# All Questions

143 views

### Is there a better way to price options than with historical volatility?

I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. ...
47 views

### Cause of long term inflation in the United States [closed]

Does the US government have a policy of printing money? If so what is this number called, who decides what it is, and where can I find it? If not what is the cause of our long term inflation? (I'm ...
216 views

### Black Scholes - how to calculate delta with a vol skew

I am trying to calculate the delta of an option at different strike prices where the underlying has a pronounced implied volatility skew in order to correctly hedge an options strategy. Researching ...
69 views

### Cobb - Douglas Production Function

let's say that we have complete data on the sample of companies about their capital (K), labor (L) and materials used in the production (M) and the total output of each company. Let's have ...
190 views

### What is a canonical book or article to learn pair trading?

Can someone suggest a resource with a clean cut explanation of pair trading?
73 views

### Binary option expression

Given r=0, σ(K)=const Binary=lim┬(ε→0)⁡〖((C(K,σ(K))-C(K+ε,σ(K+ε))))/ε〗 What is the analytical expression for the binary option value? σ(K)=const Therefore, Binary=lim┬(ε→0)⁡〖((C(K)-C(K+ε)))/ε〗 ...
13 views

It doesn't seem yahoo finance and google finance supports download of historical exchange rates. Also, where could we get more accurate exchange rate tick data? Can we get this from open Bloomberg ...
143 views

### Normalization of Market Data in Time Series Correlation

Suppose we have 2 time series of market data, one for each security and we want to correlate between these 2 securities. My question is How do we handle gaps of missing data in the time series? ...
134 views

### Kolmogorov-Smirnov test for Generalized Pareto Distribution

I've fitted my data to a generalized pareto distribution as to model the returns in the tails more accurately. The interior is fitted with kernel distributions. I would like to now test whether the ...
32 views

### How to prove following order?

Consider a consol bond, i.e. a bond which will forever pay one unit of cash at $t = 1, 2, . . ..$ Suppose that the market yield $y$ is constant for all maturities. (a) Compute the price, at $t = 0$, ...
12 views

### Distribution of the differences of the inverse of the integral of a Gaussian Distribution

I have a time series, $P$, undergoing geometric Brownian motion, which varies between $1$ and $1000$. I difference it $P(t) - P(t-1)$ and can see the differences are distributed according to a ...
61 views

### I want to Derive $P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$

Derive the pricing formula $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$$directly, by constructing a self-financing portfolio which replicates the cash flow of the floating rate bond. ...
55 views

### I want to prove Determine the coupon rate $r$, such that the price of the bond, at $T_0$, equals its face value

Consider a coupon bond, starting at $T_{0}$ , with face value $K$, coupon payments at $T_1, . . . , T_n$ and a fixed coupon rate $r$. Determine the coupon rate $r$, such that the price of the bond, at ...
144 views

### UST Yield Curve Forecasting - Bond Structure Testing

I have a project in mind that I am working on, but have little idea where to start. I am a relative newcomer to python (about 1 years exp.) and limited knowledge of quant finance. What I would like ...
372 views

### Find the order of an ARMA model (q & p )

I fit an ARMA model in Matlab and before I calculate the predicted value with the prediction error I set the order $(p,q)$ to some random value. But how can I determine the number of AR (p) and MA ...
163 views

### IR Yield Curve and Fixing Dates

Consider two FRAs. 3x6 , Effective 3 months from now, terminates in 6 months. The floating leg payer pays 3-month LIBOR. Fixing date for LIBOR 40 business days. To price this at par, the fixed leg ...
245 views

### Key Rate Duration for MBSs greater than Key Rate Tenor

Key Rate Durations (KRD) are essentially some fixed income instrument's price sensitivity to a non-parallel shift in interest rates (i.e., a shift at the "Key" Rate). For example, a 10-year bond's ...
62 views

### Model-independent dynamic portfolio optimization techniques

For a problem where we need to optimize the portfolio based on the data, going for Markowitz MPT has the following advantage: we only have to estimate mean and covariance to find optimal weights. I'd ...
132 views

### Implied volatility and pricing of vanilla options

As far as I understood, implied volatility (IV) is a lucky parametrization of the vanilla option's price. That is, instead of deciding how much the call worth now, you can decide on its IV and put ...
68 views

### An Alphabet Effect?

While I prepared some quick and lazy charts picking just the first 10 symbols out of the SP500 for this other question I observed, that the first 10 symbols (figure 1) actually outperformed the larger ...
47 views

### What is the probability distribution of the changes in $\Delta$?

What are the odds that a 10 delta option will become a 30 delta option in "N" number of days? Is that calculation possible? For instance, I want to know the probability with which my 56 day, 10 ...
691 views

### Par Yield Curves vs Zero Curves

Does it make sense to look at par yield curve for German bonds in the current environment? Because low rates mean that a lot of bonds are trading above much above par (even around 150!). I would ...
141 views

### C# - Using Black Scholes Newton returns NaN occasionally

First caveat: I'm a programmer doing this for a client, and my knowledge of options probably has holes in it. So be a little forgiving here. =) The Issue: When I run Black Scholes Newton against ...
99 views

### Stochastic Differential

Let $W_t$ be a Wiener process. It is clear to me that $dW_t$ is of size $\sqrt{dt}$. This can be seen because $$\mathrm{Var}(W_{t+\Delta} - W_{t})=\Delta.$$ But am I allowed to actually write ...
22 views

