1
vote
1answer
99 views

Mean reversion time estimation

I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.
-4
votes
1answer
27 views

Matlab loop statement is driving me mad [closed]

Can someone please help me out with this loop over here? Matlab simple refuses to consider the for o=k:k-20 statement inside the if statement. :pullingmyhair: ...
5
votes
1answer
123 views

Why Lie groups, differential geometry and string theory relate to MF?

I'm reading Peter Carr's "A Practitioner’s Guide to Mathematical Finance". When talking about the math used in mathematical finance, he mentions Lie groups, differential geometry, string theory. Can ...
2
votes
1answer
61 views

Black Scholes Model and Dividends

My question can be summarised as such: Consider a portfolio. Say it has a price $\Pi = x$. Portfolio consists of a stock and a sequence of call options underlying on the stock. It has been announced ...
3
votes
0answers
70 views

How to calculate the JdK RS-Ratio

Anyone have a clue how to calculate the JdK RS-Ratio? Let's say I want to compare the Relative strength for these: EWA iShares MSCI Australia Index Fund EWC iShares MSCI Canada Index Fund EWD ...
2
votes
4answers
65 views

Obtaining intra-day values of the EUR-USD exchange

I need for my project the values of the EUR-USD exchange (both intra-day and ticker). I've been playing around with the Yahoo's YQL API and at this moment I can obtain the current value of the ...
2
votes
0answers
42 views

pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
2
votes
1answer
68 views

Black Scholes Formula, drift term

In the formula, the stock return is modelled as a brownian motion that is a drift + a stochastic term, ok I get that. But the drift term is then modelled as r - volatility ^ 2 / 2. I am not sure how ...
6
votes
2answers
163 views

What's the point of discounting in risk-neutral pricing?

Let $\phi$ be a self-financing strategy that replicates a time $T$ option payoff $X$ on stock $S$. By definition of a trading strategy, $\phi$ is previsible. Finally, let $V_t$ be the time $t$ value ...
0
votes
1answer
43 views

Expected Utility and $\log$

I've just started reading about expected utility and utility functions and have the following question. $\textbf{Question:}$ An investor has an initial wealth of 100 and a utility function of the ...
1
vote
1answer
76 views

Markowitz portfolio optimization question

I am studying the Markowitz portfolio optimization theory, and I just wanted to ask if I understood this correctly. For a stock portfolio we distinguish two kinds of risks: an unsystematic risk, which ...
4
votes
1answer
82 views

Need for Binomial Representation Theorem

In some texts (e.g. Baxter & Rennie, Shreve I) the binomial model is first constructed using the usual backward induction argument, and it is concluded that by no-arbitrage the time $t$ value of a ...
0
votes
1answer
50 views

Portfolio volatility

Problem True or fale? The stock of a firm has an expected return of 10%, and a volatility of 10%. The weight of the stock in a portfolio is 5%, and the correlation of the stock’s return with the ...
1
vote
1answer
64 views

Option Pricing under Jump Diffusion Models

I was wondering what the overall approach/intuition behind how to price options under Jump Diffusion Models. My understanding is under Diffusion models such as Geometric Brownian Motion (Black ...
1
vote
2answers
42 views

Is the Binomial Tree Model not self-financing?

Consider a 2-period binomial tree where the derivative price is $f$ and the stock price is $S$. Also, let the bond be deterministic with continuous growth rate $r$ and initial value $B_0$. binomial ...
0
votes
1answer
60 views

Derivation o HJB equation

I am trying to derive the HJB equation in a stochastic setting. Let me exemplify my problem with the simplest case where there is no control, just one state variable. Assume the payoff is given by $$ ...
0
votes
0answers
43 views

How to create a basket of currency pairs with the lowest correlation in R?

