Questions tagged [no-arbitrage-theory]
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163
questions
0
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28 views
$aS^0 + bS^1$ is a $Q$-martingale does not imply discounted market is arbitrage-free
In the following framework : let $(S_0^{'}
, S_1^{'}
)$ be an undiscounted financial market in
discrete time on $(\Omega, F, \mathbb{F}, P)$ with a finite time horizon $T \in \mathbb{N}$ and $\mathbb{...
4
votes
0answers
81 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 $S$ ...
7
votes
0answers
112 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 ...
0
votes
1answer
61 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 ...
0
votes
1answer
132 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 ...
1
vote
2answers
237 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 ...
0
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0answers
29 views
Martingale-equivalent compound Poisson process
My question is related to the paper "a Martingale approach to premium calculation principle in an arbitrage-free market" by Delbaen and HAEZENDONCK (1989).
In short, they characterized all ...
4
votes
0answers
55 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 ...
-1
votes
1answer
145 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 ...
0
votes
0answers
57 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?
...
2
votes
0answers
59 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}
...
2
votes
1answer
174 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 ...
2
votes
1answer
121 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 ...
2
votes
1answer
195 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 ...
0
votes
0answers
41 views
Arbitrage the commodities market
Assume $F_0$ is the delivery price of a forward contract on a commodity, say oil.
Let $S_0$ be the spot price and $U$ be the present value of all storage costs net income. Also let $r$ be the risk-...
0
votes
0answers
49 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 ...
0
votes
1answer
75 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 ...
1
vote
0answers
21 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}...
1
vote
1answer
117 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 ...
0
votes
0answers
61 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 ...
2
votes
0answers
111 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 ...
1
vote
1answer
99 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 ...
0
votes
1answer
93 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 ...
2
votes
1answer
107 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 ...
0
votes
1answer
177 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 ...
2
votes
2answers
461 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 ...
0
votes
1answer
49 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)? ...
1
vote
1answer
109 views
Market price of risk of different maturities
T. Bjork Arbitrage Theory in Continuous Time Proposition 23.1 "Assume that the bond market is free of arbitrage. Then there exists a process $\lambda$ such that the relation
$\frac{\alpha_T(t)-r(...
0
votes
0answers
66 views
Determining Presence of Arbitrage
I am slightly confused by part (b) of this question. My understanding is that the easiest way to determine if there is arbitrage is to compute the state prices and then look at their sign: if one or ...
2
votes
2answers
336 views
Help reconciling incorrect reasoning in options pricing brain teaser
I'm trying to reconcile an interesting brain teaser I was recently posed and I need help understanding the flaw in the reasoning.
The problem states there is an asset which after an announcement has ...
2
votes
1answer
115 views
No-arbitrage Pricing
We have a contract whose value is $A(S_t,t) = S_t^3$ at all times, not just at expiration. $S_t$, the underlying stock, follows a Geometric Brownian Motion, $\frac{dS}{S} = \mu dt + \sigma dB$. How ...
0
votes
0answers
34 views
Binomial Model Strike Price Assumption
Let us have the standard single-period binomial pricing model, and denote the up and down states of the underlying by $S_u$,$S_d$ respectively. Let us say we have a call option on the underlying with ...
3
votes
1answer
122 views
SML Interpretation
I follow this paper and estimated two different asset pricing models via systems of deep neural networks. Both models have the exact same input: firm-specific features for 10'000 (unique) US stocks ...
1
vote
0answers
118 views
Where could I get a mathematical background on circular arbitrage?
I am particularly interested in the dependence of profit on the path length (the number of intermediate currencies) and graphical models / algorithms. More specifically:
How can we model currency ...
1
vote
0answers
59 views
Black Scholes implied volatility [closed]
I am reading up on implied volatility and I encountered the term Black-Scholes implied volatility which I haven't heard before. What is the meaning of this term?
Say I am looking at the Heston model ...
1
vote
1answer
110 views
Deriving forward rate
I want to price a 1 year future under the condition of no arbitrage and based on LOOP. At time T, I sell currency Z and buy currency L. At time $t$, we define the exchange rate as $ZL_t$. The 1 year ...
1
vote
0answers
31 views
No Arbitrage condition for assets with different time frame
In the classic literature, one always assumes that the assets in the market are all available from the very beginning ($t=0$). And under such condition the market is arbitrage free iff there exists an ...
2
votes
0answers
125 views
Linear factor representation Pricing kernel APT
following Cochrane (2005) and other insights, we know that under Arbitrage Pricing Theory (Ross, 1976), if investors believe returns follow a linear multifactor structure of the form
$x^i=r^f+\sum_{j=...
2
votes
1answer
54 views
(Self-study) Futures, bonds, and arbitrage
I'm currently self studying futures, so I'm sorry if this questions comes off a bit stupid. I'm currently reading a book by Walsh, J.B. Knowing the Odds: An Introduction to Probability.
I quote this ...
0
votes
0answers
32 views
No unique no-arbitrage price when the stock price can remain unchanged
In a 1-period binomial model, with initial stock price 100, if the stock price is either 50,100, or 150 after 1 period then how can I show there is no longer a unique no-arbitrage price for a European ...
1
vote
0answers
66 views
Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel
For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e.
$\int_{0}^{\Delta ...
1
vote
1answer
70 views
Are there values of the strike price for which an American put and European put have the same no-arbitrage price?
Assuming the options do not pay dividends, is there a strike price that satisfies this?
0
votes
2answers
3k views
STIR topics: Implied FX-OIS Basis and FX Forward/Swap Pricing
if someone could provide some clarity on the below:
What is meant by 'Implied FX-OIS Basis'? For example: "ON JPY trading at parity, 1W implied OIS basis moved 70BP" and "3M Implied OIS basis moved ...
1
vote
0answers
88 views
Some basics of option pricing
I am a mathematician trying to learn finance on my own. Try to avoid financial lingo in your answer when not necessary.
So I am trying to understand (European) option pricing under the no free lunch ...
-2
votes
1answer
189 views
Link between spot and forward rates in no-arbitrage world
With reference to the forward exchange rate definition, let be:
$S$: the spot rate
$F$: the forward rate
$r_d$ and $r_f$: respectively the domestic and foreign interest rates
$DF_d$ and $DF_f$: ...
1
vote
1answer
147 views
Vanilla Call Option Priced Using Jump Diffusion Model
I'm reading a book called Quant Job Interview Questions and Answers and came across the following question and its answer, but cannot make sense of it, so I really appreciate your advice:
Question 2....
2
votes
1answer
567 views
How to Take Advantage of Arbitrage Opportunity of Two Options
I got the following interview question and corresponding solution, but I have a different understand that might be wrong, so I really appreciate your advice on it:
A European put option on a non-...
0
votes
1answer
486 views
A financial market is complete if and only iff there exists a unique equivalent martingale measure
Do you have any intuition behind the following theorem :
A financial market is complete if and only iff there exists a unique equivalent martingale measure.
I understand the easier version of ...
8
votes
3answers
1k views
Why do we need the self-financing assumption in risk-neutral pricing?
A portfolio is self-financing if the purchase of a new asset must be financed by the sale of an old one.
\begin{align*}
x_t(1+R) + y_tS_t = x_{t+1} + y_{t+1}S_t
\end{align*}
This says that, at each ...
1
vote
1answer
140 views
some questions about pricing an asset or nothing put option with a strike price equal to St
I am working on a homework exercise where the aim is to price an asset or nothing put with K = St, offcourse the normal formula could be used St * N(-d1), but I was wondering if pricing the asset by ...
