The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
2answers
201 views

Exchange rate model and Martingales

In exchange rate model explanation, "...If under the domestic risk neutral measure $Q_d$, the process $X(t)$ satisfies $\displaystyle \frac{dX(t)}{X(t)}=\sigma dZ_d(t)$ Since $Z_d(t)$ is ...
8
votes
1answer
157 views

Strictly local martingales: what is the intuition behind them?

A process $X_t$ is a local martingale if for each increasing sequence of stopping times $\{\tau_k,k=1,2,...\}$ the stopped process is a martingale. All true martingales are local martingales, but the ...
3
votes
3answers
132 views

Martingale Stock Prices

In http://www.principlesofforecasting.com/files/pdf/Granger-stockmarket.pdf Granger makes survey of some arguments. In section I there are two hypothesis H01, and H02. H01: Stock prices are a ...
0
votes
3answers
78 views

Why is it enough to know the expected present value of cash flow in risk-neutral framework to price derivatives?

Wilmott book states that its enough to know the expected present value of all cash flow in risk-neutral framework to price derivatives. As I know, to obtain arbitrage-free market we need our ...
1
vote
0answers
41 views

Existence of a hedging portfolio and martingale property

Lets assume that the underlying follows a Brownian motion and the market has the standard properties of the Black Scholes setting. Is there a way to find a hedging portfolio for every discounted ...
0
votes
1answer
62 views

How to derive equivalent martingale measure using Ito's Lemma

Can someone explain how to get equation 27.14 below? I understand the first usage of Ito's Lemma to get $d(\ln f-\ln g)$ but I do not understand how to use Ito's Lemma to go from $d(\ln \frac{f}{g})$ ...
2
votes
3answers
97 views

Difference betweem martingale property and adapted filteration

What is the difference between a random process that is adapted to a filteration and one that had the martingale property. It seems the two notions are quite similar and would be helpful to construct ...
0
votes
0answers
65 views

EMM in incomplete markets

The simply put question is as follows: do we need to restrict ourselves to EMM exclusively when pricing European contingent claims (=option payoffs) even if markets are incomplete? In particular, a ...
4
votes
0answers
50 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 ...
2
votes
2answers
99 views

What impact does arbitrage have on realised volatility estimates?

Doing some research modeling/estimating volatility in the bitcoin market. There is quite a bit of scope for arbitrage within crypto-currency markets. Wonder if this has any impact on my volatility ...
4
votes
0answers
93 views

Finding the dynamics of a dividend paying asset under arbitrary numeraire

Assuming I have a dividend paying asset $S$ with dividend process $D$. Now I would like to use the bank account process $B$ as numeraire and determine the dynamics of $S$ under the the corresponding ...
5
votes
1answer
127 views

unique equivalent martingale measure in incomplete markets

Do you have any idea about how we can prove, and under which conditions, that an equivalent martingale measure (EMM) in an incomplete market is unique? The assumptions we have made are: 1) that the ...
2
votes
1answer
231 views

Which measure to determine Risk?

Say I hold an equity and I want to calculate the Value-at-Risk over some period. Would one calculate the Value-at-Risk of the equity under a risk-neutral (as in martingale) measure or under the ...
1
vote
3answers
585 views

Understanding the concept of Martingale pricing

I am a bit confused about how to formulate a problem where I have to price an option on a stock. Many papers say that stock prices are best modeled using a geometric Brownian motion (GBM), and I ...
3
votes
0answers
114 views

What is the stochastic differential of a general semimartingale?

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon's "Analysis of Fourier Transform Valuation Formulas and Applications", on page 3: $$H = B + H^c + h(x) ...
2
votes
0answers
149 views

Measure change in a bond option problem

This is not a homework or assignment exercise. I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
3
votes
1answer
157 views

Parameter estimation using martingale measures - include real world data?

Please note: I posted this in nuclearphynance first, but didn't get any replies. For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic ...
2
votes
1answer
137 views

Assumptions based on non-martingale?

Quantitative finance formular are mostly based on martingales, Poisson jump, GBM, CEV, etc.. The logic behind it is that martingale means the future could not be predicted, or, EMH (Efficient-market ...
5
votes
3answers
1k views

How to use Itô's formula to deduce that a stochastic process is a martingale?

I'm working through different books about financial mathematics and solving some problems I get stuck. Suppose you define an arbitrary stochastic process, for example $ X_t := W_t^8-8t $ where $ W_t ...
15
votes
5answers
3k views

Is the stock price process a martingale or a Markov process?

Some people claim that the data-generating process for stocks is a "martingale" and that is has the "Markov property". Are they unrelated? Is it that the Markov property implies some sort of ...
7
votes
2answers
466 views

Change of measure discrete time

Suppose I have a random walk $X_{n+1} = X_n+A_n$ where $A_n$ is an iid sequence, $\mathsf EA_n = A>0$. How to construct a martingale measure for this case?
7
votes
1answer
506 views

How do equivalent martingale measures arise in pricing?

I'm studying for an exam in financial models and came across this question: "An agent with $C^2$ strictly increasing concave utility $U$ has wealth $w_0$ at time 0, and wishes to invest his wealth in ...
9
votes
4answers
4k views

What is a martingale?

What is a martingale and how it compares with a random walk in the context of the Efficient Market Hypothesis?