4
votes
2answers
196 views

Itô diffusion processes in finance with unknown distribution at a terminal value

In several papers it is argued that for many Itô diffusion processes, $$dX_t = a(t,X_t)dt+b(t,X_t)dB_t,$$ in mathematical finance the distribution of $X_T$ for fixed $T>0$ is unknown, which makes ...
4
votes
0answers
486 views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed ...
1
vote
2answers
230 views

constructing best bid/ask from NASDAQ TotalView-ITCH data

anybody know how to construct a intraday stock price from NASDAQ TotalView-ITCH data? I would need to know the price in millisecond, so I would need two rows: timestamp (for every millisecond) and ...
2
votes
1answer
270 views

Pricing credit risky bonds

How do we price credit risky bonds? If I discount the cash flows using LIBOR/zero rates, it won't take the credit riskiness into account. So should I use a rate based on the issuer's credit spread? ...
1
vote
1answer
170 views

Basics about the scaling property of volatility

It is a usual practice to calculate realized volatility $\sigma$ using the square root of the usual variance estimator $\hat{{\sigma}²}$. This is done using the stock log returns (practitioners ...
3
votes
1answer
83 views

How accurately can the LIBOR market model price a floating note

I am considering some hedging strategy where portfolios of derivatives are built so that each portfolio is equivalent to a floating note, even if the instruments in the portfolio might be quite ...
1
vote
0answers
122 views

What is the right group of durations?

It seems that the group of durations commonly used in quantitative analyse is $\mathbf{R}$ but it seems to me that $\mathbf{R_+^*}$ could also be an interesting choice. While I am not aware of ...
6
votes
3answers
305 views

How to choose a risk-neutral measure when the market is incomplete?

I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model. Like most stochastic ...
1
vote
1answer
289 views

Black 76 for Options on Interest Rate Futures

This is my first time using Black76 to value options on IR futures and I have a question on $F$ and $K$. I understand the price for an IR future is usually quoted as $100 - r$. Do I use this price ...
2
votes
2answers
236 views

Shortcomings of generalized Brownian motion for asset price modelling

I'm simply interested on hearing some views on which shortcomings arise by using the (multidimensional) SDE $$dS(t)=S(t)\alpha(t,S(t))dt+S(t)\sigma(t,S(t))dW(t)$$ as a model for asset prices. I know ...
3
votes
0answers
107 views

Estimating risk aversion (power or exponential utility) from options prices

I came across this literature and it seems like there are a number of ways people do this. You can do it for an option on any underlying as long as you can create the risk-neutral p.d.f. If you agree ...
0
votes
0answers
42 views

Is this usage of “M” and commas for a cash flow statement correct? [closed]

I recently was confused by a cash flow chart produced by a company I invest in. Each bar represents a monthly cash flow, but the values are confusing. For example, "3,012 M" is used on the most ...
1
vote
2answers
647 views

HFT enhancements for FIX (Simple Binary Encoding) vs proprietary protocols performance and cost

I would like to know from those that have used FIX (with Simple Binary Encoding) for HFT compares with the current (proprietary) protocols in use that often vary per counterparty. Interested in ...
1
vote
1answer
458 views

Probability of a return from historical average and standard deviation

I have a question from a sample exam paper that I'm having some trouble figuring out. The question is: Bavarian Sausage stock has an average historical return of 16.3% and a standard deviation of ...
0
votes
1answer
157 views

download intra day data [duplicate]

I am trying to download intra day stock data for some 7000 symbols using google url : ...
4
votes
4answers
497 views

Deep bid ask orders

Why do I often see some very deep limit buys and limit sells in a limit book? For instance the bid-ask may be \$39.00-39.01 but I see some bids at \$20 or even \$10 and some ask at \$60 or even \$500. ...
3
votes
1answer
117 views

A basic question about market jargon

What does it mean by DBR 4s of Jan4, 2037? I know the Jan4, 2037 is the maturity. How about DBR and 4s?
1
vote
1answer
73 views

Get discount factors with limited knowledge?

I am facing the problem of just having this information: 6% coupon bond with 2.5 years to maturity, traded at a 100% clean price 4% coupon bond with 1.5 years to maturity, traded at a 98% clean price ...
2
votes
0answers
170 views

Potential pitfalls in the use of correlation

Background: The red line is an index, which goes from 0 to 100, measuring uncertainty in the markets. The dark blue line is a price index, which has a lower bound at 0, and virtually no upper bound. ...
1
vote
1answer
51 views

Why is the discount function non increasing if pure cash holdings are feasible?

I am struggeling with the question, for example lets take a swap with rate of 3.2 for one year and 3.6 for 2 years and Discount Factor 0.96899 for the first year and 0.93158 for the second year. ...
2
votes
0answers
84 views

Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
3
votes
2answers
211 views

Is price gaping the major risk that market maker has?

Suppose you are a market maker. So you put a limit price out and hope someone will cross bid/ask spread to take your limit. But there is risk that bad news could come out and market will gap. So ...
3
votes
1answer
128 views

Optimal Choice of exceeding time

Suppose you hold a share from company $Z$ whose vaue at time $t$ is $S_0+\sigma B_t$ where $B_t$ is Brownian Motion and $\sigma$ denotes some volatility. Now lets assume that company $Z$ may go ...
2
votes
2answers
122 views

Accrued Interest in CVA DVA

I'm implementing the CVA/DVA for some derivatives, which follows a Hull-White model (one factor). Once I have calibrated the model and I get the results with the simulation, a quite interesting ...
1
vote
1answer
366 views

Components of an index in a specific date

Objective: Get a list of all the companies that were ever part of an index (e.g.: FTSE100) in a given period of time (scale: years/decades). Method I have in mind: 1) Create an empty list k. 2) Get ...
2
votes
0answers
115 views

Can I trade the volume of a security or index?

