Questions tagged [no-arbitrage-theory]

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arbitrage proof question

prove the condition $D<R<U$ is equivalent to the absence of arbitrage: R = risk free investment rate of return. U and D are returns corresponding to the upward/downward price movements of a ...
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1answer
148 views

option time value in the pricing models

option price = intrinsic value + time value where intrinsic value (in other words payoff at N) is defined generally as difference between the underlying asset price and strike price (order depending ...
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2answers
130 views

Question about find no arbitrage trading strategy

We got the stochastic process for stock price of n stocks at continues time. We can find if there is a arbitrage trading strategy or dominant trading strategy. I wonder if we cannot find such ...
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1answer
160 views

On the existence of a perfect market with no arbitrage that contains a forward contract

Consider the following theorem from p. 31 of Steven Roman's "Introduction to the Mathematics of Finance Arbitrage and Option Pricing" (Undergraduate Texts in Mathematics, 2012), giving the forward ...
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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
46 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
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 ...
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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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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
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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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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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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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 ...
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0answers
91 views

How to Calculate the Value of a Growing Perpetuity Using a State Price Matrix?

Summary I wish to value perpetual cash flows through state contingent claims on real consumption, where the state of the economy is assumed to follow a finite markov chain (Similar to Banz and Miller ...
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0answers
410 views

Fair price and no arbitrage

The market is arbitrage-free iff there exists an equivalent martingale measure for the discounted price process of the stock. So in a world with a finite amount of possible outcomes $\Omega$ that ...
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0answers
441 views

Risk neutral pricing - Example from a book is correct?

I found the following example in a book on Model Risk, while trying to explain how risk-neutral pricing takes properly into account the risk involved in different investments. The Example is this. ...
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0answers
114 views

HJM model, existence of arbitrage:

The Setup: Suppose I know the yield curve of a Bond satisfies: f (0, t) = 0.04 for t ≥ 0 and f (ω, 1, t) = 0.06, t ≥ 1, ω = ω 1 , 0.02, t ≥ 1, ω = ω 2 , where Ω = {ω 1 , ω 2 } with P[ω i ] > 0, i = 1,...
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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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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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2answers
466 views

Solving for r in the Black Scholes equation

Could you please correct which parts of my reasoning are wrong? Let's suppose that I know for sure that my estimate for a stock volatility is right (I have a crystal ball) and that it will be for ...
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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 ...
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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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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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1answer
312 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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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
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 ...
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2answers
1k views

How does a Delta Hedged portfolio yield the Risk-free?

Here I'm considering the simple case of a dealer writing call options on a stock and hedging the short position with a "textbook" Delta Hedge, i.e. goes long on $N_c \times Delta$ stocks (where $N_c$ ...
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1answer
227 views

Arbitrage problem [closed]

Question A share of non-dividend paying stock is trading at USD 30. The maturity of both options is 1 year from now. A put with a strike of USD 28 is trading at USD 1 and call with a strike of USD 29 ...
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1answer
97 views

Mathematically: How does increasing the number of assets reduce idiosyncratic risk?

As part of an Asset Pricing Module I'm currently taking, whilst looking at APT Ross (1974), we looked at how according to this model, risk originates from both systematic and idiosyncratic asset ...
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1answer
49 views

binomial - parameters at which american option hits early exercise possibility

I am looking for a set of parameters (d,u,r,So,K, N=?) for pricing an american call using binomial where the call hits the early exercise possibility. Do you have any exemplary set?
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1answer
296 views

completeness of the binomial model - proof

I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...
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1answer
103 views

Arbitrage-free market for continuous logreturn distribution?

Is it true, that a one-period market say $(0,t)$ is arbitrage-free if the logreturn for $S_t$ is continuously distributed on $\mathbb{R}$? I.e., for continuous distributions on $\mathbb{R}$, there ...
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2answers
2k views

expected value of the discounted payoff

I don't understand the following statement: The price of a contingent claim is the expected value of the discounted payoff value under the risk neutral probability measure Q defined in complete markets ...
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40 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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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 [...
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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 ...
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0answers
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 ...
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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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1answer
295 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
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62 views

How realistic are the scenarios outlined in my course?

I am currently taking a course in Financial Mathematics as part of my Maths degree. Many of the covered topics are quite basic, and revolve around potential arbitrage opportunities. For example, ...
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59 views

Concatenation property of a set of semimartingales

Consider as in (1, Definition 2.1) a convex subset $\mathcal{X}_1$ of the set of semimartingales $\mathbb{S}$ satisfying the following properties: $X_0=0$ $X_t\geq -1$ for all $t\geq 0$ for all ...
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159 views

Deriving the yield curve from the HJM dynamics

If I know that my model follows a no-arbitrage HJM model: \begin{equation} df(\tau) = \left(\sigma(\tau)\int_0^{\tau}\sigma(u)du\right)dt +\sigma(\tau)dW_{\tau} \end{equation} (where $\tau:=T-t$, ...
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1answer
243 views

European option on a dividend paying stock, limits to arbitrage?

What is the price C of a European call option on a dividend paying stock? I believe it is: C = U. N(d1) - exp(-rt).K.N(d2) d1 = [ ln(U/K) + (r + v^2/2).t ]/[ v.sqrt(t) ] d2 = d1 - v.sqrt(t) U ...
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1answer
151 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
129 views

Implicit relation between risk and reward

I want to differentiate w.r.t. $\sigma^2$ the following equation $u'(Y)\mu$ + $\frac{u''(Y)}{2}$$(\sigma^2 + \mu^2) = 0$ where we can consider $\mu$(reward) as an implicit function of $\sigma^2$(risk) ...
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1answer
323 views

Option price in a neutral risk world is the same as in the real world. I can not understand! [closed]

Good evening. I know there are several posts on the subject but unfortunately I can not fully understand this concept and I hope you can help me. To price the option the fundamental assumption ...
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1answer
318 views

inflation > interest rate? [closed]

Currently, the federal reserve interest rate is 0-0.25%, and the inflation is 2-3%. Does this contradict the no-arbitrage principle? (The arbitrage being: borrow money at 0.25% and invest it in the "...

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