The tag has no usage guidance.

learn more… | top users | synonyms

3
votes
4answers
2k views

Simple value of a Forward contract at an intermediate time question

I am taking "Financial Engineering and Risk Management Part I" from Columbia University on coursera and I got a seemingly simple question wrong on the first quiz. This is all based on the no-arbitrage ...
3
votes
2answers
249 views

Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of d+1 assets and N states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
0
votes
1answer
104 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 ...
0
votes
2answers
104 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 ...
0
votes
1answer
61 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 ...
1
vote
1answer
32 views

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 ...
4
votes
2answers
95 views

What is the arbitrage opportunity in this simple one-period market?

I have a single period market, and three states, and I have 3 risky assets. I assume no interest. So I have three states $\Omega=\{\omega_1,\omega_2,\omega_3\}$. All assets start with the value 1, ...
1
vote
1answer
87 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 ...
0
votes
0answers
34 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 $\tau:=T-t$, ...
5
votes
1answer
91 views

Prove arbitrage opportunity

The continuously compounded interest rate is $r$. The current price of the underlying asset is $S(0)$ and the forward price with delivery time in 1 year is $F(0,1)$. Short selling of the stock ...
0
votes
0answers
47 views

Market with exponentially distributed random variable

Consider a market consisting of a stock with $S_0^1=1$ and $\log(S_1^1)=Z$, where $Z$ is an exponentially distributed random variable. $S_0^1$ denoted the prices of the stock $1$ at time $t=0$ and ...
1
vote
1answer
27 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?
0
votes
1answer
63 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 ...
1
vote
0answers
31 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
vote
1answer
40 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 ...
0
votes
0answers
24 views

Bond's bid-ask spread with no arbitrage assumption

Suppose I have a bond with unknown bid-ask spread, and a portfolio, containing it and also other bonds, all with known bid-ask spreads. How can the unknown spread be inferred? I assume there should ...
7
votes
2answers
378 views

How to check that an interest rate curve is arbitrage free

I have 2 interest rate curves (LIBOR 3M and OIS). I want to create stress scenarios for those two curves. Is it possible that some scenarios will make my term structure arbitrageable? How can I test ...
3
votes
1answer
53 views

Equivalent Definitions of Self-Financing Portfolio

Consider a multi-period model with $t=0,...,T$. Suppose there is a bond with $B_0=1$ and $B_t=(1+R)^t$ and a stock with $S_0=s_0$ and $$ S_{t+1}=S_t\,\xi_{t+1}, $$ with $\xi_t$ iid random variables....
3
votes
3answers
141 views

How to price a path dependent exchange option using?

Assume you have two stocks $S$ and $P$ so that at initial time $t = 0$: $S_0 > P_0$. You bought an option which pays off $S_T - P_T$ as long as $S_t > P_t$ through the time $0 < t < T$. ...
0
votes
0answers
21 views

Stochastic correlation arbitrage-free replication

I'm interested in possibility of stochastic correlation arbitrage-free replication (something VIX-style, mayby). To my knowledge, no such method exists. Could you provide some intro to the problem: ...
-1
votes
1answer
62 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 ...
4
votes
2answers
322 views

Does No arbitrage(NA) imply efficient markets (EMH)?

The EMH states that stocks are traded at its fair values. This means there is no arbitrage strategy in efficient markets. However, if the market is no arbitrage, can we conclude the market is ...
1
vote
1answer
28 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. ...
1
vote
2answers
88 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 ...
4
votes
1answer
172 views

Self-Frontrunning Arbitrage

If I have a large order to fill, shouldn't I always buy a derivative in the same direction to profit from the market impact? E.g. I sell 1 million shares and so I buy a put, which will hence almost ...
10
votes
7answers
849 views

What is the fair price of this option?