My strategy is designed to buy and sell all assets of a universe and rebalance periodically. It goes either long or short. To limit risk exposure to a single currency I would like the assets in the ...
-3
votes
1answer
35 views

Zero coupon bonds [closed]

Assume the zero-coupon bonds from 1 year to 4 years are all available, and the current 1-year, 2-year, 3-year and 4-year spot rates are 4%, 5%, 6% and 7% accordingly. Interest rates are annually ...
2
votes
1answer
105 views

Arbitrage question

Consider a hypothetical Payment in Kind (PIK) bond of XYZ Corporation. The bond has 2 years to maturity, a face value of $1000, and has an annual coupon rate of 10%. Coupons are paid annually. XYZ ...
1
vote
1answer
50 views

How to identify the orders p and q for ARIMA model using least squares method?

I would like to identify the orders p and q for ARIMA model using least squares method in Matlab. I have got also two data files (one with noise and one without) Previously I identified p and q for ...
1
vote
1answer
33 views

How to effectively hedge a Fixed-Term deal in a foreign currency?

Assume my firm is based in USD and agrees with some counterparty to buy, at time $T$, some quantity $Q$ of asset $A$ for a fixed price $K$. Assume also that $A$ prices and $K$ are denominated in EUR. ...
0
votes
1answer
57 views

A Difference between Local Vol and Stochastic Vol Models

For the purpose of this question a local vol model is a 1d SDE which specifies the price process and we have a contingent claim that depends on those prices (in general, at multiple times). e.g. ...
4
votes
2answers
91 views

simple, intuitive barrier option derivation

Is there a simple integral that gives barrier option prices without having to deal with messy, hard PDEs and change of variables I understand there is a reflection principle such that the simulation ...
3
votes
2answers
127 views

Negative high frequency intraday volatility - Zhou estimator

To estimate high frequency tick data stock intraday volatility, I have read Robert Almgren's notes7.pdf http://www.cims.nyu.edu/~almgren/timeseries/notes7.pdf where he talks about the bias free ...
0
votes
1answer
79 views

Calculating VaR with Monte Carlo simulation

I would like some help here :) I have a problem calculating VaR with the Monte Carlo Simulation. I have followed then next steps, is this a right way to calculate VaR or I need something more? ...
1
vote
1answer
50 views

Why we consider second derivative w.rt price but only first derivative w.r.t time and volatility

What is the reason (better if it is intuitive, and not too math heavy), that when we talk of Greeks, we consider second derivative with respect to price (gamma), but only first derivative with respect ...
3
votes
1answer
89 views

Why must a replicating portfolio be self-financing?

If I have a trading strategy such that at each time $t$ I own $\Delta_t$ units of stock $S_t$ and $\psi_t$ units of bond $B_t$, it is a replicating strategy for some claim with time $T \geq t$ payoff ...
2
votes
0answers
30 views

Value-at-Risk Calculation with respect to the Capital Requirements

I want to calculate the Value-at-Risk at date $t$ in such a way that I minimize the capital requirements given as \begin{align} \text{CR}_{\,t+1\,:\,t+250} = \sum_{h=0}^{249}\max\left( ...
1
vote
1answer
39 views

Where to get historical daily settlement price of each VSTOXX futures contract

I'm doing some analysis on VIX and VSTOXX futures and require historical prices of each contract as a result. VIX info is free to download on CBOE website: ...
0
votes
0answers
27 views

Can Yahoo Finance API work for non-US markets?

I am trying to fetch ticker prices and historical prices for major Asian exchanges (HKSE, SGX etc). I am trying to use yahoo finance API, but it is not returning any data for even SingTel, which is a ...
5
votes
1answer
98 views

Why Must Dividends Be Reinvested to Use Risk-Neutral Pricing?

Assume the price of a stock $S_t$ paying continuous dividend $a$ satisfies $$ dS_t = S_t\left((\mu - a)dt + \sigma dW_t\right). $$ The risk-neutral pricing formula states that if $\mathbb{Q}$ is any ...
4
votes
2answers
198 views

R package for portfolio

In the context of modern portfolio theory, one often wishes to minimise $\mathbf{w}^{\mathrm{{\scriptstyle T}}}\boldsymbol{\Sigma}\mathbf{w}$ subject to $\mathbf{w}^{T}\boldsymbol{\mu}=c_{1}$, ...
2
votes
1answer
88 views

