Questions tagged [volatility]

A measure of the variation in price over time. Also a measure of the risk of a financial instrument.

0
votes
0answers
9 views

How can i fit the following regression in R? Why is the coefficient [second Columns] for R so low?

'Rwml' is the monthly log return So the first column is clear, I got nearly the same values, at least the same magnitude. But: If I regress on the variance, my input values are way too low to get a ...
2
votes
1answer
2k views

What is the unconditional variance for a GARCH model?

I want to use a Matlab script to calculate Heston Nandi GARCH prices. I found an appropriate script online and it asks for the "unconditional variance" as an input. How do I calculate the appropriate ...
2
votes
1answer
69 views

Black's Approximation - Discrete dividend for Put Options

I am currently trying to price and option chain for dividend paying stocks (american style exercise). I am able to calculate the Net Present Value (NPV) of dividends until maturity and then apply ...
1
vote
1answer
97 views

Half life of Exponetial Weighted Moving Average

I am trying to apply a volatility strategy. I am reading a paper where the authors defined the volatility as: "Exponential Weighted Volatility of returns with a 1-year window and 3-month half-life" ...
6
votes
1answer
2k views

GARCH volatility modeling, squared returns, and convergence

After reading some more of Volatility Trading, I decided to try to make a simple volatility model using daily log returns of an ETF I follow. It turns out "simple" is sort of relative. Unfortunately, ...
0
votes
0answers
15 views

How to forecast monthly volatility with daily gjrGarch estimates

I'm currently writing a paper and need to regress the 22 days realized volatility of the following month on its GARCH estimate and the 126days realized volatility up to t=1 The paper im referring to ...
1
vote
1answer
102 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
1
vote
2answers
109 views

How to create a volatile market, by combining less volatile markets?

This might be against the law of gravity, but I'll give a try 🙂 Is there a way to combine two financial products $p_1$ and $p_2$, into a single product $p_c$ that is more volatile than its ...
0
votes
0answers
43 views

What is the basis for the ansatz here? [duplicate]

I'm reposting this question: Jim Gatheral's ansatz I have the same question, but the answer given in the comment is no longer applicable since the link does not work.
1
vote
1answer
79 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
-4
votes
0answers
60 views

What does this formula in Jim Gatheral's book mean?

From Jim Gatheral's "The Volatility Surface", on page 11 he introduces a formula (formula (1.7) at the bottom). Is he talking about the "future value of the option"? I do not understand the "future ...
0
votes
0answers
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 ...
0
votes
0answers
30 views

Going from normal to Log-normal implied volatility

Let's denote the Implied normal volatility (Bachelier) as $\bar{v}$, and the implied log-normal (Black Scholes) as $v$. When everything else is known (spot, strike, maturity, rates etc) how can you ...
1
vote
1answer
45 views

Why is the volatility of an Ito process not the square root of its variance?

The volatility $\sigma$ of an Ito process $dS_t = r S_t dt + \sigma S_t dW_t$ is not the square root of its variance. But you often hear that "volatility = standard deviation". What's going on here?...
1
vote
1answer
167 views

A volatility model developed by JP Morgan

I am quite confused with this predicting volatility equation: σ2t = βσ2t-1 + (1-β)ε2t Here is a section from Capital Market Expectations: CFA Level 3 Volume 3 Curriculum (page 27) https://ibb.co/...
3
votes
1answer
186 views

Mixing Black Scholes with SABR

I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp. I was wondering if the following ...
6
votes
1answer
9k views

What is the equation for Garman-Klass volatility?

I want to calculate realized/historical volatility for the underlying products of various options using the Garman-Klass estimator, but I can't see to find an equation, although I know it involves ...
-2
votes
0answers
18 views

Anyone know a GJR-GARCH-MIDAS Multivariate

I'am trying to run a model like mfGARCH package but with multivariate, not univariate like mfGARCH does.
0
votes
1answer
42 views

Interpretation conditional volatility plot

I have plotten the log differences of exchange rates and in the same plot, I show the conditional volatility $\sigma_t^2$. The conditional volatility follows approximately the same path, but is much ...
2
votes
1answer
70 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 ...
1
vote
1answer
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 ...
1
vote
0answers
43 views

How to properly hedge a short vol taking into account hedge stop loss?

Suppose a short straddle. In practice, hedging with long/short futures exposes to the risk of hitting a stop loss when market movements are wide. Eventually, it may very well happen that the hedge ...
4
votes
0answers
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 $\sigma(s,t)$...
2
votes
2answers
81 views

Hull-White zero-coupon bond price does not depend on the volatility?

So, today I started pricing zero-coupon bonds using the Hull-White model. An interesting feature is that when t = 0 the bond price does not actually depend on the volatility since the last term of A(0,...
5
votes
2answers
762 views

Ideas about Stochastic volatility models

I am currently working on comparing different models for modelling the volatility and then pricing vanilla options (I use option prices on real stocks in order to calibrate my models and then I ...
0
votes
0answers
35 views

Calculating historical volatility and returns from bond yield

I am interested to calculate the historical volatility and returns from a time series of US 3m T-bill yield (see screenshot below), for portfolio optimization. I am not too sure how to bridge the idea ...
0
votes
0answers
35 views

Fitting to Market Data in Extended Vasicek / Hull White

I need your help for my task. I need to calibrate to the market data for Hull White model for Zero Coupon Bond Price. I refer to John Hull and Alan White paper. I want to ask you a few questions and ...
2
votes
2answers
97 views

Can the dependent samples t test be used for this problem?

