All Questions

12,688 questions
61 views

How to price the american options using local volatility

I have given with a surface of american option prices $C_{am}(T, K)$. From these american option prices the implied volatility surface is deduced. Now I want to find the local volatility $\sigma(s,t)$...
56 views

Credit Scoring model IV max value

I'm making a credit scoring model and I get that one variable has Information Value (IV) more than 1, is that possible? Formulas are pretty simple for weight of evidence(WoE) and information value(IV)...
32 views

Forward swap rate calculation from the market

Following my question Swaption valuation across time using vcub where I wanted to know how to value a swaption across time using bloomberg's vcub, I remark that I have to calculate myself the ...
41 views

Difference between local volatility and implied volatility [duplicate]

I have read several articles about local volatility and implied volatility, but I am still confused with the difference between the two. Please correct me if I am wrong: Implied volatility is the ...
69 views

relationship between notional amounts of volatility swaps and variance swaps

Taking volatility swap payoff as $$( \sigma_F - \sigma_S ) * volatility~notional$$ and Taking variance swap payoff as $$( \sigma_F^2 - \sigma_S^2 ) * variance~notional$$ I am trying to understand ...
100 views

How to calculate optimal portfolio using sector constraints in python

I'm looking into CVXPY at the moment. Main goal would be to be able to calculate the optimal portfolio, which in my opinion would mean that we need to maximise (expected return - risk free) / ...
85 views

Widely accepted methods for coming up with the co-variance matrix of assets?

Question What are the widely accepted ways for coming up with co-variance matrix of assets after the Markowitz's modern portfolio theory? Question explained in more detail After Modern portfolio ...
97 views

Swaption valuation across time using vcub

On Bloomberg one has access to the rates vol cube with the VCUB function. For a given currency, today, one sees Black implied volatilities for swaptions of various expiries and strikes, for forward ...
113 views

Treasury futures cost of carry and P&L

I'm looking to understand the P&L implications of holding 2YR treasury futures. Assuming no movement in interest rates through to maturity (i.e., no capital gains or losses due to interest rate ...
37 views

Equal weight correlation swap payoff derivation

I am aware that the payoff for a equal weighted correlation swap is; $$(\rho_K-\rho)*\text{Notional}$$ where $$\rho = \frac{2} {n(n-1)}\sum_{i < j} \rho_{ij}$$ I am wondering how I can derive ...
79 views

CDS, default probability and bond price

When we calculate the implied default probabilities from CDS, can we use that information to price bonds? I am getting familiar with Fixed Income. I saw textbooks using implied default probabilities ...
92 views

Proof of the Hull & White Model calibration

I have a question about the demonstration of the formula which states that: If we have an Hull & White Model for the short rate diffusion such that Then the model is fully calibrated if and only ...
32 views

Determine same issuer from a list of ISINs?

I have a list of ISINs for all the securities that make up a fixed-income fund. Is it possible to tell from this which securities are from the same issuer? I have securities of which I know they are ...
103 views

Do cash accounts contribute to exposure?

When calculating a portfolios total exposure, should the value of the cash accounts be included? My high level view on exposure is that it should be related to the possibility of loss, usually as a ...
65 views

Small difference in IRR, big difference in NPV?

I calculated the following in Matlab 2019a, see code below. I was surprised about the big difference in present values (DiffPV, DiffPVpercentage) for only a small difference (DiffIRR, ...
73 views

Which convention drives what the result of “30 august 2017 + 6M” should be?

If I use c#'s AddMonths method, "30 august 2017 + 6M" will give "28 february 2018" (as the latter is the last day of the february month in the non leap year 2018). ...
75 views

Estimated betas and optimal portfolio

I ran a regression on 20 assets to estimate their beta with different methods. I would like to see the differences of these estimation differences in terms of mean-variance optimal portfolio. How can ...
93 views

Optimal investment mix of equity and debt in a single company, HY vs IG

What is the optimal mix of equity and debt that an investor should invest in a single company? If an investor invests in both the debt and equity of a company, they are in effect de-levering the ...
54 views

Calculating dealer gamma imbalance/exposure for an options strip

Have seen this being done for years (primarily by J.P. Morgan and a couple other bank research desks) and am attempting to re-create for my own personal research. I’ve read the forums on here but no ...
40 views

Extracting Risk Neutral Default Probabilities using Option Adjusted Bond Prices

I am currently in a project trying to quantify default risk premia for US Corporate Bonds. The data I have consists of bond prices, and other information (i.e. YTM, OAS, Effective Duration, Maturity ...
49 views

European Knock-Out Option with European Barrier

I have two problems: 1) Actually i didn't find anywhere a precise definition of European Knock-Out Option with European Barrier. 2) Assuming that European means that it depends only on starting ...
46 views