Is it possible to trade a derivative product priced on the volume traded of some underlying security or index? Does such a derivative exist on any exchange traded markets? Or anywhere?
7
votes
2answers
259 views

Extrapolating implied volatilities to small time

Could anyone please direct me to literature or methods for extrapolating the implied volatility surface towards small expiry? I'm looking to price very short time to expiry binary options (e.g. 5 ...
6
votes
0answers
166 views

Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)

In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund ...
2
votes
1answer
2k views

Why do stocks with a negative beta return less than the risk free rate?

Let's say we have two stocks, Stock A and Stock B. Both of them have the same standard deviation $\sigma$, and therefore have the same risk. The only difference is that Stock A has a perfect ...
2
votes
1answer
245 views

Closed form european option prices for a variance gamma process with a randomly distributed drift, volatility, and variance rate

Does an option pricing model with a closed form European option price exist that takes into account randomly distributed drift, volatility, and variance rate? I prefer a modification to the variance ...
1
vote
2answers
611 views

Finding Probabilities Using The Binomial Model

I was not able to find a similar question when searching, but if I've missed one please feel free to point me to it. Unfortunately the closest example in the textbook was not terribly helpful either. ...
0
votes
1answer
104 views

Why does the SMA and EMA appear to be relative to the timeframe?

Why does the value of the SMA and EMA for the current time appear to change when I change my timescale. I'm using ActiveTrader by Fidelity, but I'm hoping there's an general phenomenon so that someone ...
0
votes
1answer
511 views

Question about weighted midpoint formula

The answers from these two replies seem to contradict each other. The first numerator is bidSize*bidPrice + askSize*askPrice but the second is bidSize*askPrice + askSize*bidPrice. Price functions ...
3
votes
2answers
957 views

How do I calculate Sharpe ratio from P&L?

Say I have a market-making strategy that trades intraday. I start with a flat position and finish flat too. I end up with a daily P&L $p_{today}$. Over a year of trading I get $\vec{p} = ...
5
votes
2answers
800 views

What are common methods for modeling intraday trading volume?

What are the most common ways to model intraday trading volume, particularly for futures contracts? There are obviously a number of seasonal-type factors, like roll, economic news releases, time of ...
5
votes
5answers
1k views

Library for interactive financial charts

For my recent project I am looking to build a software capable of visualizing financial charts in a dynamically and interactive matter. The workflow is as follows: I gather data from my data ...
0
votes
1answer
103 views

How to convert trasaction log to bid-ask ticks

I have data from exchange in transaction log format that indicating: price volume timestamp That element indicating that timestamp transaction was made on price of size volume. My question is how ...
1
vote
0answers
53 views

Binary options and European option is similar?

European options and binary (digital) options is similar? How apply the Black & Scholes formula on binary option?
0
votes
0answers
58 views

I want to optimize an equity portfolio for the four central moments can anyone help me with the problem formulation

Basically i am confused as to which formula to use for portfolio skew and kurtosis and how to use the same in the optimization problem. I would also like to know the options available regarding the ...
3
votes
1answer
155 views

Cross validation of a garch model

Suppose I divide a time series into 10 sequential time windows, where each window contains 1000 data points. I want to do test 5 different garch models using cross validation. So for each model, I ...
1
vote
1answer
202 views

Portfolio risk decreased by increasing share of riskiest asset?

In Parker's The Economics of Entrepreneurship he explains how certain theoretical models predict seemingly bizzare things (e.g. people becoming more risk-averse resulting in them taking riskier jobs) ...
1
vote
3answers
785 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 ...
1
vote
1answer
403 views

How to explain the path dependency in binomial tree model to price options?

I'm new to quantitative finance, so I'm confused with the so-called path dependency in binomial tree model. Originally I thought the path dependency exists because in binomial tree model, we will ...
3
votes
0answers
78 views

Dividend Index Futures

My question is dealing with the proportionality between Dividend Index Futures prices and Index prices. Indeed, we in the past we used to do a simple regression between these variables and use the ...
3
votes
1answer
190 views

How to synthesize a futures spread option?

Is it possible to synthesize a futures spread option using only the options on the spread's underlyings? If so, how? If not, is there another way? As an example, please show me how to synthesize ...
1
vote
1answer
107 views

Analysing FX Data

When analysing currencies, the data always comes in pairs so it is hard to normalise a multivariate time series of data e.g. if I have GBPvsUSD, EURvsUSD and CADvsUSD then changes in the US economy ...
1
vote
1answer
400 views

what's the difference between Peak-Load pricing and price discrimination?

i just don't get it. Peak-load pricing wiki page gives example: in public goods such as public urban transportation, where day demand (peak period) is usually much higher than night demand ...
2
votes
1answer
327 views

Interpretation of cross-correlation matrix when one sample distribution is not normal

I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a ...
3
votes
1answer
217 views

Risk and Reward in practice

My question is a bit philosophical. As a risk manager I often have to tell portfolio managers to reduce risk (e.g. due to VaR limits or exposure limits). Then usually the discussion arises that if ...
1
vote
2answers
124 views

moody's credit ratings for senior unsecured bonds

Can 2 senior unsecured bonds from the same obligor have different moody's credit ratings? Or do they both have to have the same rating because they are in the same capital structure? Thanks

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