Questions tagged [no-arbitrage-theory]

The tag has no usage guidance.

122 questions
Filter by
Sorted by
Tagged with
21 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 ...
67 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....
70 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 ...
26 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?
2k views

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 ...
215 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-...
276 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-...
185 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 ...
72 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 ...
569 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 ...
39 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 ...
77 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 ...
129 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 ...
89 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....
1k views

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. ...
64 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 $\mathcal{X}$ ...
57 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 ...
442 views

451 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 ...
120 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 ...
249 views

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 ...
43 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 ...
42 views

Proof of no arb condition after shifting SABR’s rho

Does anyone know of any paper or research where they shift SABR’s skew and rebuild the surface? In particular, I would like to prove theoretically whether the no arbitrage condition hold for the ...
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) ... 0answers 65 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, ... 0answers 61 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 ... 1answer 142 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} ... 0answers 399 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 \... 1answer 303 views Linear interpolation of local vol no arbitrage We already know the equivalence between local vol, implied vol and option price and there ... 3answers 1k 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 ... 0answers 79 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. ... 1answer 176 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 \... 1answer 261 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 ... 2answers 421 views Dumb question: is risk-neutral pricing taking conditional expectation? Dumb question: is risk-neutral pricing taking conditional expectation? \tag{1} In trying to recall intuition for risk-neutral pricing, I think I read that we should price derivatives risk-neutrally ... 2answers 3k views Arbitrage Free Volatility Smile When ATM implied volatility is higher than OTM put and call I believe that the volatility smile is no longer arbitrage free? Why is that? On the other hand, when ATM implied volatility is lower than ... 0answers 98 views Forward spot calculation for a dividend paying no-short sell ETF I am trying to fit an implied volatility curve for options on the SSE 50 etf that has no borrow (no short selling allowed) and pays a single annual dividend. I originally thought I could use the ... 0answers 279 views Detecting butterfly spread arbitrage for American options through European option prices It's easy to demonstrate that if European option prices are concave with strike, then an arbitrage exists. For example, the risk-neutral probability density is the second derivative of European put ... 2answers 687 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 ... 2answers 483 views Does numeraire have to be a tradable asset I thought we create replicating portfolios using underlying and the numeraire i.e. the numeraire has to be a tradable asset (assuming simple binomial model). But I have seen some examples which ... 0answers 206 views American put option in binomial model - arbitrage opportunity? I'm sorry this must be an elementary question. I spent a good deal of time searching through webs including this site for the problem but I got none. Here's the problem: Say we have a binomial tree ... 0answers 75 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 ... 0answers 238 views Binomial model's Radon-Nikodym derivative Related: Dumb question: is risk-neutral pricing taking conditional expectation? In the one-step binomial model... For \frac{d \mathbb Q}{d \mathbb P}, I think it's \frac{d \mathbb Q}{d \mathbb P}... 1answer 129 views At some intermediate time t, does money actually change hands in the trading of a futures contract? Assuming that the asset underlying a futures contract pays no dividends or associated (storage, etc) costs, I have the following formula for the price F_t of a futures contract at time t:$$ F_t = ... 3answers 144 views Besides arbitrage opportunities, are there other properties that real world markets cannot have The article "What is ... a Free Lunch?" nicely explains why market models with arbitrage opportunity are unlikely to describe financial markets of the real world. Are there other properties of ... 1answer 278 views Replicating portfolio for claim on stock with discrete dividend This is a practice question for an exam: Consider a market consisting of a bank account with a constant interest rate$r$and a stock$S$. The stock pays a proportional dividend of size$\...
In a market consisting of a bank account with a constant interest rate r and a non-dividend paying stock S, consider a T-claim that pays $X = S(T)/S(T_0)$ at time T, where $T_0 < T$. a) ...