# All Questions

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### Motivation for hedging volatility using VIX ETNs

i wondered what the motivation for professional investors could be to engage in VIX ETNs. Would they even think about trading this kind of product? (they normally should have access to VIX options, ...
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### Call and Put Prices Equal at Forward Price - Why?

Consider a European call and put with values $C_t$ and $P_t$, respectively, under the Black-Scholes model. By put-call parity, $$C_t - P_t = S_t - Ke^{-r(T-t)}$$ for expiration time $T$. Note if ...
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### Intraday Value at Risk approximations

We use full valuation of derivatives portfolios using scenarios from historical data. For simple contracts, this is relatively fast. For contracts requiring monte carlo simulation, this becomes ...
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### Lambda in RiskMetrics for fixed income

What is the default lambda proposed in RiskMetrics for fixed income?
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### algorithmic trading strategy based on HHT

I would like to create some trading strategy based on the HHT or at least to try to do some analysis using this method. I read the article wrote by Huang at al. and gained some underesting of the ...
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### Stochastic correlation arbitrage-free replication

I'm interested in possibility of stochastic correlation arbitrage-free replication (something VIX-style, mayby). To my knowledge, no such method exists. Could you provide some intro to the problem: ...
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### Behaviour of out of sample efficient frontier

I am comparing the efficient frontier of a set of portfolios that are in and out of sample. The first period is from 1991-01-03 until 1992-10-03 and the second one from 1992-10-03 until 1994-03-03. I ...
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### simulation and timestep

Suppose I have a stochastic process i.e. a Vasicek process with parameteres estimated with monthly (RW measure) data and want simulate the process using a daily timestep. Is this a good practice?
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### Scalar and vectorial sensitivities

In a recent discussion about the implementation of the calculation of derivative sensitivities, the notion 'scalar' and 'vectorial sensitivities' were used. I am not familiar with this notion and ...
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### Currency risk USD>EUR>EGP

Seeking input on hedging risk on USD to Euro with a 3rd component of payroll issued in Egyptian Pounds. We are a US corp invoicing a Germany entity in Euro with massive payroll being paid in Egyptian ...
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### Delta of an option derived from the binomial model

I have the following function $V=V(S,t)$, $V^- = V(vS,t+\delta t)$, $V^+ = V(uS, t +\delta t)$. The book proceeds to explain that if we use Taylor series expansion on the above we will confirm that ...
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### Selling two uncorrelated OTM options lowers the over all probability of profit?

I am trying to simulate shorting two uncorrelated put options, I wrote a python program and used monte carlo method to simulate the PnL on expiration: gist It seems the probability of profit is ...
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### VaR mapping fixed-for-floating swap

I came across a problem that asks what risk factors to map a 5 year semi annual settle fixed-for-floating swap to given it's just before the reset date. Since a FRN prices to par just before the reset ...
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### Portfolio value containing stocks and a bond

Consider: 1000 dollars invested in stock portfolio and a zero coupon bond. Investment period: 30 years Yearly retur for the stock portfolio: Rk = eµ+σZk , k is after year k Zk are normally ...
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### delta hedging strategy for OTM option

Wondering how you would think about the following thought experiment - suppose you sell an OTM call option and plan to implement a delta hedging strategy whereby if the price of the stock were to ...
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### Difficulty understanding put-call parity for currency options

I am self-studying for an actuarial exam on models for financial economics. I am having difficulty thinking about the put-call parity for currency options, specifically how use the notation. Here is ...
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### Interest Rate and Price of Assets

I have a very basic question about finance. I know that for an asset, the price is inversly related to the yield to maturity, or the interest rate. However, I have three ways of thinking about this ...
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### What can I use to measure of diversification?

I have to come up with a measure of diversification for trade (this can tie in closely to diversification as regards portfolios). Are there any well known measures of portfolio diversification?
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### Intuitive explanation of stochastic portfolio theory

Fernholz and Karatzas have published various papers about so called stochastic portfolio theory. Basically they say that the return to be expected from a portfolio on the long run is rather the ...
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### Where can I find information about the “Target Portfolio Pattern”?

It might not be known as a "pattern" but basically it's a way of (low-frequency) order management where a 'target portfolio' is built using notional amounts which is then compared against an 'actual ...
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### Testing a Monte Carlo simulation independently

I'm building a Monte Carlo option pricing model in Python/SciPy. I want to test the results produced by the Python code by building the model independently in Excel and then comparing the results. Off ...
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A lower coupon bond exhibits higher duration, which means higher price volatility with changing YTM. A lower coupon bond also exhibits higher convexity. However, with higher convexity, bond prices ...
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### Integrated Volatility in Diffusion Processes vs Volatility of Discrete Processes

In a Diffusion Process of the form $$dX_t = \mu(X_t)dt + \sigma(X_t)dW_t$$ the Integrated Volatility is defined as $$IV_t = \int_t^{t+1} \sigma^2(X_s)ds.$$ In this case, the Integrated Volatilty ...
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### “Spot rate is not observable” meaning

