All Questions
2,052
questions
6
votes
2
answers
641
views
Choice of prior as a shrinkage target in portfolio construction?
There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction.
The sell point of these priors ...
- 13.5k
6
votes
1
answer
4k
views
How to compute the yield on the Ultra-Bond Treasury Futures
I am trying to compute the yield on the Ultra-Bond Treasury Futures which is roughly 172.2187.
Heres the description of the contract:
U.S. Treasury bonds with remaining term to maturity of not ...
- 951
6
votes
2
answers
4k
views
"Risk" Factor vs Double Sorts
With regards to a cross-sectional asset pricing (stocks) study, I am testing if one variable can explain another. One common approach to do this, is to use the double-sorting portfolio technique (sort ...
- 61
6
votes
1
answer
838
views
How is implied volatility derived?
How to compute Implied Volatility Calculation?
The above link shows that there multiple ways to calculate implied volatility. My question is that for most of the common data sources like Bloomberg, ...
- 333
6
votes
1
answer
15k
views
Marginal Risk Contribution Formula
I am trying to understand and implement the standard 'marginal risk contribution' approach to portfolio risk and hoping to reconcile the formulae provided for its calculation in different sources. ...
- 63
6
votes
2
answers
10k
views
Derive vega for Black-Scholes call from this formula?
Is it possible to get the right formula for vega of a call option under the black scholes model from this formula?
$$\frac{\partial{C}}{\partial{\sigma}}=\frac{S_0}{\sqrt{2\pi}}{e^\frac{-d_+^2}{2}}(\...
- 432
6
votes
2
answers
9k
views
How to understand micro-price (aka, weighted mid-price)?
The definition of micro-price is
S = Pa * Vb / (Va + Vb) + Pb * Va / (Va + Vb)
where Pa is the ask price, ...
- 209
6
votes
1
answer
938
views
What research is available on the performance of convertible bond arbitrage models?
The basic principles of convertible bond arbitrage have been clear at least since Thorp and Kassouf (1967). For those who are not familiar, the arbitrage entails purchasing a convertible bond and ...
- 13.5k
6
votes
3
answers
427
views
How does order fulfillment proceed with larger orders?
If a large sell order hits many bids from the book, is the order filled at once? Or is it filled one bid at a time with a chance for any new orders to come in between each trade?
- 163
6
votes
1
answer
585
views
How do you actually solve a stochastic HJB equation in practice?
I've read a number of recent papers on market making. Nearly all of the more recent papers focus on defining the problem in terms of a state and action space, deriving the relevant HJB equations and ...
- 91
6
votes
1
answer
6k
views
Excess, Residual and Active Return
in CAPM. What's the difference between these different types of returns?
Active return
Excess return
Residual return
- 341
6
votes
2
answers
840
views
Option with payoff $K^2/S^2$
Given the dynamics of the risky asset ( with dividend $q$ ),
$$
\frac{dS_t}{S_t}=(\mu-q)dt + \sigma dW_t^P
$$
Consider a european option with payoff,
$$
P_0(S) =
\begin{cases}
1, & \text{...
- 514
6
votes
1
answer
446
views
Discount curve and payment frequency
In case of uncollateralised trades, where we use LIBOR rates for discounting, does the LIBOR tenor have to match with the payment frequency?
For example, one of the swap leg pays USD floating amount ...
- 71
6
votes
1
answer
3k
views
Where can I find a clear explanation (brief derivation) of N(d1) and N(d2)?
Where can I find a good explanation (perhaps with a brief derivation) of N(d1) and N(d2) from Black-Scholes? Just trying to understand the general idea about these 2 probability functions and how they ...
- 185
6
votes
3
answers
504
views
Relationship between options open interest and spot price movement
The hypothesis that I am mulling over (and more so, its effect on stock price movement) is the following.
Hypothesis: Buyers of options do not hedge (as they don't need to) while sellers usually hedge ...
6
votes
2
answers
1k
views
How can one effectively approximate the fill portion of a limit order in a FIFO order book given it's recent state?
What methods could one use to find the step wise probability of a partial or full fill of an order in the best ask/bid level of a limit order book given the historic best ask and best bid quantities ...
- 163
6
votes
2
answers
2k
views
Calibrating stochastic volatility model from price history (not option prices)
For stochastic volatility models like Heston, it seems like the standard approach is to calibrate the models from option prices. This seems a bit like a chicken and an egg problem -- wouldn't we ...
