Questions tagged [no-arbitrage-theory]

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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 ...
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-...
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 ...
2
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1answer
136 views

Forward contract pricing of coupon paying security

PLease help me in understanding how to price forward contract for coupon paying security. For instance if we get into a contract to buy a security in next six month whose coupon due in next two month. ...
2
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1answer
224 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 $\...
2
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1answer
119 views

Pricing and Arbitrage of Inverse Asset Claim

I'm working through the following little exotic exercise and have some questions and curiosity as to whether I'm on the right track Consider the claims $$Y_t=\frac{1}{S_t}$$ $$X=\frac{1}{S_T}$$ a) ...
2
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1answer
104 views

Pricing of American Deriviatives

Reading the book by Andrea Pascucci "PDE and Martingale Method in Option Pricing" I am struggling with a very simple issue. Suppose we want to find the price of an American derivative $X$ in an ...
2
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1answer
303 views

Pricing digital options in discrete time

I am stuck in this exercise from my textbook: Consider a one-period market model with $N+1$ assets: a bond, a stock and $N-1$ call options. The prices of the bond are $B_0=1$ and $B_1 = 1+r$, where ...
2
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1answer
211 views

If the risk neutral probability measure and the real probability measure should coincide

Sorry if this may be a stupid question. I have not had that much mathematical finance, I've only learned about discrete time models. But lets for the argument say that you have a stochastic process ...
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 ...
2
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3answers
511 views

Understanding the HJM drift condition's dimensions

In an HJM model the forward rate dynamics follow $$ df_t(T) =a_t(f_t(T))dt+b_t(f_t(T))dW_t $$ where $W_t$ is a $d$-dimensional brownian motion, $b_t$ takes values in $\mathbb{R}^{d\times d}$ and $a_t$ ...
2
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1answer
141 views

“For any random variable $X$, someone will be willing to buy and someone to sell a financial instrument, whose final payoff is $X$.”

we will assume that for any random variable $X:\Omega\rightarrow\mathbb{R}$, some investor will be willing to buy and some investor will be willing to sell a 'financial instrument' whose final payoff ...
2
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1answer
179 views

Law of large numbers necessary for APT derivation?

The question refers to the well-known Ross (1976) paper with the derivation of the Asset Pricing Theory. In the APT, the return of asset $i$ is driven by a linear factor model: $$ R_i = \alpha_i + \...
2
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2answers
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. ...
2
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0answers
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 ...
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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0answers
943 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 $\...
2
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0answers
177 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. ...
2
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0answers
153 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 ...
2
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0answers
529 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 ...
2
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0answers
244 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 ...
2
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0answers
677 views

Simple Forward Interest Rate Proof

Just trying to check my logic here: Let $Z(t,T)$ be a Zero-Coupon Bond with maturity $T$ bought at time $t$, $S_m$ be the spot interest rate for time $m$ and $S_n$ for time $n$ respectively, where $n ...
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3answers
455 views

The Law of One Price in a discrete model

The following question assumes familiarity with the discrete model described in chapter 5 of Steven Roman's "Introduction to the Mathematics of Finance", 2nd edition, Springer 2012. I will not ...
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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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2answers
1k views

Option arbitrage with dividends?

If a stock pays a discrete dividend, the stock price falls by the amount of the dividend. There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of ...
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1answer
346 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 $\...
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1answer
949 views

No-arbitrage theorem: a proof

The market is arbitrage free iff there exists an equivalent martingale measure for the discounted price process of the stock. My course only provides me part of the entire proof that shows that ...
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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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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
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 $...
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1answer
171 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 = ...
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3answers
157 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 ...
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3answers
474 views

Is this arbitrage?

Assume the stockprice as in the Black-Scholes model (Geometric Brownian Motion): $$S_t=S_0e^{(\mu-\sigma^2/2)\cdot t+\sigma W_t}$$ Wouldn't there be an immediate arbitrage opportunity, to just buy ...
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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....
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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
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 ...
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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 ...
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1answer
1k views

Why does arbitrage free imply complete market?

Proposition 2.10 of Tomas Bjork's "Arbitrage Theory in Continuous Time" states that if the general binomial model is free of arbitrage then it is also complete i.e. every contingent claim has a ...
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1answer
186 views

What is the principle of determining an arbitrary option price

First I want to talk about one of my wrong ways of pricing an European call option. When I consider the simplest case of European call option, the first idea of determining the price is to calculate ...
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1answer
1k views

American Option Bounds with Dividend Yield

What are the upper and lower bound of American call and put options for an underlying with continuous dividend yield? For European options, the bounds are known as \begin{align*} [S_te^{-d\tau}-Ke^{-...
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3answers
2k views

Arbitrage free implies complete market?

In Tomas Björk's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition It seems that to show that the model is complete, we must show that the claims are reachable. That is, we ...
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3answers
94 views

Interpretation of equation derived from the delta of a call European call option

I have started reading an introductory book called: A Course in Derivative Securities by Kerry Back. On page 12 they mention the following: The delta of the call option is $\delta = (C_{u} - C_{d}) / ...
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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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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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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
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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1answer
588 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 ...
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1answer
1k 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)...
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1answer
70 views

Pricing weighted/average stock price claim

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) ...