All Questions
21,719
questions
1
vote
1
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37
views
CML equation - from where does the square come from?
In his textbook Asset management Andrew Ang uses the following CML formula (chapter 6)
E(rm) - rf = y * σ^2
Where y is risk aversion factor
What is the source of square?
When I look at CML graph there ...
- 13
1
vote
2
answers
214
views
Why does cost of borrow have anything to do with the equity forward price?
By non-arbitrage, you buy the stock and hold it to the delivery date of the forward, only cost of funding (of cash) and equity dividend would be involved in the equity forward calculation. Where does ...
- 736
0
votes
0
answers
40
views
Why a Short Iron condor payoff is showing always positive
I created a Short Iron condor on Nifty 50 index European option for 9 Nov weekly expiry on 1 Nov morning 10.30 AM (live market). It's payoff is showing always positive curve. Why ? However when same ...
- 325
0
votes
0
answers
37
views
How are VIX options priced in a mean-reverting framework?
If a trader assumes that the VIX follows a mean-reverting process like the Orstein-Uhlenbeck process, how would they price this non-martingale asset? My intuition tells me a trader would use doob-...
0
votes
0
answers
29
views
A term to compare 2 stocks based on simultaneous trending and ranging characteristics
There a 2 stocks called A and B. We take a look at the daily chart of both stocks over the last 1 year. On 90% of the days A and B both trended or at least one of A or B trended. On 10% of days both ...
- 3
2
votes
2
answers
86
views
Conditional expectation of increments of stochastic process [closed]
I have come across the following result in my book on stochastic finance and I have trouble understanding the proof.
On a filtered probability space with filtration $(\mathcal{F}_t)_{t \in \mathbb{R}^+...
- 23
1
vote
1
answer
167
views
Derivative pricing under $\mathbb{P}$
I recently learnt about the Girsanov-Cameron-Martin theorem, which basically says, that if $(\tilde{B}(t),t\in[0,T])$ is some Brownian motion with a (possibly stochastic) drift $\theta(t)$ defined on $...
- 208
3
votes
0
answers
67
views
Academic Mailing List Quantitative Finance / Machine Learning
I'm an early-stage researcher in Machine Learning for Finance. I was wondering if there are mailing lists where people post calls for papers, summer schools, conferences, open positions, and so on. ...
- 31
0
votes
0
answers
37
views
Reliability of R Package on Covariance Matrix Shrinkage
I recently used a R package CovTools in R with the command CovEst.2003LW(X), where X is your sample covariance matrix as an input, to compute the shrunk covariance matrix (an estimate that is closest ...
- 559
0
votes
0
answers
20
views
LQD and IG cash spreads
Can someone please tell me the relationship between LQD and IG cash spreads. what's the movement (widen/tighten) of the spreads can tell me about the market, supply and demand
- 41
0
votes
0
answers
68
views
Combining many trading strategies in an efficient
I have a lot (>50) of back tested (and naively "validated") trading strategies. They trade different ETFs, mostly equities, but also others (like GLD, USO, ...). These are all strategies ...
1
vote
0
answers
67
views
How can I show that these assets do not satisfy a 1-factor model?
Suppose these two assets satisfy a 1-factor model:
$$
R_1= E(R_1) + F + ε_1
\\
R_2= E(R_2) - F + ε_2
\\
$$
where: $$
E(F)=E(ε_1)=E(ε_2)=0
\\
Var(F)=1, Cov(F,ε_1)=Cov(F,ε_2)=Cov(ε_1,ε_2)=0
\\
Var(ε_1)=...
- 23
0
votes
0
answers
49
views
Machine learning techniques for small datasets
I am dealing with financial data which is available on a Monthly basis. I am planning to apply machine learning techniques like LSTM but issue here is that overall I have very limited training dataset ...
- 1,397
2
votes
0
answers
59
views
Queue Reactive Model for large spread assets
Im working on the implementation of the Queue Reactive Model by Lehalle (https://arxiv.org/pdf/1312.0563.pdf), but I have encountered some implementation problems for my specific assets.
First, the ...
0
votes
0
answers
37
views
is implied standard deviation an estimator of risk neutral measure of volatility?
I am wondering if it is, in theory, correct to assume the ISD as the risk-neutral measure of the volatility of the underlying asset and if it is appropriate to price derivatives on the ISD.
- 341
0
votes
0
answers
56
views
Satisfying put-call parity in Monte Carlo option valuation
I am trying to price European call and put options on a stock using the Monte Carlo method, given some dynamics for the underlying that may or may not have a closed-form solution (e.g. Black-Scholes, ...
0
votes
0
answers
70
views
A naive approach to choose a strike
The idea is to choose a strike base on the premium and historical data to have maximum profit.
For example a selling a (European) call.
$$Profit = Premium_K - (S(t) -K)^+$$
Replacing $(S(t) -K)^+$ for ...