- 231
6
votes
2
answers
3k
views
Why do we usually use normal distribution and not Laplace distribution to generate stochastic process?
When working with a stochastic process based on brownian motion, the increments have normal (gaussian) distribution.
However, it seems that a Laplace distribution, with density:
$$f(t) = \frac{\...
- 787
6
votes
2
answers
347
views
Mathematical proof of $g = \mu - \frac{\sigma^2}{2}$ relationship between CAGR and average returns
I found in a paper the relation between the CAGR and the arithmetic average of returns to be
$$g \sim \mu - \frac{\sigma^2}{2}$$
where g is the geometric average, $\mu$ the arithmetic average and $ ...
- 212
6
votes
1
answer
839
views
Why aren't american put options martingales?
I don't understand what's wrong in the following argument.
Assume that we have a no-arbitrage market where the following products are traded:
a risky asset $S$,
a risk-free bond $B$,
an American put ...
- 61
6
votes
6
answers
15k
views
Option trading API other than Interactive Brokers
I'm looking for an options broker that provides an execution API.
I'd like to ideally test on a papertrading version of it before connecting to a real execution engine. I know IB offers that, but they ...
- 243
6
votes
2
answers
556
views
6
votes
2
answers
1k
views
How to trade leveraged ETFs
Leveraged ETFs (LETFs) are known to lose value over time due to the "volatility decay" effect. What're the most common strategies for trading LETFs to take advantage of this volatility effect?
Also, ...
- 61
6
votes
0
answers
900
views
(C++) Monte Carlo pricer for SABR model to test Hagan / Paulot formulas
I'm trying to test the so-called Hagan formula (p.6 of this paper) and the Paulot formula, order 1 only (eq. (43) p.19 of this paper. For this, i'm trying to use both Euler and Milstein scheme ...
- 188
6
votes
2
answers
984
views
Quarterly Survival rate given there is a Quarterly Probability of Default
I am trying to calculate the Quarterly Marginal PD. I have calculated it as given in the below image but I am thinking about whether the Survival rate calculation is making sense or not.
The ...
- 61
6
votes
2
answers
638
views
Variance of a time integral with respect to a Brownian Motion function
Let process
$$I_t = \int_0^t f(s) W_s \,\mathrm d s $$
where $W_s$ is standard Brownian motion. My question are the following:
We know that $\mathbb{E} (I_{t})=0$ for all $t$ and $f$ a integrable ...
- 361
6
votes
2
answers
9k
views
Determine the carry of a treasury bond futures contract?
Hi fellow financial market enthusiasts. I'm trying to understand my options as a retail investor. I want to leverage a cash bond portfolio but my broker does not allow that, so I want to use futures ...
- 138
6
votes
2
answers
17k
views
how do I loop through all the stocks with quantmod and ttr?
I just started with quantmod package. If I want to select stocks based on their recent performance, then I need to loop through all the stocks in, say, NYSE. So I need:
get all the stock symbols
...
- 255
6
votes
1
answer
425
views
How to compute the expectation of integral of this random function?
Let $W_t$ be a standard wiener process and
$$Y_t=\int_{0}^{t}\frac{W_s}{(1+W_s^2)^2}ds$$
If $W(t_0)=\sqrt{3}$, then how can we compute $\mathbb{E}[Y(t_0)]$?
Is $\mathbb{E}[Y(t_0)]=0$?
- 248
6
votes
3
answers
4k
views
Which volatilities should I use for Quanto Options?
Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate.
How can I read the "right" volatilies ...
- 863
6
votes
1
answer
4k
views
Implied Dividend from American Options (in practice)
I just tried to price the implied dividend for a few active, liquid options markets using current prices and I am not convinced my results are accurate.
I am using American options, and using the put-...
- 745
6
votes
3
answers
7k
views
Deriving the Black-Scholes formula as the expected value on the payout of an option
My question concerns the Black-Scholes formula for the value of a European option, namely
\begin{align}
C(S_t, t) &= N(d_1)S_t - N(d_2) Ke^{-r(T - t)} \\
d_1 &= \frac{1}{\sigma\sqrt{T -...
- 275
6
votes
1
answer
981
views
Distribution of time integral of Brownian motion squared (where the Brownian motion occurs in square root time)?
