Questions tagged [no-arbitrage-theory]
The no-arbitrage-theory tag has no usage guidance.
144
questions
0
votes
1answer
279 views
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 ...
2
votes
1answer
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 ...
9
votes
2answers
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 ...
3
votes
1answer
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....
4
votes
3answers
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 $0 < t < T$.
...
-1
votes
1answer
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 ...
5
votes
2answers
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 ...
2
votes
1answer
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. ...
1
vote
2answers
129 views
Question about find no arbitrage trading strategy
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 ...
3
votes
1answer
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 ...
13
votes
7answers
3k views
What is the fair price of this option?
Without having to use Black-Scholes, how do I price this option using a basic no-arbitrage argument?
Question
Assume zero interest rate and a stock with current price at \$$1$ that pays no dividend. ...
1
vote
2answers
1k views
Option arbitrage with dividends?
If a stock pays a discrete dividend, the stock price falls by the amount of the dividend. There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of ...
5
votes
0answers
355 views
Show that in an arbitrage-free and non-redundant market a certain set is compact
Some notation: We consider a financial market with $d+1$ assets, the $0$-th asset is considered the risk-free asset, the others are the risky ones. The vector $\overline \pi \in \mathbb R^{d+1}$ ...
3
votes
1answer
679 views
Why is the volatility smile important
One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get:
People use the volatility smile as a ...
2
votes
1answer
274 views
Pricing digital options in discrete time
I am stuck in this exercise from my textbook:
Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, where ...
1
vote
3answers
425 views
The Law of One Price in a discrete model
The following question assumes familiarity with the discrete model described in chapter 5 of Steven Roman's "Introduction to the Mathematics of Finance", 2nd edition, Springer 2012. I will not ...
8
votes
1answer
223 views
FTAP a-la Harrison, Kreps and Pliska
I was reading the papers co-authored by Harrison, Kreps and Pliska, that initiated the formal research on the connection between pricing, martingale measures, arbitrage and completeness. I have some ...
1
vote
1answer
159 views
On the existence of a perfect market with no arbitrage that contains a forward contract
Consider the following theorem from p. 31 of Steven Roman's "Introduction to the Mathematics of Finance Arbitrage and Option Pricing" (Undergraduate Texts in Mathematics, 2012), giving the forward ...
2
votes
1answer
173 views
Law of large numbers necessary for APT derivation?
The question refers to the well-known Ross (1976) paper with the derivation of the Asset Pricing Theory.
In the APT, the return of asset $i$ is driven by a linear factor model:
$$ R_i = \alpha_i + \...
0
votes
1answer
103 views
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 ...
3
votes
2answers
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 ...
2
votes
1answer
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 ...
5
votes
1answer
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 ...
4
votes
2answers
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 ...
5
votes
4answers
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 ...
5
votes
2answers
654 views
arbitrage in Heston model
Really struggling in this question:
Consider a market with two assets $(B,S)$ whose price dynamics satisfy
\begin{equation}
dB_t = B_t r dt
\end{equation}
\begin{equation}
\quad \quad \quad \quad \, ...
9
votes
1answer
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, ...
8
votes
4answers
719 views
Efficient Markets Paradox
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 ...
4
votes
2answers
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 ...
1
vote
3answers
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 ...
4
votes
2answers
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 ...
1
vote
3answers
2k views
Arbitrage free implies complete market?
In Tomas Bjƶrk'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 ...
8
votes
2answers
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 ...
1
vote
3answers
93 views
Interpretation of equation derived from the delta of a call European call option
I have started reading an introductory book called: A Course in Derivative Securities by Kerry Back. On page 12 they mention the following:
The delta of the call option is $\delta = (C_{u} - C_{d}) / ...
2
votes
0answers
651 views
Simple Forward Interest Rate Proof
Just trying to check my logic here:
Let $Z(t,T)$ be a Zero-Coupon Bond with maturity $T$ bought at time $t$, $S_m$ be the spot interest rate for time $m$ and $S_n$ for time $n$ respectively, where $n ...
3
votes
1answer
313 views
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 ...
11
votes
2answers
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 ...
0
votes
2answers
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 ...
8
votes
1answer
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 $- ...
5
votes
1answer
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 ...
3
votes
0answers
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?
-5
votes
1answer
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 "...
6
votes
0answers
199 views
Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative
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 $T$...
16
votes
2answers
5k views
Fundamental Theorem of Asset Pricing (FTAP)
In the spirit of canonical questions please state here versions of the FTAP in the following form (please only one theorem by answer) :
Necessary definitions (or a direct link to definitions)
...
