# Questions tagged [no-arbitrage-theory]

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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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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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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### 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? ...
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### 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: ...
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### 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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### 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
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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