- 1
0
votes
0
answers
44
views
How to best calibrate a short rate curve using (compounded) SOFR futures & swaps
If one imposes a form $r(t) = \text{...}$ on the cc. short rate, and aims to fit the short end of a SOFR (or another modern RFR) using futures, how would one best go about this within a "curve-...
2
votes
1
answer
247
views
Should I use common equity or total equity for book value? (when replicating Lewellen's 2015 paper on a cross section of expected stock returns)
I'd hereby would like to ask if any of you know whether I should use common equity or the total equity value, when computing monthly BM ratio's as done by Lewellen is his 2015 paper on a cross section ...
- 45
0
votes
0
answers
48
views
Calibration of Covariance Matrix for a Cumulative Period Return
I am trying to compute optimized weights (minimum-variance portfolio) for a cumulative return over a period (weekly or fortnightly). In a daily return setting, it is quite simple, I just compute a ...
- 559
2
votes
0
answers
51
views
Portfolio construction: Over/underweighting assets with a given active risk budget
I am trying to refresh my knowledge of portfolio risk calculation but would like to get a second opinion on the best approach.
I have a set of 10 assets that together make up the benchmark and I have ...
- 21
0
votes
0
answers
22
views
Incorporating 10-delta RR and BFLY market quotes into Vanna Volga pricing
I am looking into pricing FX options using the Vanna Volga method. I am aware of the commonly referenced shortcomings of this approach and the superiority of SLV, still it is something I want to do.
...
- 101
0
votes
1
answer
101
views
Black Scholes/American Put/Martingale Condition
Consider a Black Scholes model with $r \geq 0$. Show that the price of an American Put Option with maturity $T > 0$ is bounded by $\frac{K}{1 + \alpha} {(\frac{\alpha K}{1 + \alpha})}^{\alpha}{S_{0}...
- 105
1
vote
1
answer
56
views
Sampling dollar bars for ML model of multiple tickers
I have a Neural Network model that provides predictions for the future returns of a portfolio comprising stocks and cryptocurrencies. The original model operates on standard time bars and generates ...
- 213
1
vote
1
answer
54
views
Why the biz day convention of OIS Rate helper is hard coded as Modified Following in QL?
I am using QuantLib OIS Rate Helpers, and traced schedule creation back to the following function, and noticed that the business convention is hard coded as MF. Is the biz day convention hard coded ...
- 11
0
votes
0
answers
60
views
When Forward is a martingale under risk-neutral measure?
Why is such a proof for futures not suitable for a forward?
For futures we have:
$V_{t}$ is self-financing portfolio: $V_t = \frac{V_t}{B_t}B_t$, where $B_t$ is a riskless asset
Suppose $H_t$ - number ...
- 13
1
vote
1
answer
89
views
Incomplete market
How to prove that market with one risky asset $S_t$ and interest rate $r = 0$ is incomplete:
$$dS_t = S_t (\mu dt + \sigma_t dW_t^{1}), \quad S_0 = 1,$$
$$\sigma_t = 1 + |W_t^{2}|,$$
$W_t^{1}$ and $...
- 13
2
votes
1
answer
147
views
From parameter risk (sensitivities) to market risk (sensitivities)
In models where the underlying is not modeled directly - such as in the HJM framework or short rate models - how does one then compute the Greeks, i.e. sensitivites wrt. market variables.
As an ...
- 548
1
vote
1
answer
106
views
Closed form solution for Mean-Variance optimization without short-selling
So I am writing my bachelor thesis about the naive portfolio vs mean-variance portfolio and I am currently a bit stuck at the part about describing the mean-variance portfolio. I know that if there ...
2
votes
2
answers
150
views
Extending/Subclassing QuantLib Classes in Python?
I'm using quantlib via the quantlib-python or open-source-risk-engine both on pypi. The question relates whether it's possible to extend QuantLib term structure base classes in python rather than C++....
- 123
0
votes
1
answer
127
views
Wrt speed, how optimised is QuantLib's Heston pricing class?
I have a pricing formula that is 300x the speed of the QuantLib's Heston pricing class. Is it incredibly slow?
For context, on a slow 1.6 GHz Dual-Core Intel Core i5 processor, my method can reliably ...
0
votes
0
answers
66
views
Why are we so focused on Zero Coupon Bonds?
In fixed income markets there seem to be two prevailing term structure modelling approaches:
Market Models
HJM Framework
In Market Models, such as the LIBOR Market Model (LMM) and SABR it is common ...
- 548
0
votes
0
answers
47
views
WHAT IS THE FX/OIS SPREAD ? WHAT CAN i USE IT FOR? [duplicate]
What's an example of fx/ois spread , lets say I am looking at BOE , what spread would I be looking at to see the funding stress or to see if year end turns is trading at a premium or now .
I am on ...
