3
votes
1answer
88 views

Understanding the derivation of a ML-estimator

I'm trying to understand the derivation of a ML-estimator and more specifically the rewriting of the covariance matrix Sigma. In this rewriting a lemma is used to show that $$ (1) \hspace{1.4 ...
5
votes
0answers
277 views

On the interface between Quant finance and actuarial-science/insurance-math

Actuaries (at least in Europe) are frequently severily lacking in quant finance topics. At best they are familiar with B&S model. People going into quant finane or striving to become a quant on ...
2
votes
2answers
161 views

Options with a stochastic strike

Do options where the strike itself is a stochastic process exist? If they do - what are the motivations for such a product and where is it used ? Example: Call-Option with stochastic strike: ...
2
votes
1answer
119 views

Where does this copula come from?

In a paper I encountered the following notation $$P(Z\leq z,u\leq Y\leq v)=C(F_{Z}(z),F_{Y}(v)-F_{Y}(u))$$ However I don't see why this holds in relation to uniform random variables. Usually ...
1
vote
2answers
229 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I think I understand the fact that when marginal utilities of the same function are equal (a consequence of the actuarially fair insurance), the independent variables in it must be equal -- right? But ...
0
votes
2answers
389 views

Are PX_BID and PX_ASK on Bloomberg closing bid/ask? or are they daily averaged?

Bloomberg provides PX_BID and PX_ASK on a daily basis, but it's not clear exactly where these numbers come from. Are they closing bid and ask prices, or are they averaged over the entire day? For ...
1
vote
0answers
117 views

Credit Spread, Transition Matrix

Consider a credit rating system consisting of three credit states, A, B and D (default) with the following annual credit transition probability: T = [0.7 0.2 0.1;0.2 0.5 0.3; 0 0 1]. For a company ...
1
vote
1answer
178 views

Given future price probability distribution, what is a strategy that maximizes return?

Say I know the price probability distribution, e.g., lognormal(p,s), of a stock X at a future time ...
0
votes
0answers
146 views

Is there a Newey West like correction for overlapping data correlation estimates?

I already posted a related question a while ago but was unsure if I should post within the same question. I want to estimate mulitperiod asset return correlations and test if there are significant ...
2
votes
2answers
110 views

What impact does arbitrage have on realised volatility estimates?

Doing some research modeling/estimating volatility in the bitcoin market. There is quite a bit of scope for arbitrage within crypto-currency markets. Wonder if this has any impact on my volatility ...
3
votes
1answer
137 views

Does risk-neutral measure have anything to deal with risk-neutrality in utility theory?

Or simply: why do we call equivalent martingale measures as risk-neutral measures? In the utility or game theory, when we consider a person's preferences to certain outcomes, we often deal with the ...
1
vote
1answer
124 views

Effects of random-generator-choice on derivative's price

There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform. My standard tool is Mersenne Twister - when I need to generate ...
1
vote
3answers
107 views

How often do banks update forward points?

My understanding is that forward rates are calculated by comparing interbank interest rates of the 2 currencies for a currency pair, with the points being the difference between spot and the forward ...
0
votes
0answers
71 views

How to determine the equiy interest of target company if there is circular ownership?

I would like to ask is there any way to determine the equity interest of target company if there is circular ownership. For example, suppose company A owns 50% of company B, company B owns 100% of ...
2
votes
1answer
112 views

Is the volatility of a trader's wealth equal to the volatility of the underlying assets traded?

Assume that a trader trades in several stocks with different volatilities. The return of the trader's portfolio would be the weighted average of returns and the risk would be a function of the the ...
1
vote
1answer
390 views

Backtesting with fundamentals

Recently I've read some books about quantative approach to fundamental investing: - What works on Wall Street - James O'Shaughnessy - Quantitative Value - Wesley Gray, Tobias Carlisle - Quantitative ...
4
votes
0answers
41 views

What type of interpolation should be used in key rate perturbation models?