In Bruno Remillard's text, "Statistical Methods for Financial Engineering," he states the following on p 148 after giving the general form of a bond price $P(t,T)$ under Vasicek's model: Note that ...
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### Smoothing factor of Exponential Moving Average

I'm trying to implement an Exponential Moving Average indicator, but I'm sort of stuck on the smoothing factor. What I've come up with: $$\frac{1}{N}\sum\limits_{k=0}^N \alpha^{k} P_k$$ Where N is ...
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### Factors to Include in a Model to Predict Gross Profitability Persistence

I am trying to build a logistic model that predicts gross profitability persistence. Specifically at the start of every July, I assign stocks to one of five gross profitability groups (5 being the ...
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### Listed companies on NASDAQ

Where can I find a list of listed companies on NASDAQ from 2000 to 2014?
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### Difference between DV01 and IR DV01

What is the difference between DV01 and IR DV01? As far as I can see DV01 is at point on the yield curve and IR DV01 represents a parallel shift of the entire yield curve? My understanding is still ...
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### How to estimate variance-covariance matrix of assets with different length of historical data? [duplicate]

Consider you have 4 assets A, B, C and D, where Asset ...
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### Basic Metrics for Option Trading Limits

Imagine a trading house that trades options in a modest way, and is looking for simple but effective metrics over which trading option limits will be set. Some random thoughts: 1) VaR is not ideal, ...
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### High Beta 'Filter' for Minimum Variance Portfolios (MVP's) - Lower Risk/Improve Return?

I am busy conducting research in South Africa on the JSE. I am investigating several risk based portfolios with an emphasis on MVP/min vol. My process is as follows: Although the JSE has around 400 ...
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### Actual volatility or realized volatility under stochastic volatility model

Does stochastic volatility model requires realized volatility to estimate parameters ? If no then what is considered proxy for actual or realized volatility, if yes then what proxy is taken for ...
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### Relationship between risk-neutral probability and subjective probability

I recently came across a Paper by a paper of Rubinstein and Jackwerth (1997): http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.441.5214&rep=rep1&type=pdf where they assume that you ...
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### Does the fact that volatility is not constant imply existence of skew?

I had a question regarding the existence of the volatility skew. I've tried researching it a fair bit and I come across a few different explanations: 1. Market participants like buying downside puts ...
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### Least-Square Monte Carlo in multiple variable

The paper by Longstaff-Schwatz on Least Square Monte Carlo offers very little proof. The only proof they have given assumed the option can only be exercised at two different time point and the price ...
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### Determining the investment strategy

I have the following problem: Consider the 5 year investment strategy and given the yearly portfolio returns $S_{t+1}/S_t$ and dividends $D_{t+1}$ paid at $t+1$ which are modeled as: ...
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### Construction of bond portfolio represented by a CDS-Index

Markit publishes investable basket CDS indices. These are indices intended to track the credit risk of a basket of issuers (e.g. in the case of iTraxx Europe Series 24 these are 125 names) in an ...
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### Calculating expected shortfall

I'm trying to calculate the expected shortfall for the below scenario. I don't understand why the 1.04% probability of 0 bonds defaulting is used as a weight when calculating ES, since the binomial ...
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### How to get list of large intraday movers for that day?

Is there a source (preferably free :) that provides a list of large intraday (versus pre market) movers for the day you look? I don't mind getting the list on market close. I don't need historical ...
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### What is mathematically rigorous way to estimate floating swap cash flow in the future?

In vanilla swap, the FL payments is fixed on one date and paid on the next reset date. So the next payment is known. However, the payment after that is not known. What would be the best estimate of ...
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### Hwo to create a benchmark for a portfolio?

How does one create a benchmark for a portfolio? I realize if I were using strategic asset allocation, I could just look at the already existing benchmarks associated with the various asset classes ...
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### European option on a dividend paying stock, limits to arbitrage?

What is the price C of a European call option on a dividend paying stock? I believe it is: C = U. N(d1) - exp(-rt).K.N(d2) d1 = [ ln(U/K) + (r + v^2/2).t ]/[ v.sqrt(t) ] d2 = d1 - v.sqrt(t) U ...
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### What should be the sign of greek letter $\rho$?

I'm reading the book Risk Management and Shareholders Value in Banking by Resti & Sironi. I quote a paragraph from the book (Chapter 5, appendix): The derivative of an option’s value with ...
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### UK company data from Datastream: FBRIT+DEAKUK versus WSCOPEUK?

I'm working on a paper investigates the existence of a profitability premium in the UK starting in 1970. (Novy-Marx, 2013) The core methodology is creating Fama and French portfolios, testing the ...
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### Market returns below risk free rate

Let's say I'm using CAPM to estimate the cost of equity, so I need expected market returns for the calculations. The standard approach is simply to compute arithmetic mean of an index (or rather its ...
Let $\{X_i\}$ be an i.i.d. sample of $X$ with $E(X) = \mu$ and $Var(X) = \sigma^2$. We know a MC estimate converges to the true value almost surely by the SLLN. That is,  \bar{X}_n \to \mu, ...