### Index tracker and inflation

I'm trying to get my head around how inflation really affects index trackers. I've been looking at this question, but somehow misses the point I want (How To Account For Inflation Over Historical ...
21 views

In various financial models such as CAPM, Black Scholes, one assumes the returns are adjusted for dividends. As I understand it, the share price often (in a relative sense) increases a bit before the ...
24 views

### simple question on DSCR

What is the DSCR for a 2.5 million property generating a 7.5% before tax annual return on equity with a 1.5 million ten year interest-only first mortgage at a 5% annual interest rate? a) 2.00 b) ...
55 views

### risk report factor exposures calculations

I am looking at a risk report which I have inherited. There are 5 lines of code that I want to make sure I understand. The risk report breaks down the exposures, contribution to variance and marginal ...
89 views

### How to compute daily compounded backtest returns closer to real-world results?

I often run quick tests of trading strategies in my analytics suites by: multiplying a vector of signal (lagged, {-1,0,1}) with a time series of daily percentage returns doing a cumulative product ...
83 views

### Best sources for worldwide balance sheet data?

I’m interested in databases with quarterly balance sheet data of the financial sector. I’m aware of the following datasets: -Compustat -Compustat Global -Bankscope Can someone point out other ...
96 views

### Index creation from multiple time-series and variable weights

I am trying to compose one index out of several (three) indices with variable weights, 50%, 25% and 25%. After normalizing and calculating the log returns, what would be the best way to create the ...
105 views

### Black scholes text book

I am looking for an easy and well presented introduction to Black-Scholes theory and stochastic calculus aimed at undergraduate mathematics students. Please can you recommend a book? How about Paul ...
187 views

### Quadratic exponential method (by Andersen) in Heston model

I am having trouble understanding the reasons that led Andersen to define his QE scheme to efficiently simulate Heston Stochastic volatility model (you may check the celebrated scheme here). The ...
23 views

### Historical list of Primary Dealers in Europe

I would be interested in a list of all the banks and financial institutions that have been Primary Dealers in the European Union from the 1980s until today. For a current list you can check this pdf ...
124 views

### LMM. Calibration to swaptions by Brigo and Morini. Volatility of swaption that matures at T=0

I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini. I ...
199 views

### In bond pricing, is negative convexity better than positive convexity?

Say that I have two bonds and one of them has positive convexity and the other negative. Which one is better (assuming that you only care about convexity)? I understand that high convexity is ...
81 views

### Optimization metric that takes into account number of trades vs expectancy

In optimizing my automated trading system I find that certain combinations while increasing the expectancy: ...
154 views

### Why is the rate of change of a stock price proportional to the stock price?

When deriving the Black Scholes equation, it is usually stated "we assume the change in the stock price is": $dS=\mu S(t) dt +$random term My question is why is the change in the stock price always ...
100 views

### Information on books about mathematical finance

In the past at my school the subject of "Mathematics of Derivative securities" has been taught out of two books. "Quantitative Finance" by T. Wake Epps and "Options, Futures and Other Derivatives" by ...
121 views

### Logging FIX Messages

I need to persist every single FIX message received or sent by my order gateway for auditing purposes, however it takes more than 1 millisecond to write the bytes to disk. I tried to write in chunks ...
86 views

### Data point discrepancy between Google Finance and Yahoo Finance

I have been comparing the historical stock data I am getting from Google Finance and Yahoo Finance. I am only getting six datapoints per day (date, open, high, low, close, volume). I have downloaded ...
88 views

### Why is OU process stationary?

The mean and variance of OU process have time dependence (exponentially decay in time). So they are not constant in time. How can it to be stationary?
26 views

### Advancers / Decliners data source

What is the best source for this data? I am trying to compute http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:mcclellan_summation in Python.
336 views

### A model to stochastic hazard rate and CDS spread term structure

I'm interested in the term structure of CDS spread. It's known that the Market CDS rate (fair CDS spread or T-maturity spread) of a CDS contract initiated at $s$, maturity $T$ and recovery function ...
162 views

### Provide a bond pricing differential equation and invoke Feynman-Kac

Grateful for any assistance. Consider the process: $dZ=r(t)Z\,dt$ , where $r(t)$ is stochastic and $Z=Z(r,t;T)$ is a zero coupon bond. Provide a bond pricing differential equation and invoke ...
35 views

### American put on a foreign currency

I know that For an American-style put option, early exercise is a optimal for deep in-the-money options. In this case, it may make sense to exercise the option early in order to obtain the profit ...
100 views

### Mean Variance Analysis: what does the solution of the following exercise tells me?

I'm new in here and I hope this is the right board to ask this question. I'm at second year of university and in the Informatics II course the lecturer made us solve the following mean variance ...
49 views

### Dummy variable and negative estimation in GARCH (1.1)

I am trying to use GARCH model for my research. However, when I am running them, I see negative value for alpha and beta. How I can restrict them so that they do not provide me any negative value. Is ...
96 views

### Combine together different strategies in one portfolio [closed]

Hi I have generate equity of my strategies which invest in commodities and currencies at daily interval. What the best method to combine together all strategies in one portfolio? I want to make the ...
106 views

### Automatic trading strategies - what are benchmarks for PL on serious backtesting?

There are plenty books and sites which offer automatic trading strategies (robots) and claim they are very profitable. On the other hand many people do not believe in such things, saying that: if ...

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