When perturbing a key rate in order to assess sensitivity of portfolio value, what sort of interpolation is standard? A book I am looking at says linear, but this seems pretty unrealistic to me--and ...
1
vote
1answer
73 views

Baye's rule for conditional expectations (Proof review)

The Baye's rule for conditional expectations states $$ E^Q[X|\mathcal{F}]E^P[f|\mathcal{F}]=E^P[Xf|\mathcal{F}] $$ With $f=dQ/dP$ - thus being the Radon-Nikodyn derivative and $X$ being ...
1
vote
1answer
109 views

Direct exchange data via a Vendor

I am considering the option between using direct exchange connections vs using a vendor like Bloomberg for market data. I am interested in daily data and potentially tick by tickdata. Initially I am ...
5
votes
3answers
279 views

Geometric Brownian motion - Volatility Interpretation (in the drift term)

A Geometric Brownian motion satisfying the SDE $dS_t = rS_t dt+\sigma S_t dW_t$ has the analytic solution $$S_t = S_0\exp\left\{\left(r-\frac{\sigma^2}{2}\right)t\right\}\exp\{\sigma W_t\}$$ Recently ...
4
votes
1answer
197 views

Definition of orthogonality and independence for a stochastic processes

Somehow I can't find the explicit definition of when two processes are supposed to be orthogonal or independent anywhere. I think orthogonality and independence should mean the same thing in this ...
0
votes
0answers
31 views

Forward Yield curve for an arbitrary company

Let say I am analyzing a company XYZ. Credit rating for this company is BB. Now I need to have the 6-month forward Yield curve for this company. Can somebody help me how to find this information from ...
2
votes
1answer
431 views

Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.
1
vote
1answer
399 views

Value Weighted Return

I recently have started to look at some data from CRSP, and they have a metric called Value Weighted Return (two versions with and without distributions). When I looked it up, it seemed that this ...
0
votes
1answer
136 views

Difference between VaR and credit VaR?

Quick question: is there a difference between credit VaR and VaR or are they the same thing?
2
votes
2answers
184 views

Backtesting Period

Views on timeframes for backtesting vary considerably. Curious on what timeframe/trade size leads to a statistically significant result. For example, what backtest period is reasonable for a system ...
1
vote
0answers
160 views

Mock/practice trading for options (delta/gamma hedging etc.)

I know there are some sites for practicing equity investing. But could you provide me with suggestions concerning options trading etc. I read Natenbergs book on Options and want to test things like ...
1
vote
1answer
183 views

List of financial derivatives Ito's Lemma does not apply

According to Ito's Lemma there is no restriction on the continuity of the stochastic process. The restrictions are on the continuity of the pay-off so that second derivatives with respect to ...
0
votes
1answer
43 views

CAPM as pricing formula

P - price that the asset was purchased. Q - price that it was sold P = Q/(1+r+B(R_m - r)) What is the financial meaning of denominator. Thanks for help.
0
votes
0answers
85 views

Detrending before cointegration

When checking for co-integration , is it necessary to detrend the time series? What is the best way to go about it?
1
vote
0answers
37 views

evaluating portfolio performance without knowing the amount held on cash accounts

I would like to evaluate the performance of a portfolio mananger. I know his trades, and the initial portfolio holdings. I do not know, however the amount held on his cash account. That is, I ...
3
votes
1answer
347 views

How is the MA (moving average model) useful?

How is the MA model useful in modeling financial data, for example the stock indices? For example, from what i understand in the AR (auto-regressive) model portion, we can use the ADF test to check ...
3
votes
1answer
210 views

Scaling of a transition matrix

I am working on a ratings transition matrix and I wondered how people scale it down to shorter time periods (although one should more or less stick to the estimation period i know). It is clear that ...
1
vote
2answers
432 views

How to incorporate fundamental analysis in quantitative trading algorithm? [closed]

I want to write a quantitative stock trading program based on fundamental analysis. It would crunch through prices, financial reports to look for value stocks. It can support backtesting of strategy ...
2
votes
1answer
101 views

QuantLibXL - Optionlet bootstrapping failure

I am trying to bootstrap the Optionlet volatility surface from a Cap/Floor volatility surface using QuantLibXL. To be specific, the data is from ICAP: ...
2
votes
2answers
535 views

How do I calculate probability distribution of stock prices given option prices?

