0
votes
0answers
94 views

Is there a strong solution to $\frac{dS}{S}=\sigma(S)dw$?

Does someone know if there is a strong solution for this SDE : $$\frac{dS_t}{S_t}=\sigma(S_t)dW_t$$ where $$\sigma(S)=\begin{cases} 1\;\;\;S>1\\2\;\;\;S\leq 1 \end{cases} $$ $S_0=1$ and $W_t$ is ...
4
votes
0answers
84 views

Risk neutral measure in exponential levy model

Is there a method of finding a risk-neutral measure for assets driven by the levy process? I understand there is the esscher transform but I think it tends to transform the processes into ...
0
votes
2answers
389 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 ...
4
votes
0answers
146 views

How to price an option with two volatilities?

Imagine you have two volatilities, the second which is "activated" when the stock crosses a barrier called $p_b$. The present price is $p_1$. ($p_b>p_1$). This can be used to price options after a ...
0
votes
0answers
235 views

what is a reasonable beta in CAPM?

I want to predict expected returns for assets using a CAPM, to calculate unexpected (unpredictable, idiosyncratic, non-systemic) returns in portfolios. My CAPM estimated on monthly total gross ...
3
votes
1answer
213 views

How to design back-testing (validation) for such modified Vasicek model?

Consider a classical Black Scholes model , $$\frac{dS}{S} = \mu dt + \sigma dW$$ , where $dW$ is a Brownian motion, that $W(t_1) - W(t_0) \sim N(0, t_1 - t_0)$. The back-testing strategy is ...
4
votes
1answer
213 views

Estimating early exercise boundary for American put

I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method. How do I obtain the early exercise boundary within ...
1
vote
1answer
202 views

Why are indifference equations in mean-variance portfolio theory convex shaped

As the title suggests why is the indifference equations in mean variance portfolio theory convex shaped? Indifference Equation: https://en.wikipedia.org/wiki/Indifference_curve A graph:
2
votes
1answer
2k views

Duration of a floating rate note

I have the following C# code for calculating the modified duration of fixed coupon bonds: ...
5
votes
1answer
220 views

How to choose a rolling window type and size?

I'm developing a trading strategy which takes into account certain parameters (e.g. avg spread, weighted price, etc). Of course, these parameters can be calculated over different window types (i.e. ...
5
votes
0answers
110 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
3
votes
1answer
162 views

Measuring and proxies for leverage in the financial system

It can be argued that the leverage - reflected by how much collateral people or firms need to put down to borrow and might lose if they fail to pay the loan back - used in the financial system is one ...
2
votes
0answers
140 views

Black-Scholes in Delphi [closed]

when trying to implement the Black-Scholes formula in Delphi, I've found this: http://www.espenhaug.com/black_scholes.html I've checked the results against option-price.com and found they are ...
2
votes
1answer
603 views

How to calculate VaR/CVaR for private equity, hedge fund, and alternative investment portfolios?

What is the best method for calculating VaR/CVaR for private equity, hedge fund, and alternative investment portfolios? I have only historical monthly return for them.
0
votes
1answer
62 views

Liquidity and Prices

Do fewer transaction costs and higher liquidity relate to lower market prices? Are there any good resources that deal with these topics in more detail?
2
votes
3answers
252 views

Smoothing Term Curve

Assume that we have current month term curve and the curves from the two previous months. The current curve may be shifted from the average of the previous two curve by some value (a parallel shift). ...
0
votes
0answers
261 views

Time-varying correlation via state-space representation and Kalman filter

Let a linear time-varying mode like this one: $y_{t}=\alpha_{t}+\beta_{t}x_{t}+\epsilon_{t}$. You can also suppress the constant term to simplify this example: $y_{t}=\beta_{t}x_{t}+\epsilon_{t}$. ...
1
vote
1answer
198 views

Modified Duration of Overnight Index Swaps

Is the modified duration of an overnight index swap zero or close to zero?
4
votes
2answers
241 views

What is the significance of Relative Risk Aversion

I know that the relative risk aversion is defined as $$R(c) = cA(c)=\frac{-cu''(c)}{u'(c)}$$ where $u(c)$ denotes the utility curve as a function of wealth $c$. But I do not understand the intuition ...
2
votes
1answer
306 views

Why is the mean time-dependent in the Hull-White interest rate model?

In the Vasicek interest-rate model, the interest rate reverts to a constant mean. This makes sense to me. In my conception, the mean ought to be time-invariant, since interest rates don't follow an ...
2
votes
1answer
164 views

Trend in Cointegration relationship

I was estimating a long-run relationship of exchange rate and purchasing power parity. The residual of the long-run relation which should be $I(0)$, but it is only $I(0)$ when I introduce trend in ...
1
vote
1answer
951 views

IMM dates in excel

I need to get the IMM dates in excel. IMM dates are defined as the third Wednesday of every March/June/September/December.
0
votes
0answers
71 views

Real value of small numbers of shares of company stock

What is the real value of a single share of company stock? Let's ignore the "the value is what someone is willing to pay for it" angle. At some point, there has to be a real inherent value to ...
2
votes
2answers
173 views

How do you handle order tracking (without unique Lot ID's)

Hypothetical Trade: I buy 10,000 shares of ASTC using a broker API. The order is filled in 4 similar lots; ...
2
votes
2answers
498 views

Does Fama French Three Factor Model Work out of Sample (after 1993)?

Does anyone know if the Fama-French three factor model has been re-examined empirically after 1993, when the original paper was first published? I am asking because there seems to be considerable ...
4
votes
3answers
487 views

Backtesting - can you buy/sell at open and closing prices?

