Questions tagged [no-arbitrage-theory]
The no-arbitrage-theory tag has no usage guidance.
141
questions
0
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1answer
29 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
90 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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0answers
42 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
270 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
74 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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0answers
27 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
88 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
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0answers
86 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
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0answers
47 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
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1answer
90 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
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0answers
22 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 ...
0
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0answers
55 views
Meta-Theorem Bjork, arbitrage and completeness
In Tomas Björk's Arbitrage Theory in Continuous Time I found this Meta-Theorem:
What does it mean "meta-Theorem"? That it cannot be proved and that this is only such an indication as to ...
2
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0answers
69 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
47 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
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0answers
24 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
52 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
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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?
0
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1answer
811 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
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0answers
68 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
90 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 $DF_f$: ...
0
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0answers
29 views
How to calculate the interest rate under no arbitrage condition
We have two forwards with the same IBM share as the underlying asset.
1) The delivery date is two months from now, the forward price is 1.1
2) The delivery date is seven months from now, the forward ...
1
vote
1answer
105 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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0answers
46 views
Deriving CAPM from APT framework
I was wondering if it is possible to derive the CAPM from the APT?
My argument is that CAPM basically just is a 1 factor model, where the APT has multiple factors.
Can any of you guys help me?
0
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0answers
72 views
Nonlinear dependency between prices
Can you help me with pricing theory?
There are three assets: $A$, $B$ and $C$ with prices $P_A$, $P_B$ and $P_C$ respectively. There are two processes (production, transportation, etc.) that ...
2
votes
1answer
335 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
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1answer
138 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
851 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
49 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 ...
1
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1answer
97 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 ...
0
votes
1answer
82 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 $\mathcal{X}$ ...
1
vote
1answer
101 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....
1
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0answers
63 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 ...
1
vote
2answers
180 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 ...
1
vote
1answer
86 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
vote
1answer
137 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
votes
1answer
131 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 ...
1
vote
2answers
189 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
votes
1answer
47 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
82 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, ...
1
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0answers
63 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
votes
1answer
187 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) $Var[S(t_{i+1})|S(t_{i})]=[S(t_{i})]^2\sigma^2\Delta{t}$
...
2
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0answers
666 views
Butterfly Arbitrage condition
I hope anybody can help me. According to Gatheral and Jacquier (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2033323) no Butterfly Arbitrage can be expressed like this:
Define the function
$\...
4
votes
4answers
2k views
arbitrage free volatility surface
Why is calendar spread arbitrage equivalent to $\partial_t \omega(k,t) \geq 0, \forall k \in \Bbb{R}$ where $\omega(k,t) = \sigma^2(k,t) t$ and $\sigma(k,t)$ represents the Black-Scholes implied ...
2
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0answers
112 views
Prove unique arbitrage-free price implies attainable
I just read a Corollary in a finance course note:
Suppose the market is arbitrage free and $C$ is a contingent claim. Then $C$ is attainable if and only if it admits a unique arbitrage-free price.
...
6
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1answer
231 views
No-arbitrage in term-structure models
I am a bit confused about what the implication of "no-arbitrage" in popular term struchture models (such as affine term struchtre models or HJM models) are?
Is it solely a restriction on the cross-...
2
votes
1answer
183 views
Showing that a market model has arbitrage and describing martingales
This is an exercise which I came upon while studying an introduction to financial mathematics.
Exercise :
Consider the finite sample space $\Omega = \{\omega_1,\omega_2,\omega_3\}$ and let $\...
1
vote
1answer
411 views
Is there an arbitrage strategy if short selling of a stock is allowed?
Consider a market with a risk-free asset such that $A(0) = 100, A(1) = 110, A(2) = 121$ dollars and a risky asset, the price of which can follow
three possible scenarios
Is there an arbitrage ...
8
votes
1answer
493 views
Linear interpolation of local vol no arbitrage
We already know the equivalence between local vol, implied vol and option price and there ...
3
votes
1answer
570 views
Prove that a market is arbitrage free
The question is based on a one period model. Let a market be arbitrage free, and then let a security $X$ be added to it. Denote $P(X)$ as the price of this security at $t=0$. The security has the ...
1
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1answer
746 views
Basic Replication of European Call Option
I am looking at the very basics of replicating an option with a portfolio of risky and risk free assets. As such we can define a portfolio of $x$ no. of shares, $y$ bonds & $z$ options at time $(T)...
