All Questions

12,264 questions
62 views

Need explanation on weird Gamma Behaviour Black Formula

I am using the RQuantlib package to price options on futures. With a slight modification one can go from the Black Model (76) to The BS Model. It can easily be shown that if we write S0 = (e-rt) * F0 ...
74 views

Market making in one tick markets?

I've searched, but found no literature on market making in single tick markets. I'd appreciate any references. Given that most literature on MM assumes micro-structure is mean-reverting due to the ...
45 views

synthetic convertible dynamics

A synthetic convertible bond can be created by combining a non-convertible bond with a long dated call option or warrant of the same issuer. Are there any papers which studies the dynamics of ...
63 views

change of measure expectation

How to find expectation of this stochastic process? Also, to show that the expectation of a stochastic process expression [Xt - St] in one measure is equal to expectation of another expression (of the ...
42 views

Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
34 views

Backtesting model results, but backtesting output sampled at different frequency than model output

So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to ...
77 views

Calculation Error or High Vega? How to interpret?

I am trying to calculate/interpret Vega. For the example below I get a Vega of ~36.36. I have checked my math multiple times, but would appreciate anyone pointing out any error that I have made. If ...
53 views

For an Ito Process, $d\ln{X} \neq \frac{dX}{X}$ and $(d\ln{X})^2 = (\frac{dX}{X})^2$, but $d\ln{X} \neq \pm \frac{dX}{X}$

In normal calculus we can write $d\ln{x} = \frac{dx}{x}$ since there is no quadratic variation to deal with. This isn't true for stochastic processes, and Ito's Lemma is used to calculate $d\ln{X}$. ...
75 views

How can I conduct a basic Monte carlo simulation on 2 stocks?

I have 2 stocks in my portfolio A and B.A is currently at 50 dollars and B at 40 dollars. Correlation between A and B is 0. Let us say I bought the stocks today at 50 and 40 dollars. If I wish to use ...
37 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
37 views

Calibration of Theta, A(t) and B(t) of Hull White 1Factor model

I’m simulating interest rates via the HullWhite One factor model. To simulate the short rate I’m using the code from the Quantlib Python Cookbook, chapter 15 and beyond (By Goutham Balaraman and Luigi ...
64 views

Volatility surface for Swaptions

I understand the volatility surface for swaption is built using implied vols of ATM swaptions. I had a question on the instruments that are used. Should the instruments used change depending on the ...
70 views

Finite difference methods for (continuously) strike-resettable American options

For simplicity, let us consider an American call/put with a continuously resettable strike price. Current time is $t=0$, maturity is at $t=T$, and the initial strike is $K_0$. We consider a "...
77 views

Why historical volatility is calculated as N-days annualized?

Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand. Compare with annualized historical return, annualized historical return is never ...
53 views

Proving Flow Property of Stochastic Differential Equation

I am trying to show that $X_t^{s,x} = X_t^{r, X_r^{s,x}}$ for $0 \leq s \leq r \leq t$, $x \in \mathbb{R}^n$ is a given initial condition for time $s$, for some SDE: \begin{equation*} d X(u)=b(X(u))d ...
63 views

Classifying groups of stocks beyond Market Cap/Industry/Sector

I'm monitoring margin values for a portfolio and I want to classify the stocks in my universe using different metrics/information. Just for the sake of making analysis/inferences on the data I have. ...
129 views

Delta Hedging/ Exchange for Currency Options

I'm looking at 2 cases of hedging EURUSD, using call spread or range forward. Lets say spot is 1.1300 and my buy call is at 1.1300 and sell call is at 1.1500. Hypothetically I'm assuming that this is ...
54 views

ISDA CDS model Upfront Fee

Can the ISDA CDS model be used for "legacy" CDS? I understand that it lets you convert from traded spread to upfront and back on the day CDS was traded but what about CDS that was traded 2 years ago ...
31 views

Holding Period Return [closed]

Bought stock for $12.00$/share. Sold 3 years later at $20$/share. Paid $1$ dividend each year for 3 years. Stock's value at the end of the first year was $18$ and $15$ at the end of the second. Find ...
97 views

Monte Carlo computational cost

Hello. I'm reading the above paper and I do not understand how they managed to solve eq (17.35) -- i've seen many papers skip through this as trivial and didn't bother to show the method to get there. ...
85 views

59 views

Tick Imbalance Bars - clarification on T index

I have been trying to learn quant related things on my own. I recently picked up a book called "Advances in Financial Machine Learning" by Marcos Lopez De Prado. I am having difficulty understanding ...
50 views

Any papers on use of convolution neural network for predicting price and hedagability when market making

My idea: CNN takes following input ...
46 views

Possible application of Polya's Urn on Portfolio's Investments?

