gibson & Schwartz two factor model: mathematical derivation of the total expected return of a commodity contingent claim
I have been recently introduced to the Gibson & Schwartz two factor model (1990, link). According to the model, the dynamics of the spot commodity (oil) price ($S$) and of the convenience yield ($\...
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Understanding No Arbitrage Assumption
I knew that If two portfolios have the same profit at maturity time T, then for all prior times $t<T$ the price of the portfolio's must be equal and this comes from no arbitrage assumption.
I am ...
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Pricing / valuing anticipated repayment date
I am a long time lurker, and frankly not a quant, but have deep respect for those that are.
I have found myself in a situation dealing with some features on debt that I am trying to figure out how ...
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Potential arbitrage opportunity or fallacy?
Suppose we have two European options with the same expiration: a call priced at $c$ with strike price $K_1$ and a put priced at $p$ with $K_2 (>K_1)$. Further, suppose the zero-points of the two ...
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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 ...
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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}\...
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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 ...
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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 ...
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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....
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