- 1
1
vote
1
answer
92
views
Total return time series for an interest rate swap
Without paying for a bespoke dataset or tool, how can I go about creating a total return time series for irs eg for 10y sofr swap such that it includes spot price move + carry/roll?
I’m doing this so ...
- 11
0
votes
0
answers
37
views
American option pricing using path integrals
I am writing a brute force code in python that implements the path integral formalism for the American put option, the goal being to obtain its price at given a price $S_0$ of the underlying asset.
...
- 101
0
votes
0
answers
25
views
Do Dividend Stocks Offer Better Resilience During Market P/E Contraction?
I'm interested in how stocks with higher dividend yields perform during periods of market P/E contraction. Specifically, I've observed that (so far I am working on the models):
Market-wide P/E ...
- 21
0
votes
1
answer
279
views
PV01: bumping all tenors along the curve or only a tenor at a time?
Item 22 from this ISDA SIMM 2.3 document gives the following definition for the PV01 of an instrument $i$ with respect to the tenor $t$:
$$s(i, r_t) = V_i(r_t+1bp, cs_t) - V_i(r_t, cs_t)$$
where $r_t$ ...
- 480
2
votes
0
answers
54
views
Delta hedge call option on short rate
Usually delta hedging an european call option in the black-scholes model is constructed of three assets; a call option, the underlying stock and the risk-free asset often assumed to have constant ...
- 21
0
votes
0
answers
46
views
Why does Theta in an OU process relate to a mispricing of a pair's spread
I am reading this article from Alex Lipton and Marcos Lopez de Prado: A closed-form solution for optimal mean-reverting trading strategies (2020) which talks about finding optimal profit taking and ...
- 1
1
vote
0
answers
30
views
Seeking a Model to Extrapolate Locate Fees for Short Selling in Absence of Historical Data
I'm in the process of developing an automated stock trading algorithm, with short selling being a significant part of the strategy. A key factor in deciding whether to short a stock is the associated &...
- 33
0
votes
0
answers
29
views
Interpolating FRA curves for MPC dates
I have data for all the "white" FRAs with 3m fixings in a given market, i.e., 1x4 up to 9x12 and all the central back MPC meeting dates over the next twelve months.
What is the recommended ...
- 440
1
vote
0
answers
51
views
Lopez de Prado Advances in Financial Machine Learning- entropy for adverse selection
In chapter 18: Entropy Features, Lopez de Prado discusses how entropy can be used to estimate adverse selection. He suggests a method where order imbalance is mapped to quantiles and entropy is ...
- 11
1
vote
1
answer
198
views
Python - yahoo finance options data - volatility smile plot
I have plotted the IV of TSLA options using yahoo options data, but the scatter plot doesn't look right, can anyone advise why the plot looks like this? I would expect to see a vol smile plotted.
EDIT ...
- 33
0
votes
0
answers
20
views
Determining an Appropriate Locate Fee Threshold for Short Selling Based on Expected Return
I'm working on an automated stock trading program and often consider short selling as part of my strategy. For each potential short sale, there's an associated "locate fee" that I have to ...
- 33
0
votes
0
answers
70
views
Analyzing the Impact of S&P Volatility Shift on ATM Straddle Sale: Calculating Loss/Gain[black scholes]
Black scholes:The 1-month implied volatility of S& ;P is 16. The slope of the skewness curve is -1 point per 1%; For example, the 99% exercise trades at a premium of 1 vol point. regarding the ...
2
votes
1
answer
112
views
Zero Coupon Bonds for Structured Products
I'd like to find out how to calculate the level of a zero coupon bond that goes into a fully funded structured product. Let's say SocGen or JPM issue a 2Y fully funded structured note (zero coupon + ...
- 23
0
votes
0
answers
45
views
FX FORWARDS Calculating funding cost and wether funding will be expensive or not
Lets say for example my TN for USDHKD point per day spot is -1.9467 and for 1mnth it is -1.4142 and the notional is 100m HKD dollars.
Would you say more or less I would be flat in terms of funding ? ...
- 1
0
votes
0
answers
25
views
Forward Skew using constant smile rule
IV1 = IV of far month.
IV2 - IV of near month.
f(1,2) = Forward volatility between the two expiries.
dx = difference between Strike volatility and ATMf volatility of IV2 column.
As per the method ...
- 21
0
votes
0
answers
34
views
Exponential smoothing - alpha choice with given half-life
I have daily data for a year and I would like to perform exponential smoothing on this data:
I want a half-life of 3 months out of 12.
What is the formula to find the alpha then?
Thanks for your ...
- 101
0
votes
0
answers
30
views
How to tell when a vector (9-tuple) changes structure over time?
I have a 9-element vector I compute at any time T that is derived from the state of the order book. I plot the elements over time and get something like this:
I'm interested to see when the nature of ...
- 1