Without having to use Black-Scholes, how do I price this option using a basic no-arbitrage argument? Question Assume zero interest rate and a stock with current price at \$$1$ that pays no dividend. ...
1
vote
2answers
310 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 ...
2
votes
0answers
52 views

Show that in an arbitrage-free and non-redundant market a certain set is compact

Some notation: We consider a financial market with $d+1$ assets, the $0$-th asset is considered the risk-free asset, the others are the risky ones. The vector $\overline \pi \in \mathbb R^{d+1}$ ...
3
votes
1answer
248 views

Why is the volatility smile important

One thing I can't understand clearly is why there is so much focus on the volatility smile. Given my knowledge of the Black and Scholes model, this is what I get: People use the volatility smile as a ...
2
votes
1answer
97 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 $B_1 = 1+r$, ...
1
vote
3answers
134 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 ...
6
votes
1answer
114 views

FTAP a-la Harrison, Kreps and Pliska

I was reading the papers co-authored by Harrison, Kreps and Pliska, that initiated the formal research on the connection between pricing, martingale measures, arbitrage and completeness. I have some ...
1
vote
1answer
81 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 ...
2
votes
1answer
107 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 + \...
0
votes
1answer
88 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 ...
3
votes
2answers
286 views

Arbitrage and dominant strategies

If there is no arbitrage there is no dominant trading strategy, but there may be arbitrage opportunities even if there are no dominant trading strategies. Could you explain this statement and bring ...
1
vote
1answer
104 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 ...
5
votes
0answers
187 views

Integral-differential equation for forward rates

I am struggling in this question: Let $P(t,T)$ denote the price of a zero-coupon bond (with marturity at time $T$) at time $t \in [0,T]$. As usual, at time $t$ for maturity $T$, the forward rate is ...
5
votes
1answer
320 views

Proving that Absence of Arbitrage does not imply law of one price

I am trying to prove that the Absence of arbitrage statement (AOA) does not necessarily imply the law of one price (LOP). For the definitions of these concepts I am using Cochrane's book "Asset ...
4
votes
2answers
351 views

Equivalent (true) Martingale Measures and no-arbitrage conditions

I hope this is the correct site for this question, as it is rather theoretical... In their famous paper, Delbaen and Schachermayer proved that the No Free Lunch with Vanishing Risk condition is ...
3
votes
4answers
144 views

risk-neutral valuation implies no arbitrage?

It is known that in an arbitrage-free continuous time market, the price of every asset is evaluated as the corresponding price in the replicating strategy using risk-neutral valuation. I want to ...
4
votes
2answers
187 views

arbitrage in Heston model

Really struggling in this question: Consider a market with two assets $(B,S)$ whose price dynamics satisfy \begin{equation} dB_t = B_t r dt \end{equation} \begin{equation} \quad \quad \quad \quad \, ...
6
votes
1answer
585 views

What is the difference between market efficiency, market equilibrium, and no-arbitrage?

Aaron Brown (in the book, The Poker Face of Wall Street, p. 196), discusses four approaches to deriving the same Black-Scholes-Merton option-pricing formula: Ed Thorp, Myron Scholes, Robert Merton,...
6
votes
4answers
354 views

Efficient Markets Paradox

Basically all Quant Finance theory is build on No-Arbitrage presumption and Efficient Markets Hypothesis. The known Grossman-Stiglitz Paradox says: if one can't make money from trading, one wouldn't ...
4
votes
2answers
172 views

How does this follow from the separating hyperplane theorem?

This is from Pliskas book in mathematical finance. I do not know what was best to write the question so I included the pages from the book. He has not written what form of the separating hyperplane ...
1
vote
3answers
351 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 ...
4
votes
2answers
395 views

law of one price, understanding

I am reading about mathematical finance, and I was tipsed to ask the quesiton on this site. It is about the "law of one price". Just first I'll make precise the model my book uses: I have a single ...
1
vote
3answers
546 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 ...
7
votes
2answers
474 views

Efficiency vs. Robustness - To use a constant or not in single factor time-series regression?

Arbitrage pricing theory states that expected returns for a security are linear combination of exposures to risk factors and the returns on these risk factors. Betas, or the exposures of the security ...
1
vote
3answers
81 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}) / ...