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1500 questions
8
votes
3 answers
How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?
In markets, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? Is it normal volatility, or lognormal volatility. because it affect our hedging positions.
So you cant say that it is always log normal…
Amiro
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8
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2 answers
Annualized Sharpe Ratio calculation
I'm trying to replicate the annualized Sharpe ratio of an buy-and-hold strategy for the Dow Jones Industrial Average index for a period consisting of multiple years. I got the daily DJIA (closing) price index (variable: "price") and the risk-free…
Wildman
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8
votes
3 answers
Is the average of independent Brownian Motions still a Brownian Motion?
If $W$ and $B$ are independent Brownian Motions (BM thereafter), then the average of $W$ and $B$ is $X_t=\frac{1}{2}(W_t+B_t)$.
Where do I begin to show that indeed it is still a BM?
Also, if both are martingales, then $X_t$ must be a martingale…
user17854
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8
votes
2 answers
What do we really mean by put-call ratio and how should it be expressed?
I need to calculate the put-call ratio for an American option. But I'm a complete naïf: I don't know how. I think I'd use the put open interest and the call open interest. I can imagine two ways to calculate PCR:
Simply (as some references tell me)…
Pete Wilson
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8
votes
2 answers
How to find funds with long history to use in backtest?
Is there a way (website/code) to find funds/etfs for a given asset class and how much data history is available (yahoo finance or other) ? It could be as simple as a list of funds by asset class and their data start date.
QPA
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8
votes
3 answers
What is an acceptable Sharpe Ratio for a prop desk?
What should be the value of a Sharpe Ratio for an intraday quantitative strategy to be accepted by a bank or hedge fund's prop desk? Let's assume the returns are daily changes in account equity, close to close.
Sergey Bushmanov
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8
votes
2 answers
KMV-Merton Probabilties of Default vs Moody's EDF
Moody's used to publish probability of default estimates from their Moody's EDF model, but they have temporarily discontinued it. I understand that the Moody's EDF model is closely based on the Merton model, so I coded a Merton model in Excel VBA to…
beeba
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8
votes
1 answer
Execution quality for illiquid securities
The SEC's execution quality statistics measurements (Rule 605) arguably does a poor job at measuring the execution quality of illiquid securities. It also does not cover over the counter securities.
What would be a good method to utilize for…
Sammy
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8
votes
1 answer
derivation of the hedging error in a black scholes setup
I'm reading the following short paper by Davis. In section 2.6 he wants to derive an expression for the hedging error. Assume we have Black scholes setup:
$$ dS_t = S_t(r dt + \sigma dW_t)$$
$$ dB_t = B_t r dt$$
and let $C_h(S, r, \sigma, t) =…
math
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8
votes
1 answer
How does rehypothecation cause systemic risk?
I've read in many places that rehypothecation causes systemic risk (not to be confused with systematic risk), but none offer an explanation. Is this because of the daisy-chain effect that would happen if a posted collateral to b who then posted it…
AfterWorkGuinness
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8
votes
2 answers
Utility Theory and portfolio optimization - Proof of a lemma
I have a question on the following problem from chapter 9 of D. Luenberger, Investment Science, International Edition:
(Portfolio Optimization)
Suppose an investor has utility function $U$. There are $n$ risky assets with rates of return $r_i$,…
James
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8
votes
2 answers
Fitting a generalized logistic distribution
I have a process that estimates the parameters for the following function using the NL2SOL algorithm.
$C-[\alpha+\frac{\beta-\alpha}{1+e^-\theta(y_t-\delta)} \vartriangle y_t]$
The process currently holds $\alpha$ and $\beta$ constant, so only $C$,…
Joshua Ulrich
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8
votes
1 answer
Density forecast of a GARCH model
I am currently working on developing a series of density forecasts and I am encountering some problems. I am working on weekly S&P 500 returns and the returns process is described as
$r_{t} = \mu + \delta r_{t-1} + h_{t}z_{t}$
where $z_{t}$ comes…
Masher
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8
votes
2 answers
Is Duration really the slope of the Price-Yield curve?
When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right?
Duration is (change in price) divided by (price times change in yield). That's hardly the…
user1443
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8
votes
5 answers
How to calculate compound returns of leveraged ETFs?
Forewarning: this is a complete newbie question :-)
I am starting to learn about ETFs by trying to do the numbers. When learning about the compounding effect in leveraged ETFs, I wanted to simulate the return for a simple ETF. Here is what I wanted…
Samik R
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