Density of Geometric BM via Fokker-Planck

Attempting to derive density of a GBM (which we know is log-normal) the long way, using the Fokker Planck-equation. Can't figure out where I went wrong - would appreciate a few sets of extra eyes! ...
1
vote
2answers
95 views

Estimate simple option price without a calculator

I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it. If you have an European ...
0
votes
1answer
28 views

Order Book vs Wallet Updates

Good morning, i am in the middle of developing my own stock exchange system and have implemented limit orders (basics) matching. The system is just a DIY solution for my own purposes and for fun ...
-4
votes
1answer
46 views

Can not understand options pricing [closed]

As we are seeing here http://www.theoptionsguide.com/strike-price.aspx Relationship between Strike Price & Call Option Price Relationship between Strike Price & Put Option Price I do not ...
1
vote
2answers
110 views

How can I make this portfolio self-financing?

$a_t S_t$ = number of shares ($S_t$ is stock price at $t$), $S_0 = 1$ $b_t \beta _t$ = saving account value , $d \beta_t = r \beta_t dt$, $r=$ interest rate So the value of the portfolio: $$V_t = ...
16
votes
5answers
1k views

Is R being replaced by Python at quant desks?

I know the title sounds a little extreme but I wonder whether R is phased out by a lot of quant desks at sell side banks as well as hedge funds in favor of Python. I get the impression that with ...
0
votes
0answers
57 views

High frequency price forecast model ARMA GARCH or another?

Can you reccomend model for high frequency data (1 second and less) (returns and volatility forecasting)? Most papers use ARMA, GARCH etc in 1 minute and lower time frame. PROBLEM ARMA does not know ...
1
vote
1answer
59 views

Why is the black-scholes model arbitrage free when σ>0?

I want to show that: if $σ$ is positive then there is no arbitrage in the model, even if $r > µ$. Whilst I have satisfied this for $ r > \mu$, I cannot see why the conditioning on $\sigma>0 $ ...
0
votes
1answer
43 views

Negative time value european options

I have a basic question for which I feel like I should have found the answer by googling it, but I didn't get a definitive answer, so here I am: Can the time value for a plain vanilla (European) ...
5
votes
2answers
181 views

Why dynamics of local volatility is wrong?

In Dupire's local volatility model, the volatility is is a deterministic function of the underlying price and time, chosen to match observed European option prices. To be more specific, given a ...
-3
votes
1answer
64 views

Show that the equation solves the Black-Scholes PDE

I have the solution as given Based on this, I have to show that this solves the Black-Scholes formula It means that I should take the partial derivatives of the solution above and then receive the ...
6
votes
1answer
84 views

Why can CDS indices be used as a bond market index?

I don't understand why the iTraxx indices family, which are credit default swap indices, are in practice often used to gauge the bond market. How are CDS prices related to bonds prices ? And what ...
3
votes
0answers
64 views

Computing Value at Risk for portfolio in R

I know how to compute VaR with long positions using PerformanceAnalytics. What about a portfolio consisting in two equities A and B, 100 USD long positions in each, and 2 stock options for the same ...
1
vote
1answer
44 views

Z-Score calculation for a win-loss streak

I am trying to find the correlation between wins and losses by applying Z-Score according to formula attached below. I put them in an array by assigning 1 to wins and -1s to losers. I am trying to ...
1
vote
1answer
48 views

Cointegration tests: how do you accurately test the necessity of time trends in the Johansen and Engle-Granger Test?

Is there a correct and up to date procedure? I just run the equation in VEC form and test the significance of the time trends? What are the possible problems that I should be aware of?
0
votes
2answers
66 views

Why does the short rate in the Hull White model follow a normal distribution?

Consider Hull White model $dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$ when we solve the SDE above we have $r(t)=e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t})+\sigma e^{-\alpha ...
2
votes
2answers
96 views

Short volatility strategy using strangles

For a short volatility strategy using option strangles, is it better to target a fixed premium to earn? Or a fixed vega? Objective is to maximise the return/risk (sharpe) of the strategy. Any help ...
1
vote
0answers
20 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 $\overline \pi \in \mathbb R^{d+1}$ ...

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