Questions tagged [no-arbitrage-theory]
The no-arbitrage-theory tag has no usage guidance.
150
questions
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65 views
Are no-arbitrage term structure models of interest rates commonly used in practice? [closed]
These models are beautiful, but I wonder whether enforcing the no-arbitrage relationships really help with explaining data and making predictions.
Are those models used in practice? If so, which ...
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1answer
56 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
85 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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38 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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107 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
45 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
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1answer
76 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 ...
1
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1answer
79 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
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1answer
173 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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71 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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88 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 [...
2
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2answers
242 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
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1answer
41 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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56 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
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2answers
309 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
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1answer
97 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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32 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
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1answer
111 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
99 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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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
107 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 ...
2
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0answers
109 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
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1answer
51 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
61 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
80 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
149 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
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1answer
133 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
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1answer
489 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
308 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
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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
85 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
109 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
139 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
110 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
208 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
114 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 ...
1
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1answer
164 views
Covered Interest Rate Parity with FX Spot-Adjustment
The Covered Interest Rate Parity for FX is often quoted simplistically as
$$
X_T \quad=\quad X_S \cdot \frac{D^{base}_T}{D^{quote}_T}
$$
where $X_t$ is the (projected) FX rate at time $t$ (denoted as $...
2
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1answer
145 views
Fair price of a coupon paying bond
Consider a coupon paying bond with a maturity of $3$ years, that pays coupon annually. Let $c$ be the coupon rate (percentage) and let $F$ be the face value. This means that the holder of the bond ...
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2answers
279 views
No-arbitrage and the sharpe ratio?
I'm reading a paper and it says that in a no-arbitrage market the sharpe ratio is the same for all bonds. I'm guessing that a difference in two bonds sharpe ratios would open the possibility of ...
0
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1answer
52 views
Infinite Binomial Pricing no arbitrage
How to price a contract that pays only 1 at the first stock price drop? The stock follows an infinite binomial with no arbitrage $d<R<u$ condition.
So the probability of the price going down is ...
4
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0answers
102 views
Why does risk-neutral price processes do not, in general, compose all arbitrage-free price processes?
I was reading reviewing my mathematical finance notes and I came across a remark I cant understand fully
Remark :Contrary to discrete time models, the risk-neutral price processes do not, in general, ...
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0answers
69 views
When does funding cost of a portfolio enter into the portfolio's present value?
This question comes from some confusion when reading Hull's book and from the general concept of no-arbitrage/self-financing portfolios in stochastic finance books. I am not fully seeing the ...
3
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1answer
266 views
How to derive no-arbitrage conditions w.r.t. the variance of a trinomial tree?
For a trinomial pricing tree, some notes say there are two no-arbitrage conditions:
(1) $E[S(t_{i+1})|S(t_{i})]=e^{r{\Delta}t}S(t_{i})$
(2) $Var[S(t_{i+1})|S(t_{i})]=[S(t_{i})]^2\sigma^2\Delta{t}$
...
