# All Questions

32 views

### How exactly are correlated defaults used/analyzed?

I've read a lot about correlate defaults but I can't seem to understand how they're used practically in a portfolio theory setting. Suppose I have two (?) companies, X and Y, and historic default ...
42 views

### Pricing of a Forward-start option in a Black-Scholes framework

I have read the pricing procedure of a Forward-start option in a Black-Scholes world in Musiela-Rutkowski, but I don't find their proof clear (pp. 195-6). Let me summarize their argument: Consider ...
49 views

### Pricing of convertible bonds

I'm trying to evaluate a convertible bond using the structural approach : the price of convertible bond is an option (call) on the firm value. We suppose that the firm value is equal to the sum of the ...
22 views

### How to calculate implied borrow rates from option chain information?

I am given information about a ticker with following options data: stock price, date, expiration date, strike price, call / put indicator, style (American or European), ask price, bid price, mean ...
83 views

### Is this a poorly written example, or could volatility in fact be negative?

I'm self-studying and I encountered the following example. It seems to suggest that volatility is negative in this example. I was under the impression that volatility can never be negative, both from ...
23 views

### Comparing Hedging Strategies

Say I am an American issuer, and I've issued some bond denominated in CAD. I've hedged the coupon by entering into an FX USD/CAD fixed for floating swap and I receive the fixed leg and pay floating, ...
28 views

### Modelling nominal interest rates

What is the best model for nominal interest rates? ARMA, VAR, VEC, FAVAR, etc? I am a R user, so please advise me the most convenient R package to use as well. I intend to model US nominal interest ...
6 views

### Stationarity in first differences of CoVar

I'm currently in the middle of my master thesis and I can't get my head around a specific problem. I have the following process: where the $\Delta CoVar$ measure is calculated in two ways. First, ...
33 views

### Robust standard errors in GARCH modelling (rugarch)

I am currently conducting some GARCH modelling and I am wondering about the robust standard errors, which I can obtain from ugarchfit() in ...
15 views

### I have a test coming up and I could really use an explanation to this example problem

This test is on CAPM and portfolio optimization Suppose that investors A and B can invest in two risky assets and a riskless asset. The first risky asset has an expected annual return of 10%. The ...
34 views

### Finding the corresponding Strike

I have been asked the following question recently, and I was unable to find the solution (I have the feeling that either a data is missing or I misunderstand a notion). Here is the following question :...
18 views

### Historic and future (next) round of machine readable dividend info

Is there a source of historic dividend dates, ex-dividend dates and dividend values? Also, the next dividend date / ex-dividend date. Ideally in a machine readable form? The publically available APIs ...
38 views

### Relation between mean and variance of a portfolio in modern portfolio theory:

I hope that this is the right place to ask my question! Let a market with $N\ge1$ risky assets and denote by $(R_i,i=1,\cdots, N)$ their returns and $R$ the vector of these $N$ returns. In addition, ...
43 views

### Triangular arbitrage formula error

I am struggling with a formula for calculating the above. I have been using the following example: https://www.youtube.com/watch?v=lKu2LAgEcpU ...
61 views

### Swaption pricing

I am trying to understand the pricing of various types of swaptions. Suppose I have a swap that starts in 3 months time. How would I go about pricing a swaption on this swap in the following cases: ...
42 views

### Volatility of CDS

I have calibrated a stochastic intensity CIR model to CDS data. The model reads $d \lambda_t = \kappa(\theta-\lambda_t)dt+\sigma \sqrt{\lambda_t} dW_t$ When calibrating the parameters I get ...
55 views

### Black-Scholes PDE boundary condition question regarding limits

I'm working with the Black-Scholes PDE and I'm testing some things out by taking an initial condition for it as $\sin(S/50)$, where $S$ is the spot price. My issue comes with attempting to find the ...
54 views

### What is the probability of defaulting in year 2?

I was asked this question the other day, but it's been years since I've done this work. If the probability of a company to default in a year is $8\%$, what is the probability that it will default in ...
44 views

### Calculation of option Greek (sensitiviety) theta via finite difference

I am able to get good approximations for delta, gamma, and rho via finite difference method, but not theta. I believe my issue is the value of h. Theta is basically the difference between the price ...
49 views

### Questions on Kelly criterion

I am new to asset allocation problems and have some concerns regarding the derivation of the continuous-time Kelly criterion (i.e. not the original version destined to discrete sports betting/Casino). ...
49 views

### Is Poisson Disk Sampling an alternative to crude Monte Carlo and QMC?

I recently stumbled over Poisson Disk Sampling (here and the meditative version). I wonder if it is an alternative to crude or quasi Monte Carlo for very high dimensional integrals. It is not ...
14 views

### Book Value of Equity

I want to calculate Book equity to market equity ratio. Market equity can be calulated by multiplying number of shares outstanding with price of share. Now as far as Book values of equity is ...
74 views

### Interpretation of Risk Premium for Schwartz one-factor model

I have to deal with this one-factor model: \begin{equation*} \begin{cases} dS_t = \alpha \bigl(\mu - \log(S_t) \bigr)S_t \, dt + \sigma S_{t} \, dW_t \, , t \geq 0,\\ S|_{t=0} = S_0 > 0, \end{...
47 views

### Code for quasi-Gaussian model (Cheyette model)

I'm looking into the quasi-Gaussian model with linear local volatility as explained by Andersen and Piterbarg (Interest Rate Modeling, Volume 2). I'm trying to calibrate this model and implement it. I ...
127 views