In backtesting (nasdaq stocks), I make the assumption that I have the ability buy/sell each day at the opening and closing prices. Is this realistic?
2
votes
3answers
4k views

Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?

I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ ...
3
votes
1answer
276 views

options pricing using vwap

This is a question about why options prices do not take volume into account. The popular option valuation formula "black-scholes" certainly does not account for this and I don't suggest that it does. ...
1
vote
2answers
115 views

how to make a distribution model tolerable of trend?

I'm building an model on different loans' NPL rate. The problem is NPL rates are always affected by the market. When NPL rates move in trend, my model will fail the back-testing. Assuming $x(t)$ is a ...
0
votes
2answers
163 views

Estimate weekly, yearly quantities from finite samples

I'd like to estimate from a daily prices serie $P_t$ with $N$ observations a quantity such as the variance of the weekly returns. I will use $\ln\left(\frac{P_{T+5}}{P_T}\right)$ assuming 5 days in a ...
-1
votes
1answer
138 views

Converting time series returns into euro

I am trying to convert various series of returns into one currency (euro). I saw from aprevious post that soemone suggested using conversion factors, where would I find these? Also, given that the ...
-3
votes
1answer
88 views

Why is there no closed-form equation for XIRR?

Everything I have read about XIRR (e.g., as calculated in Excel) says that there is no closed-form equation and it must be calculated by iterated approximation. Could someone give a brief ...
2
votes
0answers
98 views

Do some option pricing models allow for misspecification and what does it mean?

This is to some extent a theoretical question and maybe we can work together to produce some input and output. Diverse option pricing models are reported to be misspecified in various studies. One ...
0
votes
1answer
117 views

Calculating company-level market capitalisations from share quantities and values

I want to calculate company-level market cap values for stock exchanges listed by Bloomberg. I gather this can be calculated as the product of share price and the total of shares in circulation. But ...
5
votes
2answers
163 views

A question on Ito

If we know the dynamics of $S$, then we can estimate the value of $S$ at a time point, $t$. Here, I have a question concerning how to solve for $S_t$ by Itô because I obtained different results by ...
-2
votes
1answer
309 views

Order book depth views preferences: order-by-order vs. total aggregated volume by price levels

Which is best? Or is it irrelevant? Hi! Considering Level 2 Data (Market Depth), I want to understand the advantages to have all the order book on an order-by-order basis (or tick-by-tick basis) ...
1
vote
0answers
46 views

Is there a different test to check stationarity? [duplicate]

I am using the KPSS test to check stationarity of a financial time series. I would like to know if there is another test to confirm the stationarity. Any advice?
4
votes
0answers
325 views

Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$ where $\Sigma(i)$ is the lag ...
7
votes
3answers
390 views

Black--Scholes hedging argument

I'm trying to understand the standard hedging argument to derive the Black--Scholes PDE. There's one aspect of the derivation which I can't get passed and I'd be very grateful for some clarification ...
5
votes
0answers
285 views

Value-at-Risk formula when using skewed-t distribution

I am trying to find a formula for the skewed-t VaR. For example the VaR formula for a t-distribution is $$ \sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu ...
0
votes
3answers
1k views

How to calculate return rates with negative prices?

I'm dealing with electricity options and I'm considering the possibilty of negative prices. I want two estimate the historic volatility. However, an arithmetic mean doesn't feel appropriate and ...
4
votes
1answer
165 views

Statistical Power and Active Management

I was reading an article recently that pointed out the dangers of using statistical inference in evaluating active managers as the power of statistical tests diminishes with the variance of the ...
1
vote
2answers
363 views

Valuation of a Sinking Bond Fund

What would the schedule of payments be for a bond with a sinking fund? I know how to price a bond but how does the sinking fund play into it? ...
3
votes
3answers
296 views

How to most optimally perform currency conversions when backtesting on portfolio level?

I am currently expanding my own strategy profiling and testing platform which partly consists of a portfolio backtesting module. The backtest engine processes tick based data (quotes for currencies, ...
4
votes
1answer
231 views

How does out-of-sample option pricing work in practice?

When estimating in-sample option prices, one usually estimates the structural parameters $\theta_t$ using all information up to time $t$, and then prices the option at time $t$ using the obtained ...
-2
votes
1answer
328 views

How to look for fractals/harmonics patterns in time series?

I want to build trading systems based on two things: 1)Fractal Theory 2)Harmonics Pattern I have read the book : The Misbehavior of Markets: A Fractal View of Financial Turbulence By Mandelbrot ...
2
votes
2answers
236 views

Question on an approximation in pricing formula

I am reading the book An Introduction to Financial Option Valuation. The following on page 58 makes me confused: For the formula: $\exp \left\{ -1.96\sigma \sqrt{t}+(\mu-0.5 \sigma^2)t ...
-2
votes
1answer
165 views

DCF Zero Coupon Bond

Using a 30/360 day count what is the exact formula to discount this single zero coupon bond? ...
0
votes
0answers
624 views

fetch from yahoo! finance database - varying number of ticks

To test a model with real-life data, I used the fetch-function in matlab to connect to the database of yahoo! finance. My code to try and get 7 different assets' returns is the following: ...
3
votes
0answers
319 views

Definition of risk factors for market risk scenario testing

I am doing a research for stress testing in market risk. The usual process I found out for scenario testing is: Define risk factors upon the portfolio Define the desired scenarios Vary the risk ...

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