2
votes
2answers
82 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: $\log(\frac{SN'(d_1)}{e^{-...
2
votes
2answers
117 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 ...
2
votes
0answers
334 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. ...
2
votes
1answer
76 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 ...
2
votes
1answer
352 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 ...
2
votes
1answer
632 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 ...
2
votes
2answers
181 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 ...
2
votes
2answers
797 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 ...
2
votes
2answers
208 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.
2
votes
2answers
132 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 ...
2
votes
3answers
99 views

demonstrate that a Square-root process is Non-central Chi-squared distributed

how can i prove that the value at some future time $t'$, $x_{t'}$, of the Square-root process at current time $t$, $x_t$, is Chi-squared distributed? $dx_t = k(\theta - x_t)dt + \beta \sqrt{x_t}dz_t$ ...
2
votes
2answers
174 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 ...
2
votes
3answers
351 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 ...
2
votes
1answer
70 views

What is the filtration described?

What is the filtration $(\mathfrak{F}_t)$ encircled below? Is it $(\mathfrak{F}_t) = (\sigma(W_t)) = (\sigma(\tilde{W_t})), t \in [0,T]$? Or is it $(\mathfrak{F}_t) = (\sigma(\hat{W_t})), t \in [0,T]...
2
votes
1answer
69 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: ...
2
votes
1answer
332 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 ...
2
votes
1answer
396 views

What is Margin of Conservatism

In modelling loss given default,(LGD), we often encounter the term Margin of Conservatism. What is it in layman's terms? I am not able to find a wikipedia page on this.
2
votes
3answers
589 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 ...
2
votes
3answers
250 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): ...
2
votes
2answers
60 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 ...
2
votes
1answer
58 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 ...
2
votes
1answer
831 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 ...
2
votes
1answer
230 views

CIR model: is the short rate really non-central $\chi^2$ distributed?

Probably simple question. Consider the CIR (1985) model for interest rates $$ dr = k(\theta - r)dt + \sigma \sqrt{r}dz $$ Then it is known in closed form the conditional pdf $f(r(s),s|r(t),t)$ ($s \...
1
vote
1answer
68 views

Prove $E_{\mathbb Q}[X_t | \mathscr F_u] = X_u$ given $Y_t$ is a martingale

We are given a filtered probability space $(\Omega, \mathscr{F}, \{\mathscr{F}_t\}_{t \in [0,T]}, \mathbb{P})$, where $\{\mathscr{F}_t\}_{t \in [0,T]}$ is the filtration generated by standard $\mathbb ...
1
vote
2answers
193 views

Geometric brownian motion vs. Ornstein Uhlenbeck

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 ...
1
vote
1answer
186 views

Long Forward Rate Agreement, short Eurodollar futures

For this question If you are long a FRA and short a ED future with the same fixing dates, do you have positive convexity or negative convexity? The answer is positive convexity, because a ...
1
vote
2answers
593 views

garchOxFit in R

Could someone please help me with trying to get the Ox interface to work in R. I followed the steps outlined in this paper (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1752095), but I get the ...
1
vote
0answers
67 views

Portfolio Optimization with equal weight for assets selected

I have a data frame of bets, with 1 being a win and 0 being a loss. These bets are correlated so I cannot just pick the highest winning percentage. Goal is to get 2 optimizations, 1 for max sharpe ...
1
vote
0answers
113 views

Does it make sense to apply complicated mathematics to calculate with precision when the margin of error is +/-10%? [closed]

This is more of a philosophical question than general question. Quantitative finance applies highly complicated mathematics and has attracted very smart people to this field lately given the high pay ...
1
vote
3answers
161 views

Greeks of self-financing portfolio

I would like to learn more about the Greeks of portfolios of options: In textbooks and websites, I commonly encounter the unqualified claim that "The Greek measure of a portfolio is the sum of the ...
1
vote
1answer
212 views

FX Rate dynamics

Let's suppose USD/EUR price in USD follows a GBM with $$ dS_t = rS_tdt + \sigma S_tdW_t $$ What process does EUR/USD follow in EUR?
1
vote
2answers
2k views

Is there a formula for future value of a growing annuity with yearly payment growth and monthly payments?