Short story: I have 2 sets of data: Set 1: Vector with daily data of stock market returns (eg. [1%, 1.2%, -2%]) Set 2: That vector of stock market returns, multiplied by another vector (eg. [2%, 0....
0
votes
2answers
72 views

What are some scenarios where trading a risk reversal makes sense?

I understand that risk reversal is a bet on the skew of the implied volatility curve. But when would one have a view on the skew of the curve? I understand that one can have a view on the underlying. (...
2
votes
1answer
86 views

Hedging with different volatility (Ahmad and Wilmott paper)

In their paper they show that: - if you hedge with the realised volatility, the present value of the total p&l is the difference between the option value based on the realised volatility and the ...
8
votes
1answer
238 views

Why not just be long VIX and wait for the next volatile period?

Over the past 3 months, VIX has been relatively low. Therefore, there seems to be a "free-lunch" here by just being long VIX, and wait for the next market turmoil (which is happening at the moment ...
1
vote
0answers
31 views

Log Contract payoff function

I can’t get where Dr. Rouah gets payoff function of log contract. Could you please take a look at that? https://frouah.com/finance%20notes/Variance%20Swap.pdf It’s on page 2, section 3. I couldn’t ...
0
votes
0answers
40 views

What is the model behind Heston-Nandi functions in the fOptions R package?

I am dealing with Heston model in R and for this purpose I am using the package fOptions from RMetrics. The calibration formula requires the specification of some parameters (omega, lamda, alpha, ...
0
votes
1answer
103 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
3
votes
0answers
81 views

Volatility of a stock basket

to determine the volatility of a basket of stocks, I often use the following formula: $\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$ where the $\sigma$ are the constituents' ...
1
vote
1answer
248 views

How could one trade volatility skew if you think it's too flat or steep?

We all know that you can trade on a forecast of volatility by dynamically hedging, but I'm wondering if there's a similar technique where in you can trade the skew specifically? Let's say you travel ...
1
vote
0answers
49 views

Pricing forward start Cliquet option with implied volatility with Dupire

I have the following implied volatility matrix of a stock index downloaded the 15th February 2019, the value of the stock was 3188.44 at the time: ...
5
votes
1answer
156 views

Question on Local Volatility

In Gatheral's book The Volatility Surface (Wiley, 2006), a local volatility model is defined as... $$ dS_t =S_t \mu_tdt + S_t \sigma(S_t, t)dZ $$ The famous Dupire Equation is given by... $$ \sigma^2(...
2
votes
0answers
42 views

GARCH(1,1) one-step ahead volatility forecast biased, higher than Parkinson's HL volatility

I am trying to create one-step ahead forecasts for the S&P500 using a GARCH(1,1) model. I am using the rugarch package in R. As you can see, the forecasted points are consistently higher than the ...
11
votes
4answers
1k views

better estimator of volatility for small samples

One commonly used sample estimator of volatility is the standard deviation of the log returns. It is indeed a very good estimator (unbiased, ...) when the sample is large. But I don't like it for ...
2
votes
0answers
49 views

General assumptions for var swap replication

I've seen claims that the standard static-hedge for a plain vanilla variance swap holds so long as the underlying doesn't jump, but every derivation I have seen begins by assuming the asset follows a ...
1
vote
2answers
78 views

Volatility smile shows individual Put and Call IV or combination

IV is calculated per strike AND option type basis(for example WTI 50 CALL its x and WTI 50 PUT its y). The question is when its shown in "Smile" its just shown on strike basis, so does that mean lower ...
1
vote
1answer
177 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 ...
1
vote
0answers
21 views

What's the difference between demand elasticity and demand volatility? [closed]

What's the difference between demand elasticity and demand volatility? Demand elasticity: https://www.investopedia.com/terms/d/demand-elasticity.asp Demand volatility: https://www.sdcexec.com/home/...
2
votes
0answers
47 views

stochastic volatility and smile

Can we say that the volatility smile contain for sure stochastic volatility information ? If yes why ? Saying that BlackScholes does not explain the smile does not necessary mean there is an ...
2
votes
1answer
373 views

CBOE Index Minute Data

I am doing a small research and looking for a place to purchase historical minute CBOE Index data. I am interested in: VIX - CBOE Volatility Index VVIX - CBOE VIX VOLATILITY INDEX VXV - CBOE VIX ...
10
votes
1answer
463 views

Variance swap volatility - ATMF vol, Skew and Curvature

In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies \begin{align} \sigma_T^2 &= \Bbb{E}_0^...
0
votes
0answers
33 views

How is a LIBOR Market Model volatility skew determined?

LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors. These prices are generally quoted in yield vols. Their prices are given by the Black formula. ...
1
vote
2answers
67 views

1 day VaR vs 10 day VaR

Even while using historical simulation VaR, 1 day VaR is converted into 10 day VaR by multiplying 1 day VaR by Sqrt(10) for regulatory reporting purposes. What are the underlying assumptions for ...
2
votes
4answers
739 views

Evaluation of portfolio other than Sharpe Ratio

Is Sharpe ratio always the best way to evaluate a portfolio? I'm not really sure what this potential interview question wants me to answer. I have read that Sharpe ratio essentially explains how ...