Questions tagged [no-arbitrage-theory]

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82 views

Is it fair in an introductory stochastic calculus/derivatives pricing class to ask for the price when absence of arbitrage is violated? [closed]

AGAIN, Edit 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 ...
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54 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? ...
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43 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
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1answer
155 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
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1answer
86 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 ...
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1answer
179 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 ...
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39 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-...
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43 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 ...
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69 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 ...
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20 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}...
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1answer
97 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 ...
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54 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 ...
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108 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 ...
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1answer
60 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 ...
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1answer
83 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 ...
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1answer
99 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 ...
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1answer
174 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 ...
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76 views

How to price a forward-rate agreement?

I don't understand how the formula on page 24 of Joshi: Concepts and Practice of MF is derived. Here is the paragraph I don't understand: A forward-rate agreement is simply an agreement to take some ...
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133 views

Arbitrage Free Interpolation of Implied Volatility on Time Dimension

I’m working on a project to build a local volatility model out of implied volatility data and I’m currently testing the no-arbitrage version of SVI model as described in this paper Section 5.1 [...
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2answers
348 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 ...
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1answer
42 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)? ...
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1answer
106 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(...
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57 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 ...
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2answers
317 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 ...
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1answer
106 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 ...
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33 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 ...
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1answer
115 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 ...
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0answers
108 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 ...
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0answers
57 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 ...
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1answer
108 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 ...
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0answers
29 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 ...
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0answers
119 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=...
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1answer
52 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 ...
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29 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 ...
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0answers
64 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 ...
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1answer
63 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?
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2answers
2k 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 ...
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0answers
85 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 ...
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1answer
165 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 $DF_f$: ...
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1answer
143 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....
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1answer
521 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-...
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1answer
369 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 ...
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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 ...
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1answer
110 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 ...
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1answer
116 views

Required adjustments for stressed yield curves

I was looking at Basel proposed interest rate shocks. Using the standard US Treasury Yield Curve for the period starting from September 2017 to August 2019, I was able to construct Steep and Flat ...
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1answer
146 views

Exercise on arbitrage-free process

Consider the following problem, from Bjork's Arbitrage Theory in Continuous Time: Consider the standard Black-Scholes model. Derive the arbitrage free price process for the $T$-claim $\mathcal{X}$ ...
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1answer
112 views

Binomial model in Björk's Arbitrage Theory in Continuous Time

I am having some trouble with variable $Z$ introduced in chapter $2$ in Björk's text. In the beginning, it is the random variable that attains $u$ resp. $d$ with probabilities $p_{1}$ and $p_{2}$, i.e....
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0answers
65 views

Arbitrage pricing models

I have been reading Wu's Interest rate modeling and in his chapter on the HJM model he says that With arbitrage pricing models, the prices of the basic instruments are treated as model inputs ...
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2answers
216 views

Risk-neutral pricing and statistical arbitrages

I'm studying the martingale approach to asset pricing. Dealing with the concept of risk-neutral probability, I came up with a question about the possibility of "arbitrages in expectation". I'll be ...
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1answer
128 views

Is the undiscounted value process of a Euro call option under Bachelier model a Martingale? [duplicate]

Assume that $c_t$ is the UNDISCOUNTED price process for a European call option in Bachelier model. In Bachelier model call option pricing formula the formulas is discussed. The undiscounted value ...