# All Questions

477 views

### How to calculate the Sharpe ratio for market neutral strategies?

Suppose I am long one stock and short an index in a ratio effectively making market beta as zero and I close the position with some positive P&L. How should I calculate the return for the ...
236 views

### Portfolio Optimization using S&P Universes

Assuming a set portfolio optimization problem, if all optimization inputs are kept constant, what would you expect, in terms of results, if you run the same optimization using the S&P500 as ...
152 views

### What is wrong in this GBM simulation?

I am trying to generate a few samples of GBM using the following very simple MATLAB code: ...
2k views

### Can the duration of a bond be greater than Time to Maturity

In the case of a vanilla bond I know that the duration will be less than the time to maturity. But I am observing that for a non-vanilla bond, the duration is greater than time to maturity. Can ...
2k views

### Portfolio Optimization : Shrinkage of Covariance Matrix when data is available

It seems that shrinking the covariance matrix is especially useful if the number of individual stocks is greater than the number of data points. However is there any special gain if you're not ...
314 views

### Microstructure effects for a market maker? [closed]

When building a market maker that rests limits orders on both sides of the book, what microstructure effects should we be looking at to price those orders? I’m targeting liquid futures markets, and ...
928 views

### How to sum interest rate curves in QuantLib

C++ code taken from Bonds.cpp and slightly amended: ...
173 views

### Credit Rating vs Bond Yield

I am looking for some references on quantifying the dependence between credit rating and bond yield. I have some data (found some Bloomberg indices which give average yield based on credit rating), ...
886 views

### Replicating strategy in the Black-Scholes model

I have a two-asset Black-Scholes model for a financial market: $dB_t=B_t r dt$ $dS_t=S_t(\mu dt+\sigma dW_t)$ I introduce a European claim $\xi=max(K,S_T)$ with maturity $T$, for some fixed $K$. I ...
862 views

### Risk-free rate for ex-post evaluation of investment strategy

When evaluating the strategy ex-post using e.g. Sharpe ratio, what should one use as the risk-free rate? Let's suppose I am using a 1Y sample of weekly returns, sampled between 2012-01-01 and ...
339 views

### Comparison of Brownian Motion Expected Drawdown and simulated results

Can anyone tell me whether results as predicted by Brownian Motion for a given mean and std, match what you get by measuring actual drawdown from simulated results over a number of iterations?
5k views

### Why is short term implied volatility typically higher?

Why do short term implieds move more than long term?
768 views

### Yield of a risky bond

When working with risky bonds, i.e. corporate bonds, what is usually defined as the yield of such a bond? Is it the yield calculated as if the bond was riskless, or is it calculated by properly taking ...
386 views

### VaR backtesting with overlapping time intervals

Of course the issue here is dependence: can it be removed or accounted for (in independence tests too, which of course would be troublesome)? There's a lot of literature on regression in this setting, ...
3k views

### Calculating Portfolio Skewness & Kurtosis

I need to calculate the skewness and kurtosis of 2 asset portfolio, can someone please help me with the formulas and definition of terms? Thank you. I have been using the matrices method and I am not ...
995 views

### Which CEP platform is most popular for trading systems? [closed]

I heard that trading firms employ CEP platforms such as StreamBase, Marketcetera, JBoss Drools, and etc., to implement trading systems. I wonder which one is most popular and the recent trend of ...
65 views

### Calculating probability of options with normal/lognormal distribution: does time make a difference?

I'm trying to calculate the probability of a calendar spread resulting in a profit at expiration, when estimating it is modeled as a lognormal distribution, by getting: ...
59 views

### Problem with obtaining densities

For my research I need to obtain a series of densities, however, I am encountering some problems. The first problem is perhaps very simple, but the answer eludes me. Let's say I have an observation ...
56 views

### Sharpe ratio with leveraged ETFs

There has been a discussion about how leverage affects Sharpe Ratios, but not in the context of leveraged ETFs (such as 2x or 3x). I'm just wondering how leveraged ETFs, if at all, change the ...
117 views

### Greeks for binary option?

How to derive an analytic formula of greeks for binary option? We know a vanilla option can be constructed by an asset-or-nothing call and a cash-or-nothing call, does that help us? Wikipedia states ...
63 views

### How to optimize a portfolio using skewness?

I am trying to do portfolio optimization for 5 stocks taking into account skewness of the portfolio but I am unable to incorporate skewness to the mean variance model. Can anyone please help on how ...
115 views

### Fundamental CAPM questions

A couple questions about the CAPM model: If I only know the riskfree rate and expected market return, how do I solve for $\beta$ ? Given the stock's variance, how do I solve the percentage of it ...
81 views