I wanted to find some more information of this topic, but I found very little. I might be interested in optimizing a stock investment portfolio. Maybe I could use beta or some other common risk ...
43 views

Sum disappearing when we assume constant some elements to be constant over time [closed]

I have the dividend discount model, which is the following expression: $$P_{j,t} = \sum_{\tau=1}^{\infty}D_\tau(1+g)^\tau(1+r)^{-\tau}=\frac{D_{\tau+1}}{r-g}$$ Where $D_t$, is the dividend at time ...
118 views

Options Delta Meaning of Term [closed]

not able to understand delta in options. Whilst I understand, it is how much the option moves when the underlying moves by 1 unit, I fail to understand, when someone books a currency option, why does ...
391 views

Quantitative strategies in the Fixed Income space

I'm looking to learn more about systematic strategies in the the fixed income space, particularly in Rates products (anything from simple cash to inflation or vol). I've been reading a couple of ...
67 views

Eurodollar Futures - ED1, ED2 etc. How to build series?

I am looking at Eurodollar Futures contracts and was wondering how to build series ED1 up to say ED20. Let's assume I have data from 01-01-2004. My understanding is that: ED1 - perpetual front-...
138 views

bayes theorem probability Jar [closed]

I am trying to come up with different theoretical answers below. I believe the standard one is based on Bayes theorem, but I am struggling to prove it. A jar has 1000 coins, of which 999 are fair ...
27 views

Adding argument to ERC function in Python makes it break down

I am using xlwings to implement Python code in Excel. I put the following code in Spyder and imported it into Excel to arrive at equal risk contribution weights for a 7-asset portfolio. ...
78 views

Inherent volatility of selling longterm options and buying short term options

A two-month option has an implied vol of 60%, the corresponding 2-year option has an implied vol of 34%. You buy the short terms and sell the long terms. What is the inherent volatility of the total ...
77 views

Monte Carlo for Asian Pricing

I'm trying to verify the accuracy of my Monte Carlo method for pricing mean options. I came across this paper that supposedly gives an 'exact' solution for the arithmetic mean option (asian). It's a ...
102 views

Should Put/Call Parity result in Zero Return or the Risk-Free Rate?

Sorry in advance if this is a basic question. I'm examining some potential at-the-money put/call arbitrage. What I found surprised me somewhat: ...
67 views

Autoregressive Distributed Lag Models (ARDL) results analysis

When using autoregressive distributed lag models (ARDL), I usually get a counter-intuitive result for the selected lag. For example, when examining the relationship between GDP and Foreign Direct ...
38 views

High-frequency history of oil prices [duplicate]

It's fairly easy to find daily historical oil prices, but I need the history in more detail, at least hourly. I have access to Datastream, but can't find it there. Is this time series in Datastream? ...
43 views

How to optimize a series of equations whose outputs are a variable of the subsequent equatinos

The basic question is, given $f(x) = y$ and $f(y) = z$, how can you find $x$ such that $z$ is at its maximum? I can optimize each equation independently, but I do not know how to optimize when ...
116 views

CDS ISDA model/Bloomberg

I am becoming more acquainted with QuantLib as a platform. I've been using both the python implementation and QuantLib XL. As I have started to look at CDS, I would like to know if there is a ...
16 views

Termstrc data preparation from Bloomberg terminal

I am trying to use the R package termstrc to estimate yield curves for the Czech Republic. I have found the structure of the required class ...
211 views

Quantlib-Python: use zero rates to get the originally bootstrapped curve

Let's say I am trying to build a curve using deposits, future and swaps with one of the three Quantlib methods in Python as below: ...
16 views

Realised option values. (Beginner in R/ Coding****) [migrated]

I have started playing around with R and quantmod. I want to create a dataset for realised option values on the S&P500 and compare this to the Black-Scholes estimated value for a finance class ...
39 views

Can we generate(in high dimension) uniformly distributed variables in a finite volume other than a cube?

I'd like to know if there is in the literature a (computationally cheap) algorithm to generate uniformly distributed variables in high dimension for a volume other than a cube and without using ...
24 views

Moneyness for Cancellable Swaps

Hi I wanted to know we can assess the moneyness of Cancellable swaps? For example, I have a swap where I am paying the fixed rate and also have an option to cancel this option. How do I assess the ...
32 views

Overnight Indexed Swaps [duplicate]

How can one enter into a OIS for 1month, when the borrowing is only overnight? Are these punts made or does a trader have to give a Underlying to enter into the swap. If in case the trader does ...
89 views

Kalman Filter for Multiple Regression?

I'm using Kalman Filter to calculate a rolling spread between two asset price series as commonly described by Chan and many others. I would like to extend this regression to the price of three assets, ...
83 views

OIS, Fed Funds Rate and Working

I'm a bit confused about OIS. Is OIS the overnight interest rate or is it a swap. If OIS is the rate at which banks lend overnight, where does the swap come in? Don't they borrow at a fixed rate? ...
178 views

Application of Itô's lemma - Forward process

How would be applied the itô's lemma in the following equation: And we know that:
50 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
60 views

Pricing an exotic with barrier at discrete times

How would you price the following option on underlying $S$ without dividends? Time to maturity of option $\tau = 12$ months Option has a strike $K > 0$ and constant barrier $B > 0$. $t_0$ is ...
30 views

Calculating QuantLib IborCoupon with / from given index fixing

How can I calc with QuantLib the coupon amount of a floating rate IborCoupon on the 3M Euribor Index with a given 3M Euribor Index Fixing? If I try the following Python code: ...

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