Questions tagged [no-arbitrage-theory]
The no-arbitrage-theory tag has no usage guidance.
171
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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 ...
- 163
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0
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67
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Risk-neutral option pricing on a quasi-reverting underlying asset
Consider $(S_t)_{t\geq0}$, on the probability space $(\Omega,\mathcal{F},\mathbb{Q})$, which evolves according to
$$\begin{equation}
\frac{\mathop{dS_t}}{S_t}=\mu\mathop{dt}+\sigma_{t,S_t}\mathop{dW_t}...
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Deviation between spot price and implied spot price of S&P500 mini-futures
From Derivatives Markets (McDonald) it is stated that we may price a financial forward and, equivalently, get an implied spot price from a given futures price:
$$
F_{0, T}=S_0e^{(r-\delta)T} \implies ...
- 11
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32
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Generate payoff matrix of multiple BSM assets
I have some troubles generating a random one-step BSM market model that is arbitrage-free.
Concretely, the BSM market model in one time step is just a payoff matrix of $N$ assets and $K$ events, so ...
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Payoff of a Butterfly spread under risk neutral measure is always positive for any t<T
In a situation where $$K_3-K_2=K_2-K_1=h>0$$ and $$K_1\le S_t\le K_3$$ where $$S_T=S_t.e^{[(r-\sigma^2/2)(T-t)+\sigma(W_T-W_t)]}$$ (i.e. Stock process follows GBM under the risk neutral measure).
I ...
- 21
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Market models of implied volatility and no arbitrage
Something has been bugging me for a while, and I can't really find an answer to it in papers. Maybe somebody can help me out.
In addition to modelling the instantaneous vol, or modelling forward ...
- 4,893
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27
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Are risk neutral probabilities (for the arbitrage theorem) the same no matter what betting strategy is chosen?
I am learning the basics of risk neutral probability and arbitrage theorem. The arbitrage thm states that given a series of bets $r_{1}, ..., r_{n}$ either there is arbitrage, or there exists a ...
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96
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How to find state prices?
I am trying to find out how to solve state prices, but I do not know what I am supposed to do, my professor has given a solution to this problem as being (0.060 0.417 0.476), but I can't figure out ...
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$aS^0 + bS^1$ 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{...
- 1
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107
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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 $S$ ...
- 110
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119
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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 ...
- 4,893
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79
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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 ...
- 15
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189
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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 ...
- 450
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2
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394
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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 ...
- 131
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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 ...
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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 ...
- 141
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1
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189
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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 ...
- 841
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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?
...
2
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70
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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:
\begin{equation}
...
- 409
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1
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195
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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 ...
- 165
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188
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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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1
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247
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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 ...
- 165
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0
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46
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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-...
- 145
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60
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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 ...
0
votes
1
answer
81
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 ...
- 437
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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}...
- 11
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129
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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 ...
- 11
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83
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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 ...
- 141
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114
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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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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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112
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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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1
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110
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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 ...
- 29
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183
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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 ...
- 599
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2
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610
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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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53
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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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1
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112
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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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0
answers
67
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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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2
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359
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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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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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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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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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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 ...
- 161
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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 ...
- 181
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1
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120
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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 ...
- 57
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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 ...
- 51
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136
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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=...
- 103
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(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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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 ...
- 31
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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
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1
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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?
- 31