Let $I_t = \int_0^t W_{\sqrt{u}}^2du$. What is the distribution of $I$?
If I recall correctly, if the Brownian motion were instead $W_u$, then it would be $I_t \sim N\left(\frac{t^2}{2},\frac{t^4}{3}\...
- 61
6
votes
2
answers
4k
views
Why gamma and theta have opposite signs?
I saw some textbooks use B-S equation to explain why gamma and theta have opposite signs in most of the cases. For example, John Hull's classic book.
The explanation is, first write B-S equation in ...
- 321
6
votes
1
answer
2k
views
Numéraire -- couldn't understand the wiki explanation
I'm trying to understand Numéraire concept so am reading the wiki page:
I couldn't understand the last formula's 2nd equation:
$$ E_{Q}\left[\left.\frac{M(0)}{M(T)}\frac{N(T)}{N(0)}\frac{S(T)}{N(T)}\...
- 2,231
6
votes
1
answer
8k
views
Estimating the historical drift and volatility
I want to forecast prices $S(t)$ of some asset based on historical daily values. I want to use the geometric Brownian motion given by an SDE:
$$dS=\mu S t + \sigma S dB,$$
where $B$ is a Brownian ...
- 163
6
votes
2
answers
6k
views
Why a calendar spread is a preferred strategy in a low volatility period
What is it about a calendar spreads opposed to other spreads (e.g vertical spread) that makes it such a popular strategy for a period of low implied volatility?
Is it that when low volatility turns ...
- 1,404
6
votes
2
answers
13k
views
What happens to accrued interest and coupon payment if coupon date is weekend?
Say a 5% bond using 30/360 convention, 2 coupons per year. Last coupon payment was on 2016-04-01. Now 2016-10-01 is weekend and the coupon is paid on 2016-10-03. Is this coupon 2.5 or slightly more ...
- 183
6
votes
1
answer
313
views
Derivation of the Stochastic Vol PDE
I'm trying to follow the derivation of the stochastic vol pde for an option price - as given in Gatheral (The vol surface), Wilmott on Quant Finance and many other places. As usual one starts off with ...
- 205
6
votes
1
answer
1k
views
How to apply quasi-Monte Carlo to path-dependent options?
Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
- 13.5k
6
votes
0
answers
936
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 ...
- 13.7k
6
votes
2
answers
1k
views
SKEW and VIX relations?
My question is about the CBOE published index VIX and SKEW.
To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model....
- 61
6
votes
2
answers
12k
views
Can the duration of a bond be greater than Time to Maturity
In the case of a vanilla bond I know that the duration will be less than the time to maturity.
But I am observing that for a non-vanilla bond, the duration is greater than time to maturity.
Can ...
- 61
6
votes
3
answers
969
views
Uncertain volatility
Recently, I have encountered something called "uncertain volatility". Is it a popular concept in QF? Do practitioners use it nowadays? What are its pros and cons compared to e.g more familiar ...
- 766
6
votes
3
answers
5k
views
Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?
For a vanilla European call, my Monte Carlo method gives the right option price and delta but the wrong gamma. In particular, the value of gamma varies wildly each time I run the method. I estimate ...
- 161
6
votes
1
answer
344
views
Reference Request: Horse Race for Portfolio Allocation
Probably the most popular horse race study for portfolio strategies is
Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?, with DeMiguel, L. Garlappi and R. Uppal. ...
- 1,456
6
votes
2
answers
413
views
Can the concept of negative probabilities be used to price a call option?
Edit: I'm a dumbass. The thing below is supposed to be just the motivation of asking. I want to ask for below and in general, hehe.
Assume that we have a general one-period market model consisting of ...
- 921
6
votes
2
answers
779
views
Architecture of a global pricing library with immutable payoffs
By global pricing library I mean a library
handling equity, rate etc, hybrid products
having several models (BS, LV, SV, LSV)
having several numerical methods (analytic formula, MC, PDE FD/FE)
I ...
- 1,223
6
votes
1
answer
493
views
Options On Earthquakes
As a financial innovation, the options market is introducing Options contracts based on
California Earthquakes. In your own words, discuss the following:
True or False?
“The sellers of Options on ...
- 61
6
votes
0
answers
410
views
How are quants able to verify whether their calculated prices are any good
This question is related to the discussion on Model Validation Criteria
However it appeard to be very high level to me and I would like to go more into detail.
Not working at a pricing desk the ...
- 3,377