I want to estimate a ARMA-GARCH model by using the EGB2 distribution instead of the normal distribution. The model I want to estimate is: $$y_t = \mu + \phi_1 y_{t-6} + \phi_2 y_{t-8} + \theta_1 \... 0answers 83 views Swaption : Bloomberg Black implied volatility quotes and pricing in the Black model I used a lot Bloomberg's VCUB for data, but never used its integrated swaption pricer "Quick Pricer for Swaptions", nor Bloomberg's "full" swaption pricer from "SWPM -OV". I am retrospectively quite ... 0answers 46 views Arbitrage strategy one-period model Consider a one-period model with a stock S_0=1 and S_1>0. Introduce call options with strikes K_1<K_2<K_3 maturing at T=1. Assume further that$$ C(K_2)>\frac12(C(K_1)+C(K_3)) $$... 1answer 92 views Brownian Motions theorems I know that if W and W′ are two independent brownian motions, then dWt \ dWt′ = 0. How can I prove/demonstrate this theorem? Additionaly, how can we prove that if W and W′ are dependent, ... 1answer 51 views Expanding window vs Rolling window z-score I wish to find the z-score of a value measure( e/g P/E ratio) to compare them across asset classes, currently i am using an expanding window z-score to calculate the long-term mean and standard ... 0answers 39 views What 10 year bond data to use when making a risk/return scatter plot? I am making a risk/return scatter plot (seen below) (from this site): What data must be used for bonds (e.g. 3 month or 10 year US bonds)? I thought you would use this data, but if you take the years ... 0answers 31 views Option price with underlying growth rate distinct from discount rate Consider a European style option. The price equation is$$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS\frac{\partial V}{\partial S} - rV = 0 \tag1 ...
135 views

When I read up on swap spreads, the definition always goes something like this: The swap spread is the difference between the fixed leg of swap and a Treasury bond with the same maturity. So if the ...
31 views

Standard ways of simulating order books

What are some standard simple ways of simulating an order book? I have found this paper, but it is missing the implementation details. And more importantly, it appears that it ignores the size of the ...
43 views

Which machine learning model rely on the normality assumption?

In the machine learning project, when the target variable is skewed, we need to use box-cox transformation to turn that into a normal distribution. But why do we need to do that? I mean, besides the ...
33 views

Realized volatility transformation [closed]

After calculating the realized volatility as $log\Big(\sqrt{\sigma_R^2}\Big)$ and forecasting some datas as $log\Big(\sqrt{\sigma_R^2}\Big)$, how can we get back to the $\sqrt{\sigma_R^2}$ ? it's ...
424 views

Random Portfolios vs Efficient Frontier

I understand the concept of the efficient frontier and am able to calculate it in Python. But even when generating 50'000 random 10 asset portfolios, the single portfolios are not even close to the ...
39 views

Deriving Single Index Model (Market Model)

is the return of the stock of observation is the return of the reference market is the regression coefficient between the observed stock and the reference market is the regression intercept between ...
41 views

Fama French Three Factor

How to calculate the value weighted or equally weighted returns for the six portfolios SL,SM,SH,BL,BM,BH of fama french 3 factor model?
85 views

If historical returns are no indication of future returns, why are they still shown to investors?

Stock returns and fund returns are on average not autocorrelated and thus unpredictable. Consequently, looking at a historical price chart gives no indication in which direction tomorrows price will ...
37 views

Crisis in in-sample period

I am backtesting a value momentum asset allocation strategy and my in sample period is from 2003 to 2011 and out sample from 2012 to 2019. I am optimising a cutoff for value on in sample to allocate ...
50 views

Is there Carry Effect for Cash Settled Bond Future

As we know, physical settle bond future would expose carry effect which would be the deliverable bond coupon and your financing cost (cost of carry as a sum term). This is because it can be replicated ...
23 views

How to retrieve greeks and IVOL historically for listed options (using Bloomberg)?

Is there a way to get Prices, IVOL and greeks on historic option contracts (eg on the underlying RXM15) on Bloomberg, and follow this particular option with Strike K throughout its lifetime (eg on ...
42 views

Average portfolio correlation vs. external metric

I am coming across a problem I can't seem to wrap my head around, and I am not sure I am using the right words so cannot find much info in it! I have a portfolio of assets, with data on historical ...
61 views

Square Information Ratio

I have read the following sentence : " The information ratio measures the active management opportunities, and the square of the information ratio indicates our ability to add value " ( In the Grinold'...
54 views

Transforming non-normally distributed interest rates for OLS regression

I am studying the effects of short- and long-term interest rates on bank risk-taking in the Euro zone countries. To analyse the effects, I will use, amongst other, an OLS regression. However I have ...
34 views

Autocorrelation of returns vs autocorrelation of cummulative returns [closed]

Lets look at the following data: set.seed(20) acf <- acf(rnorm(100, 0.06, 0.02)) acf acf1 <- acf(cumprod(rnorm(100, 0.06, 0.02)+1)) acf While acf ...
55 views

Model calibration volatility surface

Let's say i have an exotic structure that is to be vega hedged dynamically. I choose to price it with a local volatility (which means the model prices in your future vega hedges using all options for ...
30 views

Vega computation in a stochastic volatility model

What are the possible strategies to compute analytically the Vega (not numerically) in a stochastic volatility model? The goal is to vega-hedge in a generic stochastic volatility model if possible, ...
60 views

Understanding methodology behind the covariance bucket vega

I am reading "Dynamic Hedging" from Mr. Taleb. I understand that you cannot simply aggregate all the vegas of your option portfolio and classify this as the portfolio's vega. So, now I want to ...
60 views

simple SABR model & negative strikes

My goal is to calibrate a simple SABR model. I do have $tenor$, $expiry$, $forward$ and "market volatilities for strike spread" ranging from -150 to 150 bps. I think the model can only be ...
40 views

PD for ECL modelling

I am trying to understand the interrelations between the marginal, cumulative and conditional PDs (Probabilities of Default) when modelling ECLs (Expected Credit Losses). My current understanding is ...