I'd like to calculate a probability distribution for prices given the option prices for that stock? Any ideas how to do this? My desire is to do this daily and then see how the price PD changes over ...
1
vote
2answers
526 views

Calculate volatility from call option price

Given call option price, what is the simplest formula to get the volatility value ? Test Data: ...
1
vote
1answer
152 views

Price of Bond given credit state matrix

"Consider a credit rating system consisting of four states, A,B,and D(default) with the following annual credit transition probability: A= [ 0.7, 0.2, 0.1; 0.2, 0.5,0.3; 0,0,1] For a company rated ...
3
votes
2answers
437 views

Delta hedging frequency for plain vanilla European options under trading costs

I am looking for methods to select points in time when delta hedging plain vanilla European options under trading costs. It is easy to come up with ad hoc ideas such as Time-based: for example at ...
1
vote
1answer
103 views

Discount rate, convertible debt and the effect of time

The way I understand it is that there are three main parameters to a convertible debt investment. An investment amount A discount rate A trigger event Now under most of the examples I have seen, ...
2
votes
0answers
34 views

How can dividend protection be considered in the binomial model in pricing the convertible bond?

If the convertible bond has dividend-protection, how can we cater it in the binomial model? If there is dividend protection at or above 1%, can we impose input of dividend yield of 1% in the ...
1
vote
3answers
1k views

What does it mean by autocorrelation coefficient near 1?

It is said that the time series has a stochastic trend if the first autocorrelation coefficient will be near 1. Q1) What does it mean by the above statement? Q2) How do we calculate the first ...
1
vote
1answer
98 views

What are the equation that gives hurst exponent of value >0.7 and <0.3?

I had been working on algorithm which uses the Hurst Exponent. Once i random walk simulation on matlab, x = cumsum(randm(1000,1)), I was able to get a hurst value close to 0.5. To analyze the use of ...
3
votes
2answers
158 views

How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model

Given that $e^{r\Delta t}(u+d)-ud-e^{2r\Delta t} = \sigma^2\Delta t$ I would like to show that $u=e^{\sigma\sqrt{\Delta t}}$ I know I must somehow use Taylor's approximation $e^x = 1 + x + ...
0
votes
0answers
46 views

Log returns vs Relativizing to Portfolio size of $1

In a current empirical research project, I am tracking a non-parametric measure of a transaction cost. To this extent, I track this cost in two ways Cost in terms of log returns Cost in terms of ...
1
vote
2answers
95 views

Controlling portfolio concentration

I'm working with a heterogenous basket of instruments (in volatility terms). Risk parity allocation seems to be useful for the portfolio( * 1/Volatility). However, there are times when the ...
0
votes
1answer
86 views

Volatility swaps historical data

I am preparing a study about Volatility and Variance Swaps. Does anyone know where I can found historical public data regarding this instruments? Thanks!
-1
votes
1answer
61 views

Calculating the sensitivity of the modified bond duration to changes in the coupon rate

Given that $B=Ce^{-y} + Ce^{-2y}+ (100+C)e^{-3y}$ where B is the bond price, C is the coupon. and It is a 3 years annual coupon bond. I want to find $\frac{dD}{dC}$ where $D$ is the modified ...
5
votes
2answers
175 views

Risk neutral Esscher transform of exponential Levy processes

Let $X_t$ be a Levy Process and $e^{X_t}$ the corresponding exponential Levy process. Using the Esscher transform for a change of measure for which the Radon-Nykodym derivative is ...
2
votes
2answers
489 views

Definition of Return of A Long/short Portfolio

This can either be a silly question or a question with no sure rigorous answer but defined with some convention. Any way, here it is. What is the (industrial recognized) definition of the return of a ...

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