6
votes
Is there a proxy for S&P 500 market/pricing inefficiency?
Mispricing can only be measured relative to some asset pricing model
Fama (1970) famously defined an efficient market as, "a market in which prices always 'fully reflect' all available information."
...
- 7,024
6
votes
Accepted
Correlation and implied volatility
This is a problem commonly faced by investment banks and buy-side firms (such as hedge funds) that deal in lots of derivatives.
There isn't much more one can do than employ a few rules of thumb, and ...
- 15k
5
votes
Accepted
Assuming perfect liquidity
A trading restriction could mean that you cannot short certain instruments, or that you cannot execute above/below certain volumes. For example in practice you cannot trade fractional numbers of a ...
- 2,681
4
votes
Accepted
Why does the definition of the riskless asset vary in discrete vs continuous time?
Let us say we have a yearly interest rate of $r$ that compounds over $n$ periods. With annual compounding that means $n=1$, with semi-annual compounding that means $n=2$ and with daily compounding ...
- 845
3
votes
Accepted
Calibration and pricing with the Stochastic Local Volatility model
You need to calibrate the local volatility function contingent with the stochastic volatility parameters you chose if you want to be able to price back the calibration vanillas. The standard recipe ...
- 1,100
3
votes
Accepted
Modelling limitations and understanding of long term goverment bonds
OK, your framework on this is right. Long-term yields embed "expectations" about future short rates. That is: what do I think I'll get if I sat for T years with cash in the bank for swaps, or the same ...
- 5,141
3
votes
Accepted
High Frequency Trading in LoB - Sasha Stoikov and Marco Avellaneda
The terminal condition for the HJB equation implies that you can factor the value function into
\begin{equation*}
u(s, x, q, t) = \exp(-\gamma x)\exp(-\gamma \theta(s,q,t)):
\end{equation*}
and a ...
- 1,096
3
votes
Accepted
Market making with resting orders?
The only way you can use limit orders to provide liquidity is to post prices that are the same as the prices of the limit orders, and then you will not be earning any spread. In other words, what you ...
- 96
3
votes
Market making with resting orders?
This paper Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency (by L and Mounjid) is probably exactly what you expect.
It is explained how (given a model of orderbook ...
- 12.6k
2
votes
Accepted
"Standard" Model for Effective Fed Funds Rate
In practice, most derivatives traded on Fed Funds rates are linear(i.e. Forwards) rather than non-linear (options and exotics). As such, there has not been a strong case for precise modeling of the ...
- 17.9k
2
votes
Accepted
Normal Libor Market Model
Yes I used one in the early 2000s. At the time, US interest rates were quite high (5 or 6pct) and the market skew was such that -100bp receivers were more expensive than +100 payers. The lognormal ...
- 17.9k
2
votes
Market making with resting orders?
With a resting order the market maker's client takes (buys) at the offer, or gives (sells) at the bid. The market maker prices the deal that way as with any other order type. A resting order is simply ...
- 1,156
2
votes
How to simulate market data and test strategies?
As a starting point I would make the assumption that your new orders are negligibly small, in order that their market impact does not affect the trajectory of the price. This will provide a reasonable ...
- 12.1k
2
votes
Which models have non-smooth densities?
A simple model would be the double exponential model from Kou (2002). It is very similar to the jump-diffusion model from Merton (1976) but instead of modelling the jump size by a normal distribution, ...
- 16.3k
2
votes
Accepted
Why does the LMM in Hull seem so different from the LMM in Brigo and Mercurio?
Hull used a single Brownian driver. He did add, a few pages down, equation (31.15) (in my 7th edition) with $p$ independent Brownian drivers:
$$ \frac{dF_k(t)}{F_k(t)} = \sum_{i=m(t)}^k \frac{\...
- 5,173
2
votes
Accepted
What are the parameters’ units in the Avellaneda and Stoikov model?
A good way to understand the parameters is to look where they first appear in the model:
$dS=\sigma\,dW$ means that $S$ is a price and $\sigma$ is the volatility in the same unit than $dt$ (ie dollar ...
- 12.6k
2
votes
Is beta stable over time for individual securities?
No, betas are not stable over time. That's not even true for portfolios (for individual stocks it's even worse). One of the seminal references is: Lewllen and Nagel (2006). Take a look at figure 2 ...
- 8,621
2
votes
Accepted
Is stochastic control with the HJB equation used in market making/algo trading at institutions?
I would say that there are two things that we can talk about:
Research purpose
Real Trading
Those models are a good thing to start when you try to build something that has to have characteristics of ...
- 501
1
vote
A question about the Grossman-Miller Market Making Model
if someone has a good explanation I would like to hear it as well.
I have just started reading the book as well, but to my understanding what they mean is that since it's discrete time, coming into ...
1
vote
standard/brownian market with different brownian motion
tl;dr: informally: You cannot know the value of the difference of two random variables by knowing their sum.
Consider the following set $A =\{ \omega \in \Omega | W_1(t)(\omega) - W_2(t)(\omega) \in [...
- 271
1
vote
Why is diversifiable risk unrewarded?
Equal-weighted Portfolio
The typical way to answer this is to consider an equally-weighted portfolio of $n$ assets. An asset $i$ thus has portfolio weight $w_i=\frac{1}{n}$ and excess returns $R_i$ ...
- 2,972
1
vote
Accepted
Economic interpretation of Time-varying beta (systematic risk) in portfolio analysis
There's a practical answer and a theoretical one.
Looking at a time series of any stock and market, its realised beta will naturally time-vary depending on whether company-specific good or bad news ...
- 5,141
1
vote
Currency-denomination for the index in an event study
Looking at Markit spreads, when both USD and EUR spreads are published, then usually (not always) either they are exactly the same, or differ only by 1-2%. I think this means that many contributors ...
- 13.2k
1
vote
Gibbons, Ross, Shanken Test derivation by MLE
Hi: This is an incomplete answer but I needed room. The Wald statistic for testing a linear constraint , $Rb = r$ is ,
$(Rb - r )^{\prime}[R(X^{\prime}X)^{-1} R^{\prime}]^{-1}(Rb - r)/s^2$
$X^{\...
- 1,178
1
vote
LIBOR Market Model implementation in R
Result of refined search:
https://rpubs.com/thierrymoudiki/33287
High quality material in R. No need to reinvent the wheel.
- 33
1
vote
Zero Coupon Bond prices in One Factor Hull White model
The derivative of the bond prices is very sensitive to the interpolation mode. actually, if you use a linear interpolation mode, you will have some cases for which the right derivative is different ...
- 872
1
vote
Accepted
Ho & Lee yield curve fitting with zero coupon bond market prices
When no functional form is available in differential analysis then one should use a computational method. As Daneel comments a common computational approximation of the second order derivative can be ...
- 380
1
vote
"Standard" Model for Effective Fed Funds Rate
Wu and Xia did some interesting work with modelling the effective EU, US and UK interest rates https://sites.google.com/site/jingcynthiawu/home/wu-xia-shadow-rates
- 133
1
vote
Accepted
Valuation of open FX-Forward
The flexible forward contract is very much like an American option: at each exercise date, you have the choice to receive the payoff $(S-K)$ or not. The difference with a regular option is that you ...
- 1,464
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