### What is the probability that a OU process hits an upper barrier U before a lower barrier L?

What is the probability that the arithmetic OU process $dx_t= \theta(\mu-x_t)dt+\sigma dW_t$ hits barrier $U$ before hitting barrier $L$ when $L<x_0<U$ ?
49 views

### Is there a better, more rigorous explanation for why this partial derivative is 0 using Ito's Lemma?

I encountered the following slide in a lecture on Ito's Lemma. The lecturer explained that $$\frac{\partial V}{\partial t} = 0$$ because the first two derivatives on the slide already took into ...
36 views

### How to fit a skew normal/t copula to data

I want to use either the skew normal copula or the skew t copula with a time-varying correlation matrix. But so far I haven't found any way to implement this either in R or Matlab. Would anyone be ...
243 views

### Pricing variance swaps using Monte Carlo

For pricing variance swaps there is the well-known formula as sum of OTM options weighted by the inverse of the squared strike (see e.g. here). Would it also be valid to derive the local-volatility ...
39 views

### Evaluating trading strategies by the skewness of returns

How to deal with skewness of returns when evaluating different trading strategies? More specifically, I'm back testing different strategies to be implemented as an automated black box strategy. While ...
112 views

### How does one calibrate a stochastic volatility model?

I will try to use SABR Model to price call options in FX market. What does it mean to calibrate the model? As far as my understanding of the Wikipedia article goes, it means to estimate the parameters....
25 views

### Model free estimation of convexity in Eurodollar IR Futures

Can someone please share some thoughts on how to estimate convexity for a given Eurodollar interest rate future contract, without assuming any underlying model for rates i.e. LMM, Hull-White etc. I ...
43 views

### Monte Carlo Accuracy - Antithetic Variate Method

I'm self studying for an actuarial exam and I am curious about a property of the antithetic variate method for increasing the Monte Carlo price accuracy (i.e. For every random draw of $z$, also ...
116 views

### Heston Model Integration Oscillations

Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
34 views

### Variance of a portfolio based on log-returns

Modern Portfolio Theory Optimization Problem is based on expected linear returns and covariances of linear returns. That's said, variance and expected return of a portfolio based on linear returns r ...
60 views

### How did the algo trading firms perform during Brexit? [closed]

Brexit saw a lot of volatility in the market. Pound crashed to record lows and the market still seems recovering. Manual traders lost a lot of money. How did the Algos performed?
35 views

### Is there a formula for present value of a growing annuity with yearly payment growth and monthly payments? [closed]

I have seen formulas that have cracked the future value of growing annuity where there are monthly payments and yearly growth rates. But given a future value, is it possible to derive the present ...
22 views

### Sustainability of a FOREX buy/sell signal service driven by ANN output

Sirs, This question may be off topic -- I'm not insulted if it gets labeled as such. Meta won't let me ask a question until I've actually posted a question, it seems. My question goes like this: ...
86 views

### Brownian motion simulation - scaling issue

I'm trying to simulate some BM for 500 observations. I got correlated increments as I needed and they are not exactly N(0,1), so I standardize them (x-mean(x))/sd(x). But then the resulting Brownian ...
40 views

### What is a maximal curve?

I came across the term maximals in this article. Can someone explain what a maximal curve is and how you would calculate it?
11 views

### Reference for risk conributions of fund-of-funds relative to blended benchmarks

I am looking for a reference for the attribution of relative risk of a fund-of-fund compared to a blended benchmark. I am aware of decomposition into asset allocation decisions and stock selection ...
35 views

### Merton portfolio allocation problem proportions/weights >1 or <0?

In the classical Merton portfolio problem, lets assume: $$dX_t \, = \, \frac{\pi_t X_t}{S_t} S_t(\mu dt +\sigma dW_t) = \pi_t X_t (\mu dt +\sigma dW_t)$$ ie: zero interest rates for simplicity. ...
91 views

### What is the pseudo code for a pairs trading strategy?

I am trying to learn about pairs trading strategy. I know that we have to long and short cointegrated assests simultaneously. But I still have some confusion in how the strategy works. I wrote the ...
64 views

### Black scholes model for down and out European call option using Monte Carlo

I tried to implement Matlab program computing the price of the European down and out call option using Monte Carlo and Euler discretization scheme. I have initial price S0=50, strike K=50, barrier ...
20 views

### Need a reliable source of futures expiration dates

I am trying to determine (programmatically) what the current front month contract for a given futures symbol is. I would guess that all futures contracts expire on a standard time relative to their ...
26 views

### Construction of momentum portfolio using STATA

I am working on Fama and French five factor asset pricing model in context of Asian markets. I have constructed market beta, size, value , investment and profitability factors. I would like to extend ...
53 views

### Regression coefficient and basic trading strategy

This question might be very basic but still I couldn't really find a satisfying answer anywhere. I want to analyse the effect of a repeated event (data release) on the price of a specific asset (I ...
43 views

### Probability that return exceeds a certain level before a certain time (Black-Scholes)

I am self studying for an actuarial exam on financial economics. I encountered the following problem and solution. It seems to me that the author intended to mean what is the probability that the ...
42 views

### One factor short rate model

I know one factor model assumes that one stochastic factor can explain the future evolution of all interest rates. Can someone tell me what is the one factor in economic meaning in the one-factor ...