### Verifying an identity of an equation for Black Scholes formula

I just started working on the Black Scholes formula with help of the book Financial option valuation by Higham. Apparently you are possible to derive the following function: ...
136 views

### Finding Arbitrage in two Puts

A European Put Option on a non-dividend paying stock with strike price 80 is currently priced at 8 and a put option on the same stock with strike price 90 is priced at 9. Is there an arbitrage ...
62 views

### How to find optimal noise covariance matrices Q & R

I am trying to use the discrete Kalman filter for forecasting and I wonder what is commonly considered as the optimal way of determining the measurement noise covariance constants (Q and R) for a ...
303 views

### 2-step estimation of DCC GARCH model in Python

Embedded in this thread are multiple questions. I'm currently im the process of implementing a DCC GARCH forecast model on quantopian (a python-powered trading platform). The two step consists of ...
179 views

### Forex trading scenarios - calculating units

I'm trying to build an automated forex trading system and I'm trying to understand how to calculate the number of units I should specify for each trade in different scenarios. Say for example I have ...
204 views

### probability question about brownian motion

Assume $W_{t}$ is a standard Brownian Motion, calculate the the probability that $W_{t}*W_{2t}$ is negative, i.e., $P(W_{t}*W_{2t}<0)$. I find it tricky to calculate the probability.Thank you.
126 views

### Using Black-Scholes to price a geometric average price call

Sorry if this is the wrong exchange for this question. It seems to be the most relevant, anyway. I'm trying to learn and understand the Black-Scholes framework, with a focus on the stochastic ...
171 views

### Calculating time value of an option

Can someone provide me with a robust way of calculating the future time value of an option or point in the direction? I have been reading a lot about the factors that affect it and about betas and ...
330 views

### What are pros and cons of mean absolute deviation portfolio optimization?

In this question a paper about mean absolute deviation portfolio optimization is mentioned and in the answer a spreadsheet with an implementation is attached. What is the use of this procedure? Does ...
70 views

533 views

### Calculate bond returns from yields

I have to construct and evaluate portfolio of bonds and stocks, namely I need to get return on portfolio, standard deviation and sharpe ratios. I have weekly data that contains stock prices, and I ...
227 views

### Interpolating probabilities of default

I have a table of cumulative probabilities of default of industrial bonds, in time and credit rating. It is similar to S&P whitepaper here. Basically, it looks like this (sample numbers): ...
820 views

### Risk-Free Rate determinant in CAPM

I have trouble understanding what type of maturity to use when calculating CAPM. My professor uses the 3-Month risk-free rate to ...
761 views

### How to calculate the volatility matrix with multiple stocks

calculating the volatility for a single stock is straightforward. However, I'm not sure whether my approach for calculating the volatility matrix for multiple stocks is correct: I assume a log-normal ...
573 views

### How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?

I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs $$(S_T f(S_T))^+$$ How do I express the stock dynamics using the ...
3k views

### What is the equation for Garman-Klass volatility?

I want to calculate realized/historical volatility for the underlying products of various options using the Garman-Klass estimator, but I can't see to find an equation, although I know it involves ...
596 views

### Need overlapping sample autocorrelation correction for calculating asset return correlations

I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, ...
345 views

### Recovery rate in a structured bond

I need to model the recovery rate of a structured bond whose expected cash flows, if the issuer remains solvent, will be very low. For instance, assume that I need to estimate the recovery amount of a ...
524 views

### annual excess returns from CAPM on monthly total returns

I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the ...
327 views

### Any one know how to implement the Heston and Rouwenhorst country-sector effects regression in R?

Heston and Rouwenhorst (1994) devised an empirical estimation strategy to decompose stock returns into three components: a pure industry effect, a pure country effect, and a world-factor return. ...
170 views

### Historical data on short rates

I would like to backtest a short-equity strategy. I'm looking for historical data on the availability of shares and cost to short certain stocks. Does anyone know of such data being available ...
342 views

### What is the Benefit of holding a short option?

i am new to corporate finance and ask myself why a investor is interested in being short on a Option? The only he can win is a premium but he can loose much more. I understand with being a short I can ...
627 views

### Reduce correlation in output of Minimum Variance Portfolio Optimization

After running a minimum variance portfolio optimization on a universe of ETF's I see the resulting portfolios tend to be composed of bond ETF or related treasuries/government ETFs. I suppose that ...
I'm looking at the SDE of Geometric brownian motion(*): $$d X(t) = \sigma X(t) d B(t) + \mu X(t) d t$$ (with analytic solution $X(t) = X(0) e^{(\mu - \sigma^2 / 2) t + \sigma B(t)}$) and the SDE of ...