My example is saving for college: assume a start of 0 balance deposits of 200 made monthly, every year they increase by (g) 2% to account for salary increases, first deposit made at the end of the ...
1
vote
2answers
269 views

BInary Option implied volaltility

How is implied vol calculated if the quoted prices are out of the range for any possible volatility? E.g. Current quote on CBOE for options expiring on Aug 16, 2014 ...
1
vote
2answers
133 views

How To Account For Inflation Over Historical Data

I believe inflation is greatly affecting my sample data, even when using percent-changes for movements. I have read this post, which recommends the formula ((Current-Base Year CPI) * Price) / (...
1
vote
1answer
1k views

Par and Zero Coupon Yield Curves

The government par yield curve shows a marginally lower yield than the Government zero coupon curve. What is the reason for this in general.
1
vote
0answers
475 views

Oscillatory time-series forecasting

I was wondering if this mean(160)-reverting/oscillatory time series "SUM" can be considered chaotic & forecastable to some extend short-term? http://sg.myfreepost.com/sgTOTO_analysispower.php?...
1
vote
1answer
85 views

Prove uniqueness, and prove $Y_t$ is a martingale by considering $dZ_t$ and $dL_t$

Suppose we are given a filtered probability space $(\Omega, \mathscr{F}, \{\mathscr{F}_t\}_{t \in [0,T]}, \mathbb{P})$, where $\{\mathscr{F}_t\}_{t \in [0,T]}$ is the filtration generated by standard $...
1
vote
1answer
56 views

Compute moments of aggregate loss using Monte Carlo

Spin-off from here. Richard referred to me an article that tells me how to get parameters of a translated gamma distribution to which I should consider fitting simulated aggregated loss values. The ...
1
vote
2answers
113 views

Annual dividend yield using option prices

If I have only strike, call and put prices for European options, how do I work towards computing the continuous dividend yield?
1
vote
1answer
1k views

IbPy download historical price data

How can i download historical price data from interactive brokers using IbPy and python?
1
vote
1answer
69 views

Delta derivation from the expectation

I'm trying to understand the following transformation leading to Delta $\frac{dC}{dx} = e^{-r\tau} \mathbb{E}[ \frac{\partial}{\partial x}\text{max}(xY-K,0)] = e^{-r\tau} \mathbb{E}[Y \textbf{1}(xY&...
1
vote
1answer
81 views

On a source for a mean-variance portfolio optimization result

In the context of a mean_variance framework consider an optimizing investor who chooses at time $T$ portfolio weights $w$ so as to maximize the quadratic objective function: $$U(w) = E[R_p] - \frac{\...
1
vote
2answers
119 views

Why does the short rate in the Hull White model follow a normal distribution?

Consider Hull White model $dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$ when we solve the SDE above we have $r(t)=e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t})+\sigma e^{-\alpha t}\...
1
vote
1answer
77 views

Implied volatility as price transform

Implied volatility The way I understand it, traders often think of implied volatility as a transformed price. So in a way, the Black Scholes model is considered a 'model-free' blackbox that takes a ...
1
vote
1answer
148 views

How to compute the volatility for the Merton's Model for Private firm?

After one day of research i did not figured how to compute the input volatility for PRIVATE COMPANY in order to calculate the PD. My goal is to compute the PD of each of my company in my portfolio, ...
1
vote
1answer
208 views

Understanding how to calculate Accrued Interest of Bonds

When calculating the accrued Interest of Treasury Bonds, how does one set the settlement date? And, is it possible for certain bonds that there are no coupon payments before the settlement date and ...
1
vote
1answer
38 views

Correct Theoretical Discount Factors from Nelson-Siegel-Svensson?

I am calculating the theoretical discount factors associated with a bond that has 30 months to maturity from today with the parameters below obtained from here using the Nelson-Siegel-Svensson Model. ...
1
vote
1answer
107 views

Calculating Accrued Interest of Bonds

I am trying to calculate the accrued interest for a set of Treasury Bonds. I am comparing the answer from the code below with that for the 1st Bond(row) over here. In the link the AI is ...
1
vote
1answer
73 views

Understanding Yang-Zhang Volatility Estimator

I am using TTR in R and I am trying to understand the Yang Zhang volatility estimator. The following equations seem to imply a single value: $$ \sigma = \sqrt{{\sigma_o^2}+k\sigma_c^2+(1-k)\sigma_{rs}...
1
vote
1answer
2k views

Calculating portfolio allocation beta with different asset classes?

I'd like to calculate portfolio allocation beta on a portfolio that has different asset classes. The portfolio may be made up of: ...

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