# Questions tagged [no-arbitrage-theory]

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### completeness of the binomial model - proof

I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...
100 views

### Pricing of American Deriviatives

Reading the book by Andrea Pascucci "PDE and Martingale Method in Option Pricing" I am struggling with a very simple issue. Suppose we want to find the price of an American derivative $X$ in an ...
2k 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 ...
268 views

### Equivalent Definitions of Self-Financing Portfolio

Consider a multi-period model with $t=0,...,T$. Suppose there is a bond with $B_0=1$ and $B_t=(1+R)^t$ and a stock with $S_0=s_0$ and $$S_{t+1}=S_t\,\xi_{t+1},$$ with $\xi_t$ iid random variables....
166 views

### How to price a path dependent exchange option using?

Assume you have two stocks $S$ and $P$ so that at initial time $t = 0$: $S_0 > P_0$. You bought an option which pays off $S_T - P_T$ as long as $S_t > P_t$ through the time $0 < t < T$. ...
223 views

### European option on a dividend paying stock, limits to arbitrage?

What is the price C of a European call option on a dividend paying stock? I believe it is: C = U. N(d1) - exp(-rt).K.N(d2) d1 = [ ln(U/K) + (r + v^2/2).t ]/[ v.sqrt(t) ] d2 = d1 - v.sqrt(t) U ...
2k views

### Does No arbitrage(NA) imply efficient markets (EMH)?

The EMH states that stocks are traded at its fair values. This means there is no arbitrage strategy in efficient markets. However, if the market is no arbitrage, can we conclude the market is ...
129 views

### Forward contract pricing of coupon paying security

PLease help me in understanding how to price forward contract for coupon paying security. For instance if we get into a contract to buy a security in next six month whose coupon due in next two month. ...
129 views

We got the stochastic process for stock price of n stocks at continues time. We can find if there is a arbitrage trading strategy or dominant trading strategy. I wonder if we cannot find such ...
307 views

### 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 ...
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### Arbitrage-free market for continuous logreturn distribution?

Is it true, that a one-period market say $(0,t)$ is arbitrage-free if the logreturn for $S_t$ is continuously distributed on $\mathbb{R}$? I.e., for continuous distributions on $\mathbb{R}$, there ...
648 views

### Arbitrage and dominant strategies

If there is no arbitrage there is no dominant trading strategy, but there may be arbitrage opportunities even if there are no dominant trading strategies. Could you explain this statement and bring ...
208 views

### If the risk neutral probability measure and the real probability measure should coincide

Sorry if this may be a stupid question. I have not had that much mathematical finance, I've only learned about discrete time models. But lets for the argument say that you have a stochastic process ...
1k views

### Proving that Absence of Arbitrage does not imply law of one price

I am trying to prove that the Absence of arbitrage statement (AOA) does not necessarily imply the law of one price (LOP). For the definitions of these concepts I am using Cochrane's book "Asset ...
899 views

### Equivalent (true) Martingale Measures and no-arbitrage conditions

I hope this is the correct site for this question, as it is rather theoretical... In their famous paper, Delbaen and Schachermayer proved that the No Free Lunch with Vanishing Risk condition is ...
503 views

### risk-neutral valuation implies no arbitrage?

It is known that in an arbitrage-free continuous time market, the price of every asset is evaluated as the corresponding price in the replicating strategy using risk-neutral valuation. I want to ...
654 views

### arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy $$dB_t = B_t r dt$$ \quad \quad \quad \quad \, ...
1k views

### What is the difference between market efficiency, market equilibrium, and no-arbitrage?

Aaron Brown (in the book, The Poker Face of Wall Street, p. 196), discusses four approaches to deriving the same Black-Scholes-Merton option-pricing formula: Ed Thorp, Myron Scholes, Robert Merton, ...
719 views

Basically all Quant Finance theory is build on No-Arbitrage presumption and Efficient Markets Hypothesis. The known Grossman-Stiglitz Paradox says: if one can't make money from trading, one wouldn't ...
513 views

### How does this follow from the separating hyperplane theorem?

This is from Pliskas book in mathematical finance. I do not know what was best to write the question so I included the pages from the book. He has not written what form of the separating hyperplane ...
454 views

### Is this arbitrage?

Assume the stockprice as in the Black-Scholes model (Geometric Brownian Motion): $$S_t=S_0e^{(\mu-\sigma^2/2)\cdot t+\sigma W_t}$$ Wouldn't there be an immediate arbitrage opportunity, to just buy ...
2k views

### law of one price, understanding

I am reading about mathematical finance, and I was tipsed to ask the quesiton on this site. It is about the "law of one price". Just first I'll make precise the model my book uses: I have a single ...
2k views

### Arbitrage free implies complete market?

In Tomas BjĆ¶rk's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition It seems that to show that the model is complete, we must show that the claims are reachable. That is, we ...
605 views

### Efficiency vs. Robustness - To use a constant or not in single factor time-series regression?

Arbitrage pricing theory states that expected returns for a security are linear combination of exposures to risk factors and the returns on these risk factors. Betas, or the exposures of the security ...
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### How to price this option without using BS framework

We have a stock at price 1 dollar which pays no dividend. Also we assume zero interest rate. When the price hits $H$ dollars for the first time where $H>1$, we can exercise the option and receive 1 ...
740 views

### Is it possible to understand financial theory without mathematics?

I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a ...
2k views

### expected value of the discounted payoff

I don't understand the following statement: The price of a contingent claim is the expected value of the discounted payoff value under the risk neutral probability measure Q deļ¬ned in complete markets ...
334 views

### Non-arbitrage theory and existence of a risk premium

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and isgenerated by $1 d$- ...
1k views

### Sufficient conditions for no static arbitrage

In Carr and Madan (2005), the authors give sufficient conditions for a set of call prices to arise as integrals of a risk-neutral probability distribution (See Breeden and Litzenberger (1978)), and ...
236 views

### Stochastic discount factor (aka deflator or pricing kernel) and class D processes

When (under what assumptions on the model) does a Stochastic Discount Factor need to be of Class D? What would be the implications if it was not? Is it connected to one of the no-arbitrage notions?
316 views

### inflation > interest rate? [closed]

Currently, the federal reserve interest rate is 0-0.25%, and the inflation is 2-3%. Does this contradict the no-arbitrage principle? (The arbitrage being: borrow money at 0.25% and invest it in the "...
Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time $T$...