# Tagged Questions

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### Uniqueness of equivalent martingale measure in Black Scholes-Model

Let's consider standard Black-Scholes model with price process $S_t$ satisfying SDE $$dS_t = S_t(bdt + \sigma dB_t)$$, where $B_t$ is standard Brownian Motion for probability $\mathbb{P}$. I ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $d(\ln \frac{f}{g})$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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) ...
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### 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 ...
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### 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 ...
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### 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 ...