# Questions tagged [no-arbitrage-theory]

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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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### 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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### 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 ...
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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 ...
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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 ...
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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
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### 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 ...
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### 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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### 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 ...
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### 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?
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### Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
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### 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-...
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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### Arbirtage free price process question in Bjork's Arbitrage Theory in Continuous Time

I am currently working through questions in Bjork's Arbitrage Theory in Continuous Time. However, I am unable to solve the following question, 7.2 in the book. A solution would be greatly appreciated. ...
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### 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 $